OpenCV 参考手册


OpenCV Reference Manual v2.2 December, 2010 2 Contents I C API Reference 43 1 core. The Core Functionality 45 1.1 Basic Structures...................................... 45 CvPoint........................................... 45 CvPoint2D32f........................................ 45 CvPoint3D32f........................................ 46 CvPoint2D64f........................................ 47 CvPoint3D64f........................................ 47 CvSize............................................ 48 CvSize2D32f........................................ 48 CvRect........................................... 48 CvScalar.......................................... 49 CvTermCriteria....................................... 50 CvMat............................................ 50 CvMatND.......................................... 51 CvSparseMat........................................ 52 IplImage........................................... 53 CvArr............................................ 56 1.2 Operations on Arrays.................................... 56 cv::AbsDiff......................................... 56 cv::AbsDiffS......................................... 56 cv::Add........................................... 57 cv::AddS.......................................... 57 cv::AddWeighted...................................... 58 cv::And........................................... 59 cv::AndS.......................................... 59 cv::Avg........................................... 60 cv::AvgSdv......................................... 61 cv::CalcCovarMatrix.................................... 61 3 4 CONTENTS cv::CartToPolar....................................... 63 cv::Cbrt........................................... 64 cv::ClearND......................................... 64 cv::CloneImage....................................... 64 cv::CloneMat........................................ 65 cv::CloneMatND...................................... 65 cv::CloneSparseMat.................................... 65 cv::Cmp........................................... 65 cv::CmpS.......................................... 66 cv::ConvertScale...................................... 67 cv::ConvertScaleAbs.................................... 68 cv::CvtScaleAbs...................................... 69 cv::Copy........................................... 69 cv::CountNonZero..................................... 70 cv::CreateData....................................... 70 cv::CreateImage...................................... 71 cv::CreateImageHeader.................................. 71 cv::CreateMat........................................ 72 cv::CreateMatHeader................................... 72 cv::CreateMatND...................................... 73 cv::CreateMatNDHeader.................................. 73 cv::CreateSparseMat.................................... 74 cv::CrossProduct...................................... 74 CvtPixToPlane....................................... 75 cv::DCT........................................... 75 cv::DFT........................................... 76 cv::DecRefData....................................... 79 cv::Det............................................ 79 cv::Div............................................ 79 cv::DotProduct....................................... 80 cv::EigenVV......................................... 81 cv::Exp........................................... 82 cv::FastArctan....................................... 82 cv::Flip............................................ 82 cv::GEMM.......................................... 83 cv::Get?D.......................................... 84 cv::GetCol(s)........................................ 85 cv::GetDiag......................................... 86 cvGetDims, cvGetDimSize................................. 86 cv::GetElemType...................................... 87 CONTENTS 5 cv::GetImage........................................ 87 cv::GetImageCOI...................................... 88 cv::GetImageROI...................................... 88 cv::GetMat......................................... 89 cv::GetNextSparseNode.................................. 89 cv::GetOptimalDFTSize.................................. 90 cv::GetRawData...................................... 91 cv::GetReal1D....................................... 91 cv::GetReal2D....................................... 92 cv::GetReal3D....................................... 92 cv::GetRealND....................................... 93 cv::GetRow(s)....................................... 94 cv::GetSize......................................... 94 cv::GetSubRect....................................... 95 cv::InRange......................................... 95 cv::InRangeS........................................ 96 cv::IncRefData....................................... 96 cv::InitImageHeader.................................... 97 cv::InitMatHeader...................................... 98 cv::InitMatNDHeader.................................... 99 cv::InitSparseMatIterator.................................. 99 cv::InvSqrt.......................................... 100 cv::Inv............................................ 100 cv::Invert.......................................... 100 cv::IsInf........................................... 101 cv::IsNaN.......................................... 101 cv::LUT........................................... 101 cv::Log........................................... 102 cv::Mahalanobis...................................... 103 cv::Mat........................................... 103 cv::Max........................................... 104 cv::MaxS.......................................... 104 cv::Merge.......................................... 105 cv::Min............................................ 106 cv::MinMaxLoc....................................... 106 cv::MinS........................................... 107 Mirror............................................ 107 cv::MixChannels...................................... 107 MulAddS.......................................... 108 cv::Mul............................................ 108 6 CONTENTS cv::MulSpectrums..................................... 109 cv::MulTransposed..................................... 110 cv::Norm.......................................... 110 cv::Not............................................ 111 cv::Or............................................ 112 cv::OrS........................................... 112 cv::PerspectiveTransform................................. 113 cv::PolarToCart....................................... 113 cv::Pow........................................... 114 cv::Ptr?D.......................................... 115 cv::RNG........................................... 116 cv::RandArr......................................... 116 cv::RandInt......................................... 118 cv::RandReal........................................ 119 cv::Reduce......................................... 120 cv::ReleaseData...................................... 120 cv::ReleaseImage..................................... 121 cv::ReleaseImageHeader................................. 121 cv::ReleaseMat....................................... 122 cv::ReleaseMatND..................................... 122 cv::ReleaseSparseMat................................... 123 cv::Repeat......................................... 123 cv::ResetImageROI.................................... 123 cv::Reshape........................................ 124 cv::ReshapeMatND.................................... 125 cvRound, cvFloor, cvCeil................................. 126 cv::ScaleAdd........................................ 126 cv::Set............................................ 127 cv::Set?D.......................................... 127 cv::SetData......................................... 128 cv::SetIdentity........................................ 128 cv::SetImageCOI...................................... 129 cv::SetImageROI...................................... 129 cv::SetReal?D....................................... 130 cv::SetZero......................................... 130 cv::Solve.......................................... 131 cv::SolveCubic....................................... 132 cv::Split........................................... 132 cv::Sqrt........................................... 133 cv::Sub........................................... 133 CONTENTS 7 cv::SubRS.......................................... 134 cv::SubS.......................................... 134 cv::Sum........................................... 135 cv::SVBkSb......................................... 135 cv::SVD........................................... 136 cv::Trace.......................................... 138 cv::Transform........................................ 138 cv::Transpose........................................ 139 cv::Xor............................................ 139 cv::XorS........................................... 140 cv::mGet.......................................... 141 cv::mSet........................................... 141 1.3 Dynamic Structures.................................... 142 CvMemStorage....................................... 142 CvMemBlock........................................ 143 CvMemStoragePos..................................... 143 CvSeq............................................ 143 CvSeqBlock......................................... 146 CvSlice........................................... 146 CvSet............................................ 147 CvGraph.......................................... 148 CvGraphScanner...................................... 149 CV TREE NODE FIELDS................................. 150 CvTreeNodeIterator.................................... 150 cv::ClearGraph....................................... 151 cv::ClearMemStorage................................... 151 cv::ClearSeq........................................ 152 cv::ClearSet......................................... 152 cv::CloneGraph....................................... 152 cv::CloneSeq........................................ 153 cv::CreateChildMemStorage............................... 153 cv::CreateGraph...................................... 155 cv::CreateGraphScanner................................. 155 cv::CreateMemStorage.................................. 156 cv::CreateSeq....................................... 157 cv::CreateSet........................................ 158 cv::CvtSeqToArray..................................... 158 cv::EndWriteSeq...................................... 159 cv::FindGraphEdge..................................... 159 cv::FindGraphEdgeByPtr................................. 160 8 CONTENTS cv::FlushSeqWriter..................................... 160 cv::GetGraphVtx...................................... 161 cv::GetSeqElem...................................... 161 cv::GetSeqReaderPos................................... 162 cv::GetSetElem....................................... 162 cv::GraphAddEdge..................................... 162 cv::GraphAddEdgeByPtr.................................. 163 cv::GraphAddVtx...................................... 164 cv::GraphEdgeIdx..................................... 164 cv::GraphRemoveEdge.................................. 165 cv::GraphRemoveEdgeByPtr............................... 165 cv::GraphRemoveVtx................................... 166 cv::GraphRemoveVtxByPtr................................ 166 cv::GraphVtxDegree.................................... 167 cv::GraphVtxDegreeByPtr................................. 167 cv::GraphVtxIdx...................................... 168 cv::InitTreeNodeIterator.................................. 168 cv::InsertNodeIntoTree................................... 169 cv::MakeSeqHeaderForArray............................... 169 cv::MemStorageAlloc................................... 170 cv::MemStorageAllocString................................ 170 cv::NextGraphItem..................................... 171 cv::NextTreeNode..................................... 172 cv::PrevTreeNode..................................... 172 cv::ReleaseGraphScanner................................. 172 cv::ReleaseMemStorage.................................. 173 cv::RestoreMemStoragePos................................ 173 cv::SaveMemStoragePos................................. 173 cv::SeqElemIdx....................................... 174 cv::SeqInsert........................................ 174 cv::SeqInsertSlice..................................... 175 cv::SeqInvert........................................ 176 cv::SeqPop......................................... 176 cv::SeqPopFront...................................... 176 cv::SeqPopMulti...................................... 177 cv::SeqPush........................................ 178 cv::SeqPushFront..................................... 178 cv::SeqPushMulti...................................... 179 cv::SeqRemove....................................... 180 cv::SeqRemoveSlice.................................... 180 CONTENTS 9 cv::SeqSearch....................................... 180 cv::SeqSlice......................................... 181 cv::SeqSort......................................... 182 cv::SetAdd......................................... 183 cv::SetNew......................................... 184 cv::SetRemove....................................... 184 cv::SetRemoveByPtr.................................... 185 cv::SetSeqBlockSize.................................... 185 cv::SetSeqReaderPos................................... 186 cv::StartAppendToSeq................................... 186 cv::StartReadSeq..................................... 187 cv::StartWriteSeq...................................... 188 cv::TreeToNodeSeq.................................... 189 1.4 Drawing Functions..................................... 189 cv::Circle.......................................... 190 cv::ClipLine......................................... 191 cv::DrawContours..................................... 191 cv::Ellipse.......................................... 193 cv::EllipseBox........................................ 194 cv::FillConvexPoly..................................... 195 cv::FillPoly.......................................... 196 cv::GetTextSize....................................... 197 cv::InitFont......................................... 197 cv::InitLineIterator..................................... 198 cv::Line........................................... 200 cv::PolyLine......................................... 201 cv::PutText......................................... 202 cv::Rectangle........................................ 202 CV RGB........................................... 203 1.5 XML/YAML Persistence.................................. 204 CvFileStorage....................................... 204 CvFileNode......................................... 205 CvAttrList.......................................... 207 CvTypeInfo......................................... 207 cv::Clone.......................................... 208 cv::EndWriteStruct..................................... 209 cv::FindType........................................ 209 cv::FirstType........................................ 209 cv::GetFileNode...................................... 210 cv::GetFileNodeByName................................. 210 10 CONTENTS cv::GetFileNodeName................................... 211 cv::GetHashedKey..................................... 211 cv::GetRootFileNode.................................... 213 cv::Load........................................... 214 cv::OpenFileStorage.................................... 214 cv::Read........................................... 215 cv::ReadByName...................................... 216 cv::ReadInt......................................... 216 cv::ReadIntByName.................................... 217 cv::ReadRawData..................................... 217 cv::ReadRawDataSlice.................................. 218 cv::ReadReal........................................ 218 cv::ReadRealByName................................... 219 cv::ReadString....................................... 219 cv::ReadStringByName.................................. 220 cv::RegisterType...................................... 220 cv::Release......................................... 221 cv::ReleaseFileStorage.................................. 221 cv::Save........................................... 221 cv::StartNextStream.................................... 222 cv::StartReadRawData................................... 222 cv::StartWriteStruct.................................... 223 cv::TypeOf.......................................... 224 cv::UnregisterType..................................... 224 cv::Write........................................... 224 cv::WriteComment..................................... 226 cv::WriteFileNode..................................... 226 cv::WriteInt......................................... 227 cv::WriteRawData..................................... 227 cv::WriteReal........................................ 229 cv::WriteString....................................... 229 1.6 Clustering.......................................... 230 cv::KMeans2........................................ 230 cv::SeqPartition....................................... 233 1.7 Utility and System Functions and Macros........................ 235 Error Handling....................................... 235 Example: Use of Error Handling Macros......................... 237 cv::GetErrStatus...................................... 239 cv::SetErrStatus...................................... 239 cv::GetErrMode....................................... 239 CONTENTS 11 cv::SetErrMode....................................... 240 cv::Error........................................... 240 cv::ErrorStr......................................... 241 cv::RedirectError...................................... 241 cvNulDevReport cvStdErrReport cvGuiBoxReport................... 242 cv::Alloc........................................... 243 cv::Free........................................... 243 cv::GetTickCount...................................... 244 cv::GetTickFrequency................................... 244 cv::RegisterModule..................................... 244 cv::GetModuleInfo..................................... 245 cv::UseOptimized...................................... 246 cv::SetMemoryManager.................................. 246 cv::SetIPLAllocators.................................... 247 2 imgproc. Image Processing 249 2.1 Histograms......................................... 249 CvHistogram........................................ 249 cv::CalcBackProject.................................... 249 cv::CalcBackProjectPatch................................. 250 cv::CalcHist......................................... 252 cv::CalcProbDensity.................................... 253 cv::ClearHist........................................ 254 cv::CompareHist...................................... 255 cv::CopyHist........................................ 256 cv::CreateHist........................................ 256 cv::GetHistValue*D..................................... 257 cv::GetMinMaxHistValue.................................. 258 cv::MakeHistHeaderForArray............................... 259 cv::NormalizeHist...................................... 260 cv::QueryHistValue*D................................... 260 cv::ReleaseHist....................................... 261 cv::SetHistBinRanges................................... 261 cv::ThreshHist....................................... 261 2.2 Image Filtering....................................... 262 IplConvKernel........................................ 262 cv::CopyMakeBorder.................................... 262 cv::CreateStructuringElementEx............................. 263 cv::Dilate.......................................... 264 cv::Erode.......................................... 265 12 CONTENTS cv::Filter2D......................................... 266 cv::Laplace......................................... 267 cv::MorphologyEx..................................... 267 cv::PyrDown........................................ 269 cv::ReleaseStructuringElement.............................. 269 cv::Smooth......................................... 270 cv::Sobel.......................................... 271 2.3 Geometric Image Transformations............................ 273 cv::GetRotationMatrix2D.................................. 274 cv::GetAffineTransform................................... 274 cv::GetPerspectiveTransform............................... 275 cv::GetQuadrangleSubPix................................. 276 cv::GetRectSubPix..................................... 276 cv::LogPolar......................................... 277 cv::Remap......................................... 279 cv::Resize.......................................... 280 cv::WarpAffine....................................... 281 cv::WarpPerspective.................................... 282 2.4 Miscellaneous Image Transformations.......................... 283 cv::AdaptiveThreshold................................... 283 cv::CvtColor......................................... 284 cv::DistTransform...................................... 289 CvConnectedComp.................................... 291 cv::FloodFill......................................... 291 cv::Inpaint.......................................... 293 cv::Integral......................................... 294 cv::PyrMeanShiftFiltering................................. 295 cv::PyrSegmentation.................................... 296 cv::Threshold........................................ 297 2.5 Structural Analysis and Shape Descriptors........................ 299 cv::ApproxChains...................................... 299 cv::ApproxPoly....................................... 300 cv::ArcLength........................................ 301 cv::BoundingRect...................................... 302 cv::BoxPoints........................................ 302 cv::CalcPGH........................................ 303 cv::CalcEMD2....................................... 304 cv::CheckContourConvexity................................ 305 CvConvexityDefect..................................... 305 cv::ContourArea...................................... 306 CONTENTS 13 cv::ContourFromContourTree............................... 307 cv::ConvexHull2...................................... 308 cv::ConvexityDefects.................................... 310 cv::CreateContourTree................................... 311 cv::EndFindContours.................................... 312 cv::FindContours...................................... 312 cv::FindNextContour.................................... 314 cv::FitEllipse2........................................ 314 cv::FitLine.......................................... 314 cv::GetCentralMoment................................... 316 cv::GetHuMoments..................................... 316 cv::GetNormalizedCentralMoment............................ 317 cv::GetSpatialMoment................................... 318 cv::MatchContourTrees.................................. 318 cv::MatchShapes...................................... 319 cv::MinAreaRect2..................................... 320 cv::MinEnclosingCircle................................... 321 cv::Moments........................................ 322 cv::PointPolygonTest.................................... 322 cv::PointSeqFromMat................................... 323 cv::ReadChainPoint.................................... 324 cv::StartFindContours................................... 325 cv::StartReadChainPoints................................. 325 cv::SubstituteContour................................... 326 2.6 Planar Subdivisions.................................... 326 CvSubdiv2D........................................ 326 CvQuadEdge2D...................................... 327 CvSubdiv2DPoint...................................... 328 cv::CalcSubdivVoronoi2D................................. 329 cv::ClearSubdivVoronoi2D................................. 329 cv::CreateSubdivDelaunay2D............................... 329 cv::FindNearestPoint2D.................................. 330 cv::Subdiv2DEdgeDst................................... 330 cv::Subdiv2DGetEdge................................... 331 cv::Subdiv2DNextEdge.................................. 332 cv::Subdiv2DLocate.................................... 333 cv::Subdiv2DRotateEdge................................. 334 cv::SubdivDelaunay2DInsert............................... 335 2.7 Motion Analysis and Object Tracking........................... 336 cv::Acc........................................... 336 14 CONTENTS cv::MultiplyAcc....................................... 336 cv::RunningAvg....................................... 337 cv::SquareAcc....................................... 338 2.8 Feature Detection..................................... 338 cv::Canny.......................................... 338 cv::CornerEigenValsAndVecs............................... 339 cv::CornerHarris...................................... 340 cv::CornerMinEigenVal................................... 341 cv::FindCornerSubPix................................... 341 cv::GoodFeaturesToTrack................................. 343 cv::HoughLines2...................................... 344 cv::PreCornerDetect.................................... 348 cv::SampleLine....................................... 349 2.9 Object Detection...................................... 350 cv::MatchTemplate..................................... 350 3 features2d. Feature Detection and Descriptor Extraction 353 3.1 Feature detection and description............................. 353 cv::ExtractSURF...................................... 353 cv::GetStarKeypoints.................................... 355 4 flann. Clustering and Search in Multi-Dimensional Spaces 359 4.1 Fast Approximate Nearest Neighbor Search....................... 359 5 objdetect. Object Detection 361 5.1 Cascade Classification................................... 361 Haar Feature-based Cascade Classifier for Object Detection............. 361 CvHaarFeature, CvHaarClassifier, CvHaarStageClassifier, CvHaarClassifierCascade 362 cv::LoadHaarClassifierCascade.............................. 365 cv::HaarDetectObjects................................... 365 cv::SetImagesForHaarClassifierCascade........................ 368 cv::ReleaseHaarClassifierCascade............................ 369 cv::RunHaarClassifierCascade.............................. 369 6 video. Video Analysis 371 6.1 Motion Analysis and Object Tracking........................... 371 cv::CalcGlobalOrientation................................. 371 cv::CalcMotionGradient.................................. 372 cv::CalcOpticalFlowBM.................................. 373 cv::CalcOpticalFlowHS................................... 374 CONTENTS 15 cv::CalcOpticalFlowLK................................... 375 cv::CalcOpticalFlowPyrLK................................. 375 cv::CamShift........................................ 377 CvConDensation...................................... 378 cv::CreateConDensation.................................. 378 cv::ConDensInitSampleSet................................ 379 CvKalman.......................................... 379 cv::CreateKalman..................................... 381 cv::KalmanCorrect..................................... 381 cv::KalmanPredict..................................... 384 KalmanUpdateByMeasurement.............................. 385 KalmanUpdateByTime................................... 385 cv::MeanShift........................................ 385 cv::ReleaseConDensation................................. 386 cv::ReleaseKalman..................................... 386 cv::SegmentMotion..................................... 387 cv::SnakeImage...................................... 388 cv::UpdateMotionHistory.................................. 389 7 highgui. High-level GUI and Media I/O 391 7.1 User Interface........................................ 391 cv::ConvertImage...................................... 391 cv::CreateTrackbar..................................... 392 cv::DestroyAllWindows................................... 393 cv::DestroyWindow..................................... 393 cv::GetTrackbarPos..................................... 394 cv::GetWindowHandle................................... 394 cv::GetWindowName.................................... 395 cv::InitSystem........................................ 395 cv::MoveWindow...................................... 396 cv::NamedWindow..................................... 396 cv::ResizeWindow..................................... 397 cv::SetMouseCallback................................... 397 cv::SetTrackbarPos..................................... 399 cv::ShowImage....................................... 399 cv::WaitKey......................................... 400 7.2 Reading and Writing Images and Video......................... 400 cv::LoadImage....................................... 400 cv::LoadImageM...................................... 401 cv::SaveImage....................................... 402 16 CONTENTS CvCapture......................................... 402 cv::CaptureFromCAM................................... 403 cv::CaptureFromFile.................................... 403 cv::GetCaptureProperty.................................. 404 cv::GrabFrame....................................... 405 cv::QueryFrame...................................... 405 cv::ReleaseCapture.................................... 406 cv::RetrieveFrame..................................... 406 cv::SetCaptureProperty.................................. 406 cv::CreateVideoWriter................................... 408 cv::ReleaseVideoWriter.................................. 408 cv::WriteFrame....................................... 409 7.3 Qt new functions...................................... 410 cv::SetWindowProperty.................................. 411 cv::GetWindowProperty.................................. 412 cv::FontQt.......................................... 413 cv::AddText......................................... 414 cv::DisplayOverlay..................................... 414 cv::DisplayStatusBar.................................... 415 cv::CreateOpenGLCallback................................ 415 cv::SaveWindowParameters................................ 417 cv::LoadWindowParameters................................ 417 cv::CreateButton...................................... 417 8 calib3d. Camera Calibration, Pose Estimation and Stereo 419 8.1 Camera Calibration and 3d Reconstruction....................... 419 cv::CalcImageHomography................................ 421 cv::CalibrateCamera2................................... 421 cv::ComputeCorrespondEpilines............................. 424 cv::ConvertPointsHomogeneous............................. 425 cv::CreatePOSITObject.................................. 426 cv::CreateStereoBMState................................. 426 cv::CreateStereoGCState................................. 427 CvStereoBMState..................................... 427 CvStereoGCState..................................... 429 cv::DecomposeProjectionMatrix.............................. 430 cv::DrawChessboardCorners............................... 431 cv::FindChessboardCorners................................ 432 cv::FindExtrinsicCameraParams2............................. 433 cv::FindFundamentalMat................................. 434 CONTENTS 17 cv::FindHomography.................................... 436 cv::FindStereoCorrespondenceBM............................ 438 cv::FindStereoCorrespondenceGC............................ 439 cv::GetOptimalNewCameraMatrix............................ 441 cv::InitIntrinsicParams2D................................. 442 cv::InitUndistortMap.................................... 443 cv::InitUndistortRectifyMap................................ 444 cv::POSIT.......................................... 445 cv::ProjectPoints2..................................... 446 cv::ReprojectImageTo3D.................................. 447 cv::RQDecomp3x3..................................... 448 cv::ReleasePOSITObject................................. 449 cv::ReleaseStereoBMState................................ 449 cv::ReleaseStereoGCState................................ 450 cv::Rodrigues2....................................... 450 cv::StereoCalibrate..................................... 451 cv::StereoRectify...................................... 454 cv::StereoRectifyUncalibrated............................... 457 cv::Undistort2........................................ 458 cv::UndistortPoints..................................... 459 9 ml. Machine Learning 461 II C++ API Reference 463 10 Introduction 465 10.1 C++ Cheatsheet...................................... 468 10.2 Namespace cv and Function Naming........................... 469 10.3 Memory Management................................... 470 10.4 Memory Management Part II. Automatic Data Allocation................ 471 10.5 Algebraic Operations.................................... 473 10.6 Fast Element Access.................................... 473 10.7 Saturation Arithmetics................................... 474 10.8 Error handling........................................ 474 10.9 Threading and Reenterability............................... 475 11 core. The Core Functionality 477 11.1 Basic Structures...................................... 477 DataType.......................................... 477 18 CONTENTS Point ............................................ 479 Point3 ............................................ 480 Size ............................................. 481 Rect ............................................. 482 RotatedRect........................................ 484 TermCriteria......................................... 484 Matx............................................. 485 Vec.............................................. 486 Scalar ............................................ 487 Range............................................ 488 Ptr.............................................. 488 Mat............................................. 491 Matrix Expressions..................................... 496 cv::Mat::Mat......................................... 497 cv::Mat::Mat......................................... 499 cv::Mat::operator =..................................... 499 cv::Mat::operator MatExpr................................. 500 cv::Mat::row......................................... 500 cv::Mat::col......................................... 501 cv::Mat::rowRange..................................... 502 cv::Mat::colRange..................................... 502 cv::Mat::diag........................................ 502 cv::Mat::clone........................................ 503 cv::Mat::copyTo....................................... 503 cv::Mat::convertTo..................................... 504 cv::Mat::assignTo...................................... 505 cv::Mat::setTo........................................ 505 cv::Mat::reshape...................................... 505 cv::Mat::t.......................................... 506 cv::Mat::inv......................................... 506 cv::Mat::mul......................................... 507 cv::Mat::cross........................................ 508 cv::Mat::dot......................................... 508 cv::Mat::zeros........................................ 508 cv::Mat::ones........................................ 509 cv::Mat::eye......................................... 510 cv::Mat::create....................................... 510 cv::Mat::addref....................................... 511 cv::Mat::release....................................... 512 cv::Mat::resize....................................... 512 CONTENTS 19 Mat::push back....................................... 513 Mat::pop back....................................... 513 cv::Mat::locateROI..................................... 513 cv::Mat::adjustROI..................................... 514 cv::Mat::operator()..................................... 515 cv::Mat::operator CvMat.................................. 515 cv::Mat::operator IplImage................................. 516 cv::Mat::total........................................ 516 cv::Mat::isContinuous................................... 516 cv::Mat::elemSize..................................... 518 cv::Mat::elemSize1..................................... 518 cv::Mat::type........................................ 519 cv::Mat::depth........................................ 519 cv::Mat::channels...................................... 520 cv::Mat::step1........................................ 520 cv::Mat::size........................................ 520 cv::Mat::empty....................................... 521 cv::Mat::ptr......................................... 521 cv::Mat::at.......................................... 521 cv::Mat::begin........................................ 522 cv::Mat::end......................................... 523 Mat ............................................. 524 NAryMatIterator....................................... 525 SparseMat......................................... 526 SparseMat ......................................... 532 11.2 Operations on Arrays.................................... 534 cv::abs............................................ 534 cv::absdiff.......................................... 534 cv::add........................................... 535 cv::addWeighted...................................... 536 bitwise and......................................... 537 bitwise not......................................... 538 bitwise or.......................................... 539 bitwise xor......................................... 540 cv::calcCovarMatrix.................................... 541 cv::cartToPolar....................................... 542 cv::checkRange...................................... 543 cv::compare......................................... 544 cv::completeSymm..................................... 545 cv::convertScaleAbs.................................... 545 20 CONTENTS cv::countNonZero..................................... 546 cv::cubeRoot........................................ 547 cv::cvarrToMat....................................... 547 cv::dct............................................ 549 cv::dft............................................ 550 cv::divide.......................................... 554 cv::determinant....................................... 555 cv::eigen.......................................... 556 cv::exp............................................ 556 cv::extractImageCOI.................................... 557 cv::fastAtan2........................................ 558 cv::flip............................................ 558 cv::gemm.......................................... 559 cv::getConvertElem.................................... 560 cv::getOptimalDFTSize.................................. 561 cv::idct............................................ 561 cv::idft............................................ 562 cv::inRange......................................... 562 cv::invert.......................................... 563 cv::log............................................ 564 cv::LUT........................................... 564 cv::magnitude........................................ 565 cv::Mahalanobis...................................... 566 cv::max........................................... 566 cv::mean.......................................... 567 cv::meanStdDev...................................... 568 cv::merge.......................................... 569 cv::min............................................ 569 cv::minMaxLoc....................................... 570 cv::mixChannels...................................... 571 cv::mulSpectrums..................................... 573 cv::multiply......................................... 574 cv::mulTransposed..................................... 574 cv::norm........................................... 575 cv::normalize........................................ 576 cv::PCA........................................... 578 cv::PCA::PCA........................................ 579 cv::PCA::operator ().................................... 580 cv::PCA::project...................................... 581 cv::PCA::backProject.................................... 581 CONTENTS 21 cv::perspectiveTransform................................. 582 cv::phase.......................................... 583 cv::polarToCart....................................... 584 cv::pow........................................... 584 RNG............................................. 585 cv::RNG::RNG....................................... 586 cv::RNG::next........................................ 587 cv::RNG::operator T.................................... 587 cv::RNG::operator ().................................... 587 cv::RNG::uniform...................................... 588 cv::RNG::gaussian..................................... 589 cv::RNG::fill......................................... 589 cv::randu.......................................... 590 cv::randn.......................................... 590 cv::randShuffle....................................... 591 cv::reduce.......................................... 592 cv::repeat.......................................... 592 saturate cast........................................ 593 cv::scaleAdd........................................ 594 cv::setIdentity........................................ 595 cv::solve........................................... 595 cv::solveCubic....................................... 596 cv::solvePoly........................................ 597 cv::sort........................................... 597 cv::sortIdx.......................................... 598 cv::split........................................... 599 cv::sqrt........................................... 599 cv::subtract......................................... 600 cv::SVD........................................... 601 cv::SVD::SVD........................................ 602 cv::SVD::operator ().................................... 603 cv::SVD::solveZ....................................... 603 cv::SVD::backSubst.................................... 604 cv::sum........................................... 604 cv::theRNG......................................... 605 cv::trace........................................... 605 cv::transform........................................ 606 cv::transpose........................................ 607 11.3 Dynamic Structures.................................... 607 11.4 Drawing Functions..................................... 607 22 CONTENTS cv::circle........................................... 608 cv::clipLine......................................... 608 cv::ellipse.......................................... 609 cv::ellipse2Poly....................................... 610 cv::fillConvexPoly...................................... 611 cv::fillPoly.......................................... 612 cv::getTextSize....................................... 612 cv::line............................................ 613 cv::LineIterator....................................... 614 cv::rectangle........................................ 615 cv::polylines......................................... 616 cv::putText.......................................... 617 11.5 XML/YAML Persistence.................................. 617 cv::FileStorage....................................... 617 cv::FileNode........................................ 619 cv::FileNodeIterator.................................... 620 11.6 Clustering.......................................... 620 cv::kmeans......................................... 620 cv::partition......................................... 622 11.7 Utility and System Functions and Macros........................ 622 cv::alignPtr......................................... 622 cv::alignSize........................................ 623 cv::allocate......................................... 623 cv::deallocate........................................ 623 CV Assert.......................................... 624 cv::error........................................... 624 cv::Exception........................................ 625 cv::fastMalloc........................................ 625 cv::fastFree......................................... 626 cv::format.......................................... 626 cv::getNumThreads.................................... 627 cv::getThreadNum..................................... 627 cv::getTickCount...................................... 627 cv::getTickFrequency................................... 628 cv::setNumThreads.................................... 628 12 imgproc. Image Processing 629 12.1 Histograms......................................... 629 cv::calcHist......................................... 629 cv::calcBackProject.................................... 632 CONTENTS 23 cv::compareHist...................................... 633 cv::equalizeHist....................................... 634 12.2 Image Filtering....................................... 635 cv::BaseColumnFilter................................... 636 cv::BaseFilter........................................ 636 cv::BaseRowFilter..................................... 637 cv::FilterEngine....................................... 638 cv::bilateralFilter...................................... 643 cv::blur........................................... 644 cv::borderInterpolate.................................... 644 cv::boxFilter......................................... 645 cv::buildPyramid...................................... 646 cv::copyMakeBorder.................................... 646 cv::createBoxFilter..................................... 648 cv::createDerivFilter.................................... 649 cv::createGaussianFilter.................................. 649 cv::createLinearFilter.................................... 650 cv::createMorphologyFilter................................ 651 cv::createSeparableLinearFilter.............................. 652 cv::dilate........................................... 653 cv::erode.......................................... 654 cv::filter2D.......................................... 655 cv::GaussianBlur...................................... 656 cv::getDerivKernels.................................... 657 cv::getGaussianKernel................................... 658 cv::getKernelType..................................... 658 cv::getStructuringElement................................. 659 cv::medianBlur....................................... 660 cv::morphologyEx..................................... 660 cv::Laplacian........................................ 661 cv::pyrDown......................................... 662 cv::pyrUp.......................................... 663 cv::sepFilter2D....................................... 664 cv::Sobel.......................................... 665 cv::Scharr.......................................... 666 12.3 Geometric Image Transformations............................ 667 cv::convertMaps...................................... 668 cv::getAffineTransform................................... 669 cv::getPerspectiveTransform................................ 669 cv::getRectSubPix..................................... 670 24 CONTENTS cv::getRotationMatrix2D.................................. 671 cv::invertAffineTransform.................................. 671 cv::remap.......................................... 672 cv::resize.......................................... 673 cv::warpAffine........................................ 674 cv::warpPerspective.................................... 675 12.4 Miscellaneous Image Transformations.......................... 676 cv::adaptiveThreshold................................... 676 cv::cvtColor......................................... 677 cv::distanceTransform................................... 683 cv::floodFill......................................... 684 cv::inpaint.......................................... 686 cv::integral......................................... 687 cv::threshold........................................ 688 cv::watershed........................................ 690 cv::grabCut......................................... 691 12.5 Structural Analysis and Shape Descriptors........................ 692 cv::moments........................................ 692 cv::HuMoments....................................... 693 cv::findContours...................................... 694 cv::drawContours...................................... 696 cv::approxPolyDP...................................... 697 cv::arcLength........................................ 698 cv::boundingRect...................................... 699 cv::estimateRigidTransform................................ 699 cv::estimateAffine3D.................................... 700 cv::contourArea....................................... 700 cv::convexHull....................................... 701 cv::fitEllipse......................................... 702 cv::fitLine.......................................... 702 cv::isContourConvex.................................... 704 cv::minAreaRect...................................... 704 cv::minEnclosingCircle................................... 705 cv::matchShapes...................................... 705 cv::pointPolygonTest.................................... 706 12.6 Planar Subdivisions.................................... 707 12.7 Motion Analysis and Object Tracking........................... 707 cv::accumulate....................................... 707 cv::accumulateSquare................................... 708 cv::accumulateProduct................................... 709 CONTENTS 25 cv::accumulateWeighted.................................. 709 12.8 Feature Detection..................................... 710 cv::Canny.......................................... 710 cv::cornerEigenValsAndVecs............................... 711 cv::cornerHarris...................................... 712 cv::cornerMinEigenVal................................... 712 cv::cornerSubPix...................................... 713 cv::goodFeaturesToTrack................................. 714 cv::HoughCircles...................................... 716 cv::HoughLines....................................... 718 cv::HoughLinesP...................................... 719 cv::preCornerDetect.................................... 721 12.9 Object Detection...................................... 722 cv::matchTemplate..................................... 722 13 features2d. Feature Detection and Descriptor Extraction 725 13.1 Feature detection and description............................. 725 cv::FAST.......................................... 725 cv::MSER.......................................... 725 cv::StarDetector...................................... 726 cv::SIFT........................................... 727 cv::SURF.......................................... 729 cv::RandomizedTree.................................... 729 cv::RandomizedTree::train................................. 731 cv::RandomizedTree::read................................. 732 cv::RandomizedTree::write................................ 732 cv::RandomizedTree::applyQuantization......................... 733 cv::RTreeNode....................................... 733 cv::RTreeClassifier..................................... 733 cv::RTreeClassifier::train.................................. 735 cv::RTreeClassifier::getSignature............................. 736 cv::RTreeClassifier::getSparseSignature......................... 736 cv::RTreeClassifier::countNonZeroElements....................... 737 cv::RTreeClassifier::read.................................. 737 cv::RTreeClassifier::write................................. 737 cv::RTreeClassifier::setQuantization........................... 738 13.2 Common Interfaces of Feature Detectors........................ 740 cv::KeyPoint......................................... 740 cv::FeatureDetector.................................... 741 cv::FeatureDetector::detect................................ 742 26 CONTENTS cv::FeatureDetector::read................................. 743 cv::FeatureDetector::write................................. 743 cv::FeatureDetector::create................................ 743 cv::FastFeatureDetector.................................. 744 cv::GoodFeaturesToTrackDetector............................ 744 cv::MserFeatureDetector.................................. 745 cv::StarFeatureDetector.................................. 745 cv::SiftFeatureDetector................................... 746 cv::SurfFeatureDetector.................................. 746 cv::GridAdaptedFeatureDetector............................. 747 cv::PyramidAdaptedFeatureDetector........................... 747 cv::DynamicAdaptedFeatureDetector........................... 747 cv::DynamicAdaptedFeatureDetector::DynamicAdaptedFeatureDetector....... 748 cv::AdjusterAdapter.................................... 749 cv::AdjusterAdapter::tooFew............................... 749 cv::AdjusterAdapter::tooMany............................... 750 cv::AdjusterAdapter::good................................. 750 cv::FastAdjuster...................................... 751 cv::StarAdjuster....................................... 751 cv::SurfAdjuster....................................... 751 13.3 Common Interfaces of Descriptor Extractors....................... 751 cv::DescriptorExtractor................................... 752 cv::DescriptorExtractor::compute............................. 752 cv::DescriptorExtractor::read............................... 753 cv::DescriptorExtractor::write............................... 753 cv::DescriptorExtractor::create.............................. 754 cv::SiftDescriptorExtractor................................. 754 cv::SurfDescriptorExtractor................................ 755 cv::CalonderDescriptorExtractor............................. 755 cv::OpponentColorDescriptorExtractor.......................... 755 cv::BriefDescriptorExtractor................................ 756 13.4 Common Interfaces of Descriptor Matchers....................... 756 cv::DMatch......................................... 757 cv::DescriptorMatcher................................... 757 cv::DescriptorMatcher::add................................ 758 cv::DescriptorMatcher::getTrainDescriptors....................... 759 cv::DescriptorMatcher::clear................................ 759 cv::DescriptorMatcher::empty............................... 759 cv::DescriptorMatcher::isMaskSupported........................ 759 cv::DescriptorMatcher::train................................ 760 CONTENTS 27 cv::DescriptorMatcher::match............................... 760 cv::DescriptorMatcher::knnMatch............................. 761 cv::DescriptorMatcher::radiusMatch........................... 762 cv::DescriptorMatcher::clone............................... 762 cv::DescriptorMatcher::create............................... 763 cv::BruteForceMatcher................................... 763 cv::FlannBasedMatcher.................................. 765 13.5 Common Interfaces of Generic Descriptor Matchers.................. 765 cv::GenericDescriptorMatcher............................... 766 cv::GenericDescriptorMatcher::add............................ 767 cv::GenericDescriptorMatcher::getTrainImages..................... 768 cv::GenericDescriptorMatcher::getTrainKeypoints.................... 768 cv::GenericDescriptorMatcher::clear........................... 768 cv::GenericDescriptorMatcher::train........................... 768 cv::GenericDescriptorMatcher::isMaskSupported.................... 768 cv::GenericDescriptorMatcher::classify.......................... 768 cv::GenericDescriptorMatcher::match.......................... 769 cv::GenericDescriptorMatcher::knnMatch........................ 770 cv::GenericDescriptorMatcher::radiusMatch....................... 771 cv::GenericDescriptorMatcher::read........................... 771 cv::GenericDescriptorMatcher::write........................... 772 cv::GenericDescriptorMatcher::clone........................... 772 cv::OneWayDescriptorMatcher.............................. 772 cv::FernDescriptorMatcher................................ 773 cv::VectorDescriptorMatcher............................... 775 13.6 Drawing Function of Keypoints and Matches....................... 775 cv::drawMatches...................................... 775 cv::drawKeypoints..................................... 777 13.7 Object Categorization................................... 778 cv::BOWTrainer....................................... 778 cv::BOWTrainer::add.................................... 778 cv::BOWTrainer::getDescriptors.............................. 779 cv::BOWTrainer::descripotorsCount........................... 779 cv::BOWTrainer::cluster.................................. 779 cv::BOWKMeansTrainer.................................. 779 cv::BOWImgDescriptorExtractor............................. 780 cv::BOWImgDescriptorExtractor::BOWImgDescriptorExtractor............. 781 cv::BOWImgDescriptorExtractor::setVocabulary..................... 781 cv::BOWImgDescriptorExtractor::getVocabulary..................... 781 cv::BOWImgDescriptorExtractor::compute........................ 782 28 CONTENTS cv::BOWImgDescriptorExtractor::descriptorSize..................... 782 cv::BOWImgDescriptorExtractor::descriptorType.................... 782 14 flann. Clustering and Search in Multi-Dimensional Spaces 783 14.1 Fast Approximate Nearest Neighbor Search....................... 783 cv::flann::Index ....................................... 783 cvflann::Index < T >::Index ............................... 784 cv::flann::Index < T >::knnSearch............................ 787 cv::flann::Index < T >::radiusSearch........................... 788 cv::flann::Index < T >::save................................ 789 cv::flann::Index < T >::getIndexParameters....................... 789 14.2 Clustering.......................................... 789 cv::cv::flann::hierarchicalClustering¡ET,DT¿....................... 789 15 objdetect. Object Detection 791 15.1 Cascade Classification................................... 791 cv::FeatureEvaluator.................................... 791 cv::FeatureEvaluator::read................................. 791 cv::FeatureEvaluator::clone................................ 792 cv::FeatureEvaluator::getFeatureType.......................... 792 cv::FeatureEvaluator::setImage.............................. 792 cv::FeatureEvaluator::setWindow............................. 793 cv::FeatureEvaluator::calcOrd............................... 793 cv::FeatureEvaluator::calcCat............................... 793 cv::FeatureEvaluator::create................................ 794 cv::CascadeClassifier................................... 794 cv::CascadeClassifier::CascadeClassifier........................ 795 cv::CascadeClassifier::empty............................... 796 cv::CascadeClassifier::load................................ 796 cv::CascadeClassifier::read................................ 796 cv::CascadeClassifier::detectMultiScale......................... 796 cv::CascadeClassifier::setImage............................. 797 cv::CascadeClassifier::runAt............................... 797 cv::groupRectangles.................................... 798 16 video. Video Analysis 799 16.1 Motion Analysis and Object Tracking........................... 799 cv::calcOpticalFlowPyrLK................................. 799 cv::calcOpticalFlowFarneback............................... 800 cv::updateMotionHistory.................................. 801 CONTENTS 29 cv::calcMotionGradient................................... 802 cv::calcGlobalOrientation................................. 803 cv::CamShift........................................ 803 cv::meanShift........................................ 804 cv::KalmanFilter...................................... 805 17 highgui. High-level GUI and Media I/O 807 17.1 User Interface........................................ 807 cv::createTrackbar..................................... 807 cv::getTrackbarPos..................................... 808 cv::imshow......................................... 809 cv::namedWindow..................................... 809 cv::setTrackbarPos..................................... 811 cv::waitKey......................................... 811 17.2 Reading and Writing Images and Video......................... 812 cv::imdecode........................................ 812 cv::imencode........................................ 812 cv::imread.......................................... 813 cv::imwrite.......................................... 814 cv::VideoCapture...................................... 815 cv::VideoCapture::VideoCapture............................. 816 cv::VideoCapture::get................................... 817 cv::VideoCapture::set................................... 818 cv::VideoWriter....................................... 819 17.3 Qt new functions...................................... 820 cv::setWindowProperty.................................. 821 cv::getWindowProperty.................................. 822 cv::fontQt.......................................... 823 cv::addText......................................... 824 cv::displayOverlay..................................... 824 cv::displayStatusBar.................................... 825 cv::createOpenGLCallback................................ 825 cv::saveWindowParameters................................ 827 cv::loadWindowParameters................................ 827 cv::createButton...................................... 827 18 calib3d. Camera Calibration, Pose Estimation and Stereo 829 18.1 Camera Calibration and 3d Reconstruction....................... 829 cv::calibrateCamera.................................... 831 cv::calibrationMatrixValues................................ 833 30 CONTENTS cv::composeRT....................................... 834 cv::computeCorrespondEpilines............................. 835 cv::convertPointsHomogeneous.............................. 836 cv::decomposeProjectionMatrix.............................. 836 cv::drawChessboardCorners............................... 837 cv::findChessboardCorners................................ 838 cv::solvePnP........................................ 839 cv::findFundamentalMat.................................. 840 cv::findHomography.................................... 842 cv::getDefaultNewCameraMatrix............................. 844 cv::getOptimalNewCameraMatrix............................. 845 cv::initCameraMatrix2D.................................. 845 cv::initUndistortRectifyMap................................ 846 cv::matMulDeriv...................................... 848 cv::projectPoints...................................... 848 cv::reprojectImageTo3D.................................. 850 cv::RQDecomp3x3..................................... 851 cv::Rodrigues........................................ 851 cv::StereoBM........................................ 852 cv::StereoSGBM...................................... 853 cv::StereoSGBM::StereoSGBM.............................. 854 cv::StereoSGBM::operator ()............................... 855 cv::stereoCalibrate..................................... 856 cv::stereoRectify...................................... 858 cv::stereoRectifyUncalibrated............................... 862 cv::undistort......................................... 863 cv::undistortPoints..................................... 863 19 ml. Machine Learning 867 19.1 Statistical Models...................................... 867 cv::CvStatModel...................................... 867 CvStatModel::CvStatModel................................ 868 CvStatModel::CvStatModel(...).............................. 868 CvStatModel:: CvStatModel................................ 869 CvStatModel::clear..................................... 869 CvStatModel::save..................................... 869 CvStatModel::load..................................... 870 CvStatModel::write..................................... 870 CvStatModel::read..................................... 870 CvStatModel::train..................................... 871 CONTENTS 31 CvStatModel::predict.................................... 872 19.2 Normal Bayes Classifier.................................. 872 cv::CvNormalBayesClassifier............................... 873 CvNormalBayesClassifier::train.............................. 873 CvNormalBayesClassifier::predict............................ 874 19.3 K Nearest Neighbors.................................... 874 cv::CvKNearest....................................... 874 CvKNearest::train..................................... 875 CvKNearest::find nearest................................. 876 19.4 Support Vector Machines................................. 878 cv::CvSVM......................................... 879 cv::CvSVMParams..................................... 880 CvSVM::train........................................ 881 CvSVM::train auto..................................... 881 CvSVM::get default grid.................................. 882 CvSVM::get params.................................... 883 CvSVM::get support vector*................................ 883 19.5 Decision Trees....................................... 884 Predicting with Decision Trees.............................. 884 Training Decision Trees.................................. 884 Variable importance.................................... 885 cv::CvDTreeSplit...................................... 885 cv::CvDTreeNode...................................... 886 cv::CvDTreeParams.................................... 886 cv::CvDTreeTrainData................................... 887 cv::CvDTree......................................... 890 CvDTree::train....................................... 892 CvDTree::predict...................................... 892 19.6 Boosting........................................... 893 cv::CvBoostParams.................................... 895 cv::CvBoostTree...................................... 895 cv::CvBoost......................................... 896 CvBoost::train........................................ 897 CvBoost::predict...................................... 898 CvBoost::prune....................................... 898 CvBoost::get weak predictors............................... 898 19.7 Random Trees....................................... 899 cv::CvRTParams...................................... 900 cv::CvRTrees........................................ 900 CvRTrees::train....................................... 901 32 CONTENTS CvRTrees::predict..................................... 902 CvRTrees::get var importance.............................. 902 CvRTrees::get proximity.................................. 903 19.8 Expectation-Maximization................................. 906 cv::CvEMParams...................................... 907 cv::CvEM.......................................... 908 CvEM::train......................................... 909 19.9 Neural Networks...................................... 912 cv::CvANN MLP TrainParams............................... 915 cv::CvANN MLP...................................... 916 CvANN MLP::create.................................... 918 CvANN MLP::train..................................... 918 III Python API Reference 921 20 Introduction 923 20.1 Cookbook.......................................... 923 Convert an image..................................... 923 Resize an image...................................... 924 Compute the Laplacian.................................. 924 Using GoodFeaturesToTrack............................... 924 Using GetSubRect..................................... 924 Using CreateMat, and accessing an element...................... 925 ROS image message to OpenCV............................. 925 PIL Image to OpenCV................................... 925 OpenCV to PIL Image................................... 925 NumPy and OpenCV.................................... 926 OpenCV to pygame.................................... 926 OpenCV and OpenEXR.................................. 927 21 core. The Core Functionality 929 21.1 Basic Structures...................................... 929 CvPoint........................................... 929 CvPoint2D32f........................................ 929 CvPoint3D32f........................................ 929 CvPoint2D64f........................................ 929 CvPoint3D64f........................................ 929 CvSize............................................ 930 CvSize2D32f........................................ 930 CONTENTS 33 CvRect........................................... 930 CvScalar.......................................... 930 CvTermCriteria....................................... 930 CvMat............................................ 931 CvMatND.......................................... 931 IplImage........................................... 931 CvArr............................................ 932 21.2 Operations on Arrays.................................... 932 cv::AbsDiff......................................... 932 cv::AbsDiffS......................................... 933 cv::Add........................................... 933 cv::AddS.......................................... 934 cv::AddWeighted...................................... 934 cv::And........................................... 935 cv::AndS.......................................... 935 cv::Avg........................................... 936 cv::AvgSdv......................................... 936 cv::CalcCovarMatrix.................................... 937 cv::CartToPolar....................................... 938 cv::Cbrt........................................... 939 cv::ClearND......................................... 939 cv::CloneImage....................................... 940 cv::CloneMat........................................ 940 cv::CloneMatND...................................... 940 cv::Cmp........................................... 940 cv::CmpS.......................................... 941 cv::Convert......................................... 942 cv::ConvertScale...................................... 943 cv::ConvertScaleAbs.................................... 943 cv::CvtScaleAbs...................................... 944 cv::Copy........................................... 944 cv::CountNonZero..................................... 945 cv::CreateData....................................... 945 cv::CreateImage...................................... 946 cv::CreateImageHeader.................................. 946 cv::CreateMat........................................ 947 cv::CreateMatHeader................................... 947 cv::CreateMatND...................................... 947 cv::CreateMatNDHeader.................................. 948 cv::CrossProduct...................................... 948 34 CONTENTS CvtPixToPlane....................................... 949 cv::DCT........................................... 949 cv::DFT........................................... 950 cv::Det............................................ 952 cv::Div............................................ 952 cv::DotProduct....................................... 953 cv::EigenVV......................................... 953 cv::Exp........................................... 954 cv::FastArctan....................................... 954 cv::Flip............................................ 955 cv::fromarray........................................ 956 cv::GEMM.......................................... 957 cv::Get1D.......................................... 957 cv::Get2D.......................................... 958 cv::Get3D.......................................... 958 cv::GetND.......................................... 959 cv::GetCol.......................................... 959 cv::GetCols......................................... 959 cv::GetDiag......................................... 960 cv::GetDims......................................... 960 cv::GetElemType...................................... 961 cv::GetImage........................................ 961 cv::GetImageCOI...................................... 961 cv::GetImageROI...................................... 962 cv::GetMat......................................... 962 cv::GetOptimalDFTSize.................................. 963 cv::GetReal1D....................................... 963 cv::GetReal2D....................................... 964 cv::GetReal3D....................................... 964 cv::GetRealND....................................... 965 cv::GetRow......................................... 965 cv::GetRows........................................ 965 cv::GetSize......................................... 966 cv::GetSubRect....................................... 966 cv::InRange......................................... 967 cv::InRangeS........................................ 967 cv::InvSqrt.......................................... 968 cv::Inv............................................ 968 cv::Invert.......................................... 969 cv::IsInf........................................... 969 CONTENTS 35 cv::IsNaN.......................................... 970 cv::LUT........................................... 970 cv::Log........................................... 971 cv::Mahalanobis...................................... 971 cv::Max........................................... 972 cv::MaxS.......................................... 972 cv::Merge.......................................... 973 cv::Min............................................ 973 cv::MinMaxLoc....................................... 974 cv::MinS........................................... 974 Mirror............................................ 975 cv::MixChannels...................................... 975 MulAddS.......................................... 976 cv::Mul............................................ 976 cv::MulSpectrums..................................... 976 cv::MulTransposed..................................... 977 cv::Norm.......................................... 978 cv::Not............................................ 979 cv::Or............................................ 979 cv::OrS........................................... 980 cv::PerspectiveTransform................................. 980 cv::PolarToCart....................................... 981 cv::Pow........................................... 982 cv::RNG........................................... 982 cv::RandArr......................................... 983 cv::RandInt......................................... 983 cv::RandReal........................................ 984 cv::Reduce......................................... 984 cv::Repeat......................................... 985 cv::ResetImageROI.................................... 985 cv::Reshape........................................ 986 cv::ReshapeMatND.................................... 986 cv::Round.......................................... 987 cv::Floor........................................... 987 cv::Ceil........................................... 988 cv::ScaleAdd........................................ 988 cv::Set............................................ 988 cv::Set1D.......................................... 989 cv::Set2D.......................................... 989 cv::Set3D.......................................... 990 36 CONTENTS cv::SetND.......................................... 990 cv::SetData......................................... 991 cv::SetIdentity........................................ 991 cv::SetImageCOI...................................... 992 cv::SetImageROI...................................... 992 cv::SetReal1D....................................... 993 cv::SetReal2D....................................... 993 cv::SetReal3D....................................... 993 cv::SetRealND....................................... 994 cv::SetZero......................................... 994 cv::Solve.......................................... 995 cv::SolveCubic....................................... 995 cv::Split........................................... 996 cv::Sqrt........................................... 997 cv::Sub........................................... 997 cv::SubRS.......................................... 997 cv::SubS.......................................... 998 cv::Sum........................................... 999 cv::SVBkSb......................................... 999 cv::SVD........................................... 1000 cv::Trace.......................................... 1001 cv::Transform........................................ 1002 cv::Transpose........................................ 1002 cv::Xor............................................ 1003 cv::XorS........................................... 1003 cv::mGet.......................................... 1004 cv::mSet........................................... 1004 21.3 Dynamic Structures.................................... 1005 CvMemStorage....................................... 1005 CvSeq............................................ 1005 CvSet............................................ 1006 cv::CloneSeq........................................ 1006 cv::CreateMemStorage.................................. 1006 cv::SeqInvert........................................ 1007 cv::SeqRemove....................................... 1007 cv::SeqRemoveSlice.................................... 1007 21.4 Drawing Functions..................................... 1008 cv::Circle.......................................... 1008 cv::ClipLine......................................... 1009 cv::DrawContours..................................... 1009 CONTENTS 37 cv::Ellipse.......................................... 1010 cv::EllipseBox........................................ 1011 cv::FillConvexPoly..................................... 1012 cv::FillPoly.......................................... 1012 cv::GetTextSize....................................... 1013 cv::InitFont......................................... 1013 cv::InitLineIterator..................................... 1014 cv::Line........................................... 1015 cv::PolyLine......................................... 1016 cv::PutText......................................... 1017 cv::Rectangle........................................ 1017 CV RGB........................................... 1018 21.5 XML/YAML Persistence.................................. 1018 cv::Load........................................... 1018 cv::Save........................................... 1019 21.6 Clustering.......................................... 1019 cv::KMeans2........................................ 1019 21.7 Utility and System Functions and Macros........................ 1020 Error Handling....................................... 1020 cv::GetTickCount...................................... 1020 cv::GetTickFrequency................................... 1021 22 imgproc. Image Processing 1023 22.1 Histograms......................................... 1023 CvHistogram........................................ 1023 cv::CalcBackProject.................................... 1023 cv::CalcBackProjectPatch................................. 1024 cv::CalcHist......................................... 1025 cv::CalcProbDensity.................................... 1027 cv::ClearHist........................................ 1027 cv::CompareHist...................................... 1028 cv::CreateHist........................................ 1029 cv::GetMinMaxHistValue.................................. 1030 cv::NormalizeHist...................................... 1031 QueryHistValue 1D..................................... 1031 QueryHistValue 2D..................................... 1031 QueryHistValue 3D..................................... 1032 QueryHistValue nD..................................... 1032 cv::ThreshHist....................................... 1032 22.2 Image Filtering....................................... 1033 38 CONTENTS IplConvKernel........................................ 1033 cv::CopyMakeBorder.................................... 1033 cv::CreateStructuringElementEx............................. 1034 cv::Dilate.......................................... 1035 cv::Erode.......................................... 1036 cv::Filter2D......................................... 1036 cv::Laplace......................................... 1037 cv::MorphologyEx..................................... 1038 cv::PyrDown........................................ 1039 cv::Smooth......................................... 1039 cv::Sobel.......................................... 1041 22.3 Geometric Image Transformations............................ 1042 cv::GetRotationMatrix2D.................................. 1043 cv::GetAffineTransform................................... 1044 cv::GetPerspectiveTransform............................... 1044 cv::GetQuadrangleSubPix................................. 1045 cv::GetRectSubPix..................................... 1046 cv::LogPolar......................................... 1046 cv::Remap......................................... 1047 cv::Resize.......................................... 1048 cv::WarpAffine....................................... 1048 cv::WarpPerspective.................................... 1049 22.4 Miscellaneous Image Transformations.......................... 1050 cv::AdaptiveThreshold................................... 1050 cv::CvtColor......................................... 1052 cv::DistTransform...................................... 1056 CvConnectedComp.................................... 1058 cv::FloodFill......................................... 1058 cv::Inpaint.......................................... 1060 cv::Integral......................................... 1061 cv::PyrMeanShiftFiltering................................. 1062 cv::PyrSegmentation.................................... 1063 cv::Threshold........................................ 1064 22.5 Structural Analysis and Shape Descriptors........................ 1066 cv::ApproxChains...................................... 1066 cv::ApproxPoly....................................... 1066 cv::ArcLength........................................ 1067 cv::BoundingRect...................................... 1068 cv::BoxPoints........................................ 1068 cv::CalcPGH........................................ 1069 CONTENTS 39 cv::CalcEMD2....................................... 1069 cv::CheckContourConvexity................................ 1070 CvConvexityDefect..................................... 1071 cv::ContourArea...................................... 1071 cv::ContourFromContourTree............................... 1072 cv::ConvexHull2...................................... 1073 cv::ConvexityDefects.................................... 1073 cv::CreateContourTree................................... 1074 cv::FindContours...................................... 1074 cv::FitEllipse2........................................ 1076 cv::FitLine.......................................... 1076 cv::GetCentralMoment................................... 1077 cv::GetHuMoments..................................... 1078 cv::GetNormalizedCentralMoment............................ 1079 cv::GetSpatialMoment................................... 1079 cv::MatchContourTrees.................................. 1080 cv::MatchShapes...................................... 1080 cv::MinAreaRect2..................................... 1081 cv::MinEnclosingCircle................................... 1082 cv::Moments........................................ 1083 cv::PointPolygonTest.................................... 1083 22.6 Planar Subdivisions.................................... 1084 CvSubdiv2D........................................ 1084 CvSubdiv2DPoint...................................... 1085 cv::CalcSubdivVoronoi2D................................. 1085 cv::ClearSubdivVoronoi2D................................. 1086 cv::CreateSubdivDelaunay2D............................... 1086 cv::FindNearestPoint2D.................................. 1086 cv::Subdiv2DEdgeDst................................... 1087 cv::Subdiv2DGetEdge................................... 1087 cv::Subdiv2DNextEdge.................................. 1088 cv::Subdiv2DLocate.................................... 1089 cv::Subdiv2DRotateEdge................................. 1090 cv::SubdivDelaunay2DInsert............................... 1091 22.7 Motion Analysis and Object Tracking........................... 1091 cv::Acc........................................... 1091 cv::MultiplyAcc....................................... 1092 cv::RunningAvg....................................... 1092 cv::SquareAcc....................................... 1093 22.8 Feature Detection..................................... 1093 40 CONTENTS cv::Canny.......................................... 1093 cv::CornerEigenValsAndVecs............................... 1094 cv::CornerHarris...................................... 1094 cv::CornerMinEigenVal................................... 1095 cv::FindCornerSubPix................................... 1096 cv::GoodFeaturesToTrack................................. 1097 cv::HoughLines2...................................... 1098 cv::PreCornerDetect.................................... 1099 22.9 Object Detection...................................... 1100 cv::MatchTemplate..................................... 1100 23 features2d. Feature Detection and Descriptor Extraction 1103 23.1 Feature detection and description............................. 1103 CvSURFPoint........................................ 1103 cv::ExtractSURF...................................... 1104 cv::GetStarKeypoints.................................... 1105 24 flann. Clustering and Search in Multi-Dimensional Spaces 1107 24.1 Fast Approximate Nearest Neighbor Search....................... 1107 25 objdetect. Object Detection 1109 25.1 Cascade Classification................................... 1109 Haar Feature-based Cascade Classifier for Object Detection............. 1109 cv::HaarDetectObjects................................... 1110 26 video. Video Analysis 1113 26.1 Motion Analysis and Object Tracking........................... 1113 cv::CalcGlobalOrientation................................. 1113 cv::CalcMotionGradient.................................. 1114 cv::CalcOpticalFlowBM.................................. 1115 cv::CalcOpticalFlowHS................................... 1115 cv::CalcOpticalFlowLK................................... 1116 cv::CalcOpticalFlowPyrLK................................. 1117 cv::CamShift........................................ 1118 CvKalman.......................................... 1119 cv::CreateKalman..................................... 1120 cv::KalmanCorrect..................................... 1120 cv::KalmanPredict..................................... 1121 KalmanUpdateByMeasurement.............................. 1122 KalmanUpdateByTime................................... 1122 CONTENTS 41 cv::MeanShift........................................ 1122 cv::SegmentMotion..................................... 1122 cv::SnakeImage...................................... 1123 cv::UpdateMotionHistory.................................. 1124 27 highgui. High-level GUI and Media I/O 1125 27.1 User Interface........................................ 1125 cv::CreateTrackbar..................................... 1125 cv::DestroyAllWindows................................... 1126 cv::DestroyWindow..................................... 1126 cv::GetTrackbarPos..................................... 1127 cv::MoveWindow...................................... 1127 cv::NamedWindow..................................... 1128 cv::ResizeWindow..................................... 1129 cv::SetMouseCallback................................... 1129 cv::SetTrackbarPos..................................... 1130 cv::ShowImage....................................... 1131 cv::WaitKey......................................... 1131 27.2 Reading and Writing Images and Video......................... 1132 cv::LoadImage....................................... 1132 cv::LoadImageM...................................... 1133 cv::SaveImage....................................... 1134 CvCapture......................................... 1134 cv::CaptureFromCAM................................... 1134 cv::CaptureFromFile.................................... 1135 cv::GetCaptureProperty.................................. 1135 cv::GrabFrame....................................... 1136 cv::QueryFrame...................................... 1137 cv::RetrieveFrame..................................... 1137 cv::SetCaptureProperty.................................. 1137 cv::CreateVideoWriter................................... 1139 cv::WriteFrame....................................... 1139 28 calib3d. Camera Calibration, Pose Estimation and Stereo 1141 28.1 Camera Calibration and 3d Reconstruction....................... 1141 cv::CalibrateCamera2................................... 1143 cv::ComputeCorrespondEpilines............................. 1145 cv::ConvertPointsHomogeneous............................. 1146 cv::CreatePOSITObject.................................. 1146 cv::CreateStereoBMState................................. 1147 42 CONTENTS cv::CreateStereoGCState................................. 1147 CvStereoBMState..................................... 1148 CvStereoGCState..................................... 1149 cv::DecomposeProjectionMatrix.............................. 1150 cv::DrawChessboardCorners............................... 1151 cv::FindChessboardCorners................................ 1151 cv::FindExtrinsicCameraParams2............................. 1153 cv::FindFundamentalMat................................. 1153 cv::FindHomography.................................... 1155 cv::FindStereoCorrespondenceBM............................ 1156 cv::FindStereoCorrespondenceGC............................ 1157 cv::GetOptimalNewCameraMatrix............................ 1159 cv::InitIntrinsicParams2D................................. 1160 cv::InitUndistortMap.................................... 1161 cv::InitUndistortRectifyMap................................ 1161 cv::POSIT.......................................... 1163 cv::ProjectPoints2..................................... 1164 cv::ReprojectImageTo3D.................................. 1165 cv::RQDecomp3x3..................................... 1166 cv::Rodrigues2....................................... 1166 cv::StereoCalibrate..................................... 1167 cv::StereoRectify...................................... 1170 cv::StereoRectifyUncalibrated............................... 1173 cv::Undistort2........................................ 1174 cv::UndistortPoints..................................... 1175 29 ml. Machine Learning 1177 Bibliography 1177 Index 1180 Part I C API Reference 43 Chapter 1 core. The Core Functionality 1.1 Basic Structures CvPoint (view/add comments) 2D point with integer coordinates (usually zero-based). typedef struct CvPoint { int x; int y; } CvPoint; x x-coordinate y y-coordinate /* Constructor */ inline CvPoint cvPoint( int x, int y ); /* Conversion from CvPoint2D32f */ inline CvPoint cvPointFrom32f( CvPoint2D32f point ); CvPoint2D32f (view/add comments) 2D point with floating-point coordinates 45 46 CHAPTER 1. CORE. THE CORE FUNCTIONALITY typedef struct CvPoint2D32f { float x; float y; } CvPoint2D32f; x x-coordinate y y-coordinate /* Constructor */ inline CvPoint2D32f cvPoint2D32f( double x, double y ); /* Conversion from CvPoint */ inline CvPoint2D32f cvPointTo32f( CvPoint point ); CvPoint3D32f (view/add comments) 3D point with floating-point coordinates typedef struct CvPoint3D32f { float x; float y; float z; } CvPoint3D32f; x x-coordinate y y-coordinate z z-coordinate /* Constructor */ inline CvPoint3D32f cvPoint3D32f( double x, double y, double z ); 1.1. BASIC STRUCTURES 47 CvPoint2D64f (view/add comments) 2D point with double precision floating-point coordinates typedef struct CvPoint2D64f { double x; double y; } CvPoint2D64f; x x-coordinate y y-coordinate /* Constructor */ inline CvPoint2D64f cvPoint2D64f( double x, double y ); /* Conversion from CvPoint */ inline CvPoint2D64f cvPointTo64f( CvPoint point ); CvPoint3D64f (view/add comments) 3D point with double precision floating-point coordinates typedef struct CvPoint3D64f { double x; double y; double z; } CvPoint3D64f; x x-coordinate y y-coordinate z z-coordinate /* Constructor */ inline CvPoint3D64f cvPoint3D64f( double x, double y, double z ); 48 CHAPTER 1. CORE. THE CORE FUNCTIONALITY CvSize (view/add comments) Pixel-accurate size of a rectangle. typedef struct CvSize { int width; int height; } CvSize; width Width of the rectangle height Height of the rectangle /* Constructor */ inline CvSize cvSize( int width, int height ); CvSize2D32f (view/add comments) Sub-pixel accurate size of a rectangle. typedef struct CvSize2D32f { float width; float height; } CvSize2D32f; width Width of the rectangle height Height of the rectangle /* Constructor */ inline CvSize2D32f cvSize2D32f( double width, double height ); CvRect (view/add comments) Offset (usually the top-left corner) and size of a rectangle. 1.1. BASIC STRUCTURES 49 typedef struct CvRect { int x; int y; int width; int height; } CvRect; x x-coordinate of the top-left corner y y-coordinate of the top-left corner (bottom-left for Windows bitmaps) width Width of the rectangle height Height of the rectangle /* Constructor */ inline CvRect cvRect( int x, int y, int width, int height ); CvScalar (view/add comments) A container for 1-,2-,3- or 4-tuples of doubles. typedef struct CvScalar { double val[4]; } CvScalar; /* Constructor: initializes val[0] with val0, val[1] with val1, etc. */ inline CvScalar cvScalar( double val0, double val1=0, double val2=0, double val3=0 ); /* Constructor: initializes all of val[0]...val[3] with val0123 */ inline CvScalar cvScalarAll( double val0123 ); /* Constructor: initializes val[0] with val0, and all of val[1]...val[3] with zeros */ inline CvScalar cvRealScalar( double val0 ); 50 CHAPTER 1. CORE. THE CORE FUNCTIONALITY CvTermCriteria (view/add comments) Termination criteria for iterative algorithms. #define CV_TERMCRIT_ITER 1 #define CV_TERMCRIT_NUMBER CV_TERMCRIT_ITER #define CV_TERMCRIT_EPS 2 typedef struct CvTermCriteria { int type; int max_iter; double epsilon; } CvTermCriteria; type A combination of CV TERMCRIT ITER and CV TERMCRIT EPS max iter Maximum number of iterations epsilon Required accuracy /* Constructor */ inline CvTermCriteria cvTermCriteria( int type, int max_iter, double epsilon ); /* Check and transform a CvTermCriteria so that type=CV_TERMCRIT_ITER+CV_TERMCRIT_EPS and both max_iter and epsilon are valid */ CvTermCriteria cvCheckTermCriteria( CvTermCriteria criteria, double default_eps, int default_max_iters ); CvMat (view/add comments) A multi-channel matrix. typedef struct CvMat { int type; int step; int* refcount; union 1.1. BASIC STRUCTURES 51 { uchar* ptr; short* s; int* i; float* fl; double* db; } data; #ifdef __cplusplus union { int rows; int height; }; union { int cols; int width; }; #else int rows; int cols; #endif } CvMat; type A CvMat signature (CV MAT MAGIC VAL) containing the type of elements and flags step Full row length in bytes refcount Underlying data reference counter data Pointers to the actual matrix data rows Number of rows cols Number of columns Matrices are stored row by row. All of the rows are aligned by 4 bytes. CvMatND (view/add comments) Multi-dimensional dense multi-channel array. 52 CHAPTER 1. CORE. THE CORE FUNCTIONALITY typedef struct CvMatND { int type; int dims; int* refcount; union { uchar* ptr; short* s; int* i; float* fl; double* db; } data; struct { int size; int step; } dim[CV_MAX_DIM]; } CvMatND; type A CvMatND signature (CV MATND MAGIC VAL), combining the type of elements and flags dims The number of array dimensions refcount Underlying data reference counter data Pointers to the actual matrix data dim For each dimension, the pair (number of elements, distance between elements in bytes) CvSparseMat (view/add comments) Multi-dimensional sparse multi-channel array. typedef struct CvSparseMat { int type; int dims; int* refcount; 1.1. BASIC STRUCTURES 53 struct CvSet* heap; void** hashtable; int hashsize; int total; int valoffset; int idxoffset; int size[CV_MAX_DIM]; } CvSparseMat; type A CvSparseMat signature (CV SPARSE MAT MAGIC VAL), combining the type of elements and flags. dims Number of dimensions refcount Underlying reference counter. Not used. heap A pool of hash table nodes hashtable The hash table. Each entry is a list of nodes. hashsize Size of the hash table total Total number of sparse array nodes valoffset The value offset of the array nodes, in bytes idxoffset The index offset of the array nodes, in bytes size Array of dimension sizes IplImage (view/add comments) IPL image header typedef struct _IplImage { int nSize; int ID; int nChannels; int alphaChannel; int depth; char colorModel[4]; char channelSeq[4]; 54 CHAPTER 1. CORE. THE CORE FUNCTIONALITY int dataOrder; int origin; int align; int width; int height; struct _IplROI *roi; struct _IplImage *maskROI; void *imageId; struct _IplTileInfo *tileInfo; int imageSize; char *imageData; int widthStep; int BorderMode[4]; int BorderConst[4]; char *imageDataOrigin; } IplImage; nSize sizeof(IplImage) ID Version, always equals 0 nChannels Number of channels. Most OpenCV functions support 1-4 channels. alphaChannel Ignored by OpenCV depth Channel depth in bits + the optional sign bit (IPL DEPTH SIGN). The supported depths are: IPL DEPTH 8U Unsigned 8-bit integer IPL DEPTH 8S Signed 8-bit integer IPL DEPTH 16U Unsigned 16-bit integer IPL DEPTH 16S Signed 16-bit integer IPL DEPTH 32S Signed 32-bit integer IPL DEPTH 32F Single-precision floating point IPL DEPTH 64F Double-precision floating point colorModel Ignored by OpenCV. The OpenCV function CvtColor requires the source and des- tination color spaces as parameters. channelSeq Ignored by OpenCV 1.1. BASIC STRUCTURES 55 dataOrder 0 = IPL DATA ORDER PIXEL - interleaved color channels, 1 - separate color chan- nels. CreateImage only creates images with interleaved channels. For example, the usual layout of a color image is: b00g00r00b10g10r10... origin 0 - top-left origin, 1 - bottom-left origin (Windows bitmap style) align Alignment of image rows (4 or 8). OpenCV ignores this and uses widthStep instead. width Image width in pixels height Image height in pixels roi Region Of Interest (ROI). If not NULL, only this image region will be processed. maskROI Must be NULL in OpenCV imageId Must be NULL in OpenCV tileInfo Must be NULL in OpenCV imageSize Image data size in bytes. For interleaved data, this equals image->height·image->widthStep imageData A pointer to the aligned image data widthStep The size of an aligned image row, in bytes BorderMode Border completion mode, ignored by OpenCV BorderConst Border completion mode, ignored by OpenCV imageDataOrigin A pointer to the origin of the image data (not necessarily aligned). This is used for image deallocation. The IplImage structure was inherited from the Intel Image Processing Library, in which the format is native. OpenCV only supports a subset of possible IplImage formats, as outlined in the parameter list above. In addition to the above restrictions, OpenCV handles ROIs differently. OpenCV functions require that the image size or ROI size of all source and destination images match exactly. On the other hand, the Intel Image Processing Library processes the area of intersection between the source and destination images (or ROIs), allowing them to vary independently. 56 CHAPTER 1. CORE. THE CORE FUNCTIONALITY CvArr (view/add comments) Arbitrary array typedef void CvArr; The metatype CvArr is used only as a function parameter to specify that the function accepts arrays of multiple types, such as IplImage*, CvMat* or even CvSeq* sometimes. The particular array type is determined at runtime by analyzing the first 4 bytes of the header. 1.2 Operations on Arrays cvAbsDiff (view/add comments) Calculates absolute difference between two arrays. void cvAbsDiff(const CvArr* src1, const CvArr* src2, CvArr* dst); src1 The first source array src2 The second source array dst The destination array The function calculates absolute difference between two arrays. dst(i)c = |src1(I)c − src2(I)c| All the arrays must have the same data type and the same size (or ROI size). cvAbsDiffS (view/add comments) Calculates absolute difference between an array and a scalar. void cvAbsDiffS(const CvArr* src, CvArr* dst, CvScalar value); 1.2. OPERATIONS ON ARRAYS 57 #define cvAbs(src, dst) cvAbsDiffS(src, dst, cvScalarAll(0)) src The source array dst The destination array value The scalar The function calculates absolute difference between an array and a scalar. dst(i)c = |src(I)c − valuec| All the arrays must have the same data type and the same size (or ROI size). cvAdd (view/add comments) Computes the per-element sum of two arrays. void cvAdd(const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL); src1 The first source array src2 The second source array dst The destination array mask Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed The function adds one array to another: dst(I)=src1(I)+src2(I) if mask(I)!=0 All the arrays must have the same type, except the mask, and the same size (or ROI size). For types that have limited range this operation is saturating. cvAddS (view/add comments) Computes the sum of an array and a scalar. 58 CHAPTER 1. CORE. THE CORE FUNCTIONALITY void cvAddS(const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL); src The source array value Added scalar dst The destination array mask Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed The function adds a scalar value to every element in the source array src1 and stores the result in dst. For types that have limited range this operation is saturating. dst(I)=src(I)+value if mask(I)!=0 All the arrays must have the same type, except the mask, and the same size (or ROI size). cvAddWeighted (view/add comments) Computes the weighted sum of two arrays. void cvAddWeighted(const CvArr* src1, double alpha, const CvArr* src2, double beta, double gamma, CvArr* dst); src1 The first source array alpha Weight for the first array elements src2 The second source array beta Weight for the second array elements dst The destination array gamma Scalar, added to each sum 1.2. OPERATIONS ON ARRAYS 59 The function calculates the weighted sum of two arrays as follows: dst(I)=src1(I)*alpha+src2(I)*beta+gamma All the arrays must have the same type and the same size (or ROI size). For types that have limited range this operation is saturating. cvAnd (view/add comments) Calculates per-element bit-wise conjunction of two arrays. void cvAnd(const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL); src1 The first source array src2 The second source array dst The destination array mask Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed The function calculates per-element bit-wise logical conjunction of two arrays: dst(I)=src1(I)&src2(I) if mask(I)!=0 In the case of floating-point arrays their bit representations are used for the operation. All the arrays must have the same type, except the mask, and the same size. cvAndS (view/add comments) Calculates per-element bit-wise conjunction of an array and a scalar. void cvAndS(const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL); src The source array 60 CHAPTER 1. CORE. THE CORE FUNCTIONALITY value Scalar to use in the operation dst The destination array mask Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed The function calculates per-element bit-wise conjunction of an array and a scalar: dst(I)=src(I)&value if mask(I)!=0 Prior to the actual operation, the scalar is converted to the same type as that of the array(s). In the case of floating-point arrays their bit representations are used for the operation. All the arrays must have the same type, except the mask, and the same size. The following sample demonstrates how to calculate the absolute value of floating-point array elements by clearing the most-significant bit: float a[] = { -1, 2, -3, 4, -5, 6, -7, 8, -9 }; CvMat A = cvMat(3, 3, CV\_32F, &a); int i, absMask = 0x7fffffff; cvAndS(&A, cvRealScalar(*(float*)&absMask), &A, 0); for(i = 0; i < 9; i++ ) printf("%.1f ", a[i]); The code should print: 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 cvAvg (view/add comments) Calculates average (mean) of array elements. CvScalar cvAvg(const CvArr* arr, const CvArr* mask=NULL); arr The array mask The optional operation mask The function calculates the average value M of array elements, independently for each channel: N = P I(mask(I) 6= 0) Mc = P I, mask(I)6=0 arr(I)c N If the array is IplImage and COI is set, the function processes the selected channel only and stores the average to the first scalar component S0 . 1.2. OPERATIONS ON ARRAYS 61 cvAvgSdv (view/add comments) Calculates average (mean) of array elements. void cvAvgSdv(const CvArr* arr, CvScalar* mean, CvScalar* stdDev, const CvArr* mask=NULL); arr The array mean Pointer to the output mean value, may be NULL if it is not needed stdDev Pointer to the output standard deviation mask The optional operation mask The function calculates the average value and standard deviation of array elements, indepen- dently for each channel: N = P I(mask(I) 6= 0) meanc = 1 N P I, mask(I)6=0 arr(I)c stdDevc = q 1 N P I, mask(I)6=0(arr(I)c − meanc)2 If the array is IplImage and COI is set, the function processes the selected channel only and stores the average and standard deviation to the first components of the output scalars (mean0 and stdDev0). cvCalcCovarMatrix (view/add comments) Calculates covariance matrix of a set of vectors. void cvCalcCovarMatrix( const CvArr** vects, int count, CvArr* covMat, CvArr* avg, int flags); 62 CHAPTER 1. CORE. THE CORE FUNCTIONALITY vects The input vectors, all of which must have the same type and the same size. The vectors do not have to be 1D, they can be 2D (e.g., images) and so forth count The number of input vectors covMat The output covariance matrix that should be floating-point and square avg The input or output (depending on the flags) array - the mean (average) vector of the input vectors flags The operation flags, a combination of the following values CV COVAR SCRAMBLED The output covariance matrix is calculated as: scale ∗ [vects[0] − avg, vects[1] − avg, ...]T·[vects[0] − avg, vects[1] − avg, ...] , that is, the covariance matrix is count × count. Such an unusual covariance matrix is used for fast PCA of a set of very large vectors (see, for example, the EigenFaces technique for face recognition). Eigenvalues of this ”scrambled” matrix will match the eigenvalues of the true covariance matrix and the ”true” eigenvectors can be easily calculated from the eigenvectors of the ”scrambled” covariance matrix. CV COVAR NORMAL The output covariance matrix is calculated as: scale ∗ [vects[0] − avg, vects[1] − avg, ...]·[vects[0] − avg, vects[1] − avg, ...]T , that is, covMat will be a covariance matrix with the same linear size as the total number of elements in each input vector. One and only one of CV COVAR SCRAMBLED and CV COVAR NORMAL must be specified CV COVAR USE AVG If the flag is specified, the function does not calculate avg from the input vectors, but, instead, uses the passed avg vector. This is useful if avg has been already calculated somehow, or if the covariance matrix is calculated by parts - in this case, avg is not a mean vector of the input sub-set of vectors, but rather the mean vector of the whole set. CV COVAR SCALE If the flag is specified, the covariance matrix is scaled. In the ”normal” mode scale is ’1./count’; in the ”scrambled” mode scale is the reciprocal of the total number of elements in each input vector. By default (if the flag is not specified) the covariance matrix is not scaled (’scale=1’). CV COVAR ROWS Means that all the input vectors are stored as rows of a single matrix, vects[0]. count is ignored in this case, and avg should be a single-row vector of an appropriate size. 1.2. OPERATIONS ON ARRAYS 63 CV COVAR COLS Means that all the input vectors are stored as columns of a single matrix, vects[0]. count is ignored in this case, and avg should be a single-column vector of an appropriate size. The function calculates the covariance matrix and, optionally, the mean vector of the set of input vectors. The function can be used for PCA, for comparing vectors using Mahalanobis distance and so forth. cvCartToPolar (view/add comments) Calculates the magnitude and/or angle of 2d vectors. void cvCartToPolar( const CvArr* x, const CvArr* y, CvArr* magnitude, CvArr* angle=NULL, int angleInDegrees=0); x The array of x-coordinates y The array of y-coordinates magnitude The destination array of magnitudes, may be set to NULL if it is not needed angle The destination array of angles, may be set to NULL if it is not needed. The angles are measured in radians (0 to 2π) or in degrees (0 to 360 degrees). angleInDegrees The flag indicating whether the angles are measured in radians, which is de- fault mode, or in degrees The function calculates either the magnitude, angle, or both of every 2d vector (x(I),y(I)): magnitude(I)=sqrt(x(I)ˆ2ˆ+y(I)ˆ2ˆ ), angle(I)=atan(y(I)/x(I) ) The angles are calculated with 0.1 degree accuracy. For the (0,0) point, the angle is set to 0. 64 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvCbrt (view/add comments) Calculates the cubic root float cvCbrt(float value); value The input floating-point value The function calculates the cubic root of the argument, and normally it is faster than pow(value,1./3). In addition, negative arguments are handled properly. Special values (±∞, NaN) are not handled. cvClearND (view/add comments) Clears a specific array element. void cvClearND(CvArr* arr, int* idx); arr Input array idx Array of the element indices The function cvClearND clears (sets to zero) a specific element of a dense array or deletes the element of a sparse array. If the sparse array element does not exists, the function does nothing. cvCloneImage (view/add comments) Makes a full copy of an image, including the header, data, and ROI. IplImage* cvCloneImage(const IplImage* image); image The original image The returned IplImage* points to the image copy. 1.2. OPERATIONS ON ARRAYS 65 cvCloneMat (view/add comments) Creates a full matrix copy. CvMat* cvCloneMat(const CvMat* mat); mat Matrix to be copied Creates a full copy of a matrix and returns a pointer to the copy. cvCloneMatND (view/add comments) Creates full copy of a multi-dimensional array and returns a pointer to the copy. CvMatND* cvCloneMatND(const CvMatND* mat); mat Input array cvCloneSparseMat (view/add comments) Creates full copy of sparse array. CvSparseMat* cvCloneSparseMat(const CvSparseMat* mat); mat Input array The function creates a copy of the input array and returns pointer to the copy. cvCmp (view/add comments) Performs per-element comparison of two arrays. 66 CHAPTER 1. CORE. THE CORE FUNCTIONALITY void cvCmp(const CvArr* src1, const CvArr* src2, CvArr* dst, int cmpOp); src1 The first source array src2 The second source array. Both source arrays must have a single channel. dst The destination array, must have 8u or 8s type cmpOp The flag specifying the relation between the elements to be checked CV CMP EQ src1(I) ”equal to” value CV CMP GT src1(I) ”greater than” value CV CMP GE src1(I) ”greater or equal” value CV CMP LT src1(I) ”less than” value CV CMP LE src1(I) ”less or equal” value CV CMP NE src1(I) ”not equal” value The function compares the corresponding elements of two arrays and fills the destination mask array: dst(I)=src1(I) op src2(I), dst(I) is set to 0xff (all 1-bits) if the specific relation between the elements is true and 0 otherwise. All the arrays must have the same type, except the destination, and the same size (or ROI size) cvCmpS (view/add comments) Performs per-element comparison of an array and a scalar. void cvCmpS(const CvArr* src, double value, CvArr* dst, int cmpOp); src The source array, must have a single channel value The scalar value to compare each array element with 1.2. OPERATIONS ON ARRAYS 67 dst The destination array, must have 8u or 8s type cmpOp The flag specifying the relation between the elements to be checked CV CMP EQ src1(I) ”equal to” value CV CMP GT src1(I) ”greater than” value CV CMP GE src1(I) ”greater or equal” value CV CMP LT src1(I) ”less than” value CV CMP LE src1(I) ”less or equal” value CV CMP NE src1(I) ”not equal” value The function compares the corresponding elements of an array and a scalar and fills the des- tination mask array: dst(I)=src(I) op scalar where op is =, >, ≥, <, ≤ or 6=. dst(I) is set to 0xff (all 1-bits) if the specific relation between the elements is true and 0 otherwise. All the arrays must have the same size (or ROI size). cvConvertScale (view/add comments) Converts one array to another with optional linear transformation. void cvConvertScale(const CvArr* src, CvArr* dst, double scale=1, double shift=0); #define cvCvtScale cvConvertScale #define cvScale cvConvertScale #define cvConvert(src, dst ) cvConvertScale((src), (dst), 1, 0 ) src Source array dst Destination array scale Scale factor shift Value added to the scaled source array elements 68 CHAPTER 1. CORE. THE CORE FUNCTIONALITY The function has several different purposes, and thus has several different names. It copies one array to another with optional scaling, which is performed first, and/or optional type conversion, performed after: dst(I) = scalesrc(I) + (shift0, shift1, ...) All the channels of multi-channel arrays are processed independently. The type of conversion is done with rounding and saturation, that is if the result of scaling + conversion can not be represented exactly by a value of the destination array element type, it is set to the nearest representable value on the real axis. In the case of scale=1, shift=0 no prescaling is done. This is a specially optimized case and it has the appropriate cvConvert name. If source and destination array types have equal types, this is also a special case that can be used to scale and shift a matrix or an image and that is caled cvScale. cvConvertScaleAbs (view/add comments) Converts input array elements to another 8-bit unsigned integer with optional linear transformation. void cvConvertScaleAbs(const CvArr* src, CvArr* dst, double scale=1, double shift=0); src Source array dst Destination array (should have 8u depth) scale ScaleAbs factor shift Value added to the scaled source array elements The function is similar to cvConvertScale, but it stores absolute values of the conversion results: dst(I) = |scalesrc(I) + (shift0, shift1, ...)| The function supports only destination arrays of 8u (8-bit unsigned integers) type; for other types the function can be emulated by a combination of cvConvertScale and cvAbs functions. 1.2. OPERATIONS ON ARRAYS 69 cvCvtScaleAbs (view/add comments) Converts input array elements to another 8-bit unsigned integer with optional linear transformation. void cvCvtScaleAbs(const CvArr* src, CvArr* dst, double scale=1, double shift=0); src Source array dst Destination array (should have 8u depth) scale ScaleAbs factor shift Value added to the scaled source array elements The function is similar to cvConvertScale, but it stores absolute values of the conversion results: dst(I) = |scalesrc(I) + (shift0, shift1, ...)| The function supports only destination arrays of 8u (8-bit unsigned integers) type; for other types the function can be emulated by a combination of cvConvertScale and cvAbs functions. cvCopy (view/add comments) Copies one array to another. void cvCopy(const CvArr* src, CvArr* dst, const CvArr* mask=NULL); src The source array dst The destination array mask Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed 70 CHAPTER 1. CORE. THE CORE FUNCTIONALITY The function copies selected elements from an input array to an output array: dst(I) = src(I) if mask(I) 6= 0. If any of the passed arrays is of IplImage type, then its ROI and COI fields are used. Both arrays must have the same type, the same number of dimensions, and the same size. The function can also copy sparse arrays (mask is not supported in this case). cvCountNonZero (view/add comments) Counts non-zero array elements. int cvCountNonZero(const CvArr* arr); arr The array must be a single-channel array or a multi-channel image with COI set The function returns the number of non-zero elements in arr: X I (arr(I) 6= 0) In the case of IplImage both ROI and COI are supported. cvCreateData (view/add comments) Allocates array data void cvCreateData(CvArr* arr); arr Array header The function allocates image, matrix or multi-dimensional array data. Note that in the case of matrix types OpenCV allocation functions are used and in the case of IplImage they are used unless CV TURN ON IPL COMPATIBILITY was called. In the latter case IPL functions are used to allocate the data. 1.2. OPERATIONS ON ARRAYS 71 cvCreateImage (view/add comments) Creates an image header and allocates the image data. IplImage* cvCreateImage(CvSize size, int depth, int channels); size Image width and height depth Bit depth of image elements. See IplImage for valid depths. channels Number of channels per pixel. See IplImage for details. This function only creates images with interleaved channels. This call is a shortened form of header = cvCreateImageHeader(size, depth, channels); cvCreateData(header); cvCreateImageHeader (view/add comments) Creates an image header but does not allocate the image data. IplImage* cvCreateImageHeader(CvSize size, int depth, int channels); size Image width and height depth Image depth (see cvCreateImage) channels Number of channels (see cvCreateImage) This call is an analogue of hdr=iplCreateImageHeader(channels, 0, depth, channels == 1 ? "GRAY" : "RGB", channels == 1 ? "GRAY" : channels == 3 ? "BGR" : channels == 4 ? "BGRA" : "", IPL_DATA_ORDER_PIXEL, IPL_ORIGIN_TL, 4, size.width, size.height, 0,0,0,0); but it does not use IPL functions by default (see the CV TURN ON IPL COMPATIBILITY macro). 72 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvCreateMat (view/add comments) Creates a matrix header and allocates the matrix data. CvMat* cvCreateMat( int rows, int cols, int type); rows Number of rows in the matrix cols Number of columns in the matrix type The type of the matrix elements in the form CV C, where S=signed, U=unsigned, F=float. For example, CV 8UC1 means the elements are 8-bit unsigned and the there is 1 channel, and CV 32SC2 means the elements are 32-bit signed and there are 2 channels. This is the concise form for: CvMat* mat = cvCreateMatHeader(rows, cols, type); cvCreateData(mat); cvCreateMatHeader (view/add comments) Creates a matrix header but does not allocate the matrix data. CvMat* cvCreateMatHeader( int rows, int cols, int type); rows Number of rows in the matrix cols Number of columns in the matrix 1.2. OPERATIONS ON ARRAYS 73 type Type of the matrix elements, see cvCreateMat The function allocates a new matrix header and returns a pointer to it. The matrix data can then be allocated using cvCreateData or set explicitly to user-allocated data via cvSetData. cvCreateMatND (view/add comments) Creates the header and allocates the data for a multi-dimensional dense array. CvMatND* cvCreateMatND( int dims, const int* sizes, int type); dims Number of array dimensions. This must not exceed CV MAX DIM (32 by default, but can be changed at build time). sizes Array of dimension sizes. type Type of array elements, see cvCreateMat. This is a short form for: CvMatND* mat = cvCreateMatNDHeader(dims, sizes, type); cvCreateData(mat); cvCreateMatNDHeader (view/add comments) Creates a new matrix header but does not allocate the matrix data. CvMatND* cvCreateMatNDHeader( int dims, const int* sizes, int type); dims Number of array dimensions 74 CHAPTER 1. CORE. THE CORE FUNCTIONALITY sizes Array of dimension sizes type Type of array elements, see cvCreateMat The function allocates a header for a multi-dimensional dense array. The array data can further be allocated using cvCreateData or set explicitly to user-allocated data via cvSetData. cvCreateSparseMat (view/add comments) Creates sparse array. CvSparseMat* cvCreateSparseMat(int dims, const int* sizes, int type); dims Number of array dimensions. In contrast to the dense matrix, the number of dimensions is practically unlimited (up to 216). sizes Array of dimension sizes type Type of array elements. The same as for CvMat The function allocates a multi-dimensional sparse array. Initially the array contain no elements, that is cvGet or cvGetReal returns zero for every index. cvCrossProduct (view/add comments) Calculates the cross product of two 3D vectors. void cvCrossProduct(const CvArr* src1, const CvArr* src2, CvArr* dst); src1 The first source vector src2 The second source vector dst The destination vector 1.2. OPERATIONS ON ARRAYS 75 The function calculates the cross product of two 3D vectors: dst = src1 × src2 or: dst1 = src12src23 − src13src22 dst2 = src13src21 − src11src23 dst3 = src11src22 − src12src21 CvtPixToPlane Synonym for Split. cvDCT (view/add comments) Performs a forward or inverse Discrete Cosine transform of a 1D or 2D floating-point array. void cvDCT(const CvArr* src, CvArr* dst, int flags); src Source array, real 1D or 2D array dst Destination array of the same size and same type as the source flags Transformation flags, a combination of the following values CV DXT FORWARD do a forward 1D or 2D transform. CV DXT INVERSE do an inverse 1D or 2D transform. CV DXT ROWS do a forward or inverse transform of every individual row of the input matrix. This flag allows user to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself), to do 3D and higher-dimensional transforms and so forth. The function performs a forward or inverse transform of a 1D or 2D floating-point array: Forward Cosine transform of 1D vector of N elements: Y = C(N)·X where C(N) jk = qαj/N cos π(2k + 1)j 2N  76 CHAPTER 1. CORE. THE CORE FUNCTIONALITY and α0 = 1, αj = 2 for j > 0. Inverse Cosine transform of 1D vector of N elements: X = C(N)−1 ·Y = C(N)T ·Y (since C(N) is orthogonal matrix, C(N)· C(N)T = I) Forward Cosine transform of 2D M × N matrix: Y = C(N)·X· C(N)T Inverse Cosine transform of 2D vector of M × N elements: X = C(N)T ·X·C(N) cvDFT (view/add comments) Performs a forward or inverse Discrete Fourier transform of a 1D or 2D floating-point array. void cvDFT(const CvArr* src, CvArr* dst, int flags, int nonzeroRows=0); src Source array, real or complex dst Destination array of the same size and same type as the source flags Transformation flags, a combination of the following values CV DXT FORWARD do a forward 1D or 2D transform. The result is not scaled. CV DXT INVERSE do an inverse 1D or 2D transform. The result is not scaled. CV DXT FORWARD and CV DXT INVERSE are mutually exclusive, of course. CV DXT SCALE scale the result: divide it by the number of array elements. Usually, it is combined with CV DXT INVERSE, and one may use a shortcut CV DXT INV SCALE. CV DXT ROWS do a forward or inverse transform of every individual row of the input matrix. This flag allows the user to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself), to do 3D and higher-dimensional transforms and so forth. CV DXT INVERSE SCALE same as CV DXT INVERSE + CV DXT SCALE 1.2. OPERATIONS ON ARRAYS 77 nonzeroRows Number of nonzero rows in the source array (in the case of a forward 2d trans- form), or a number of rows of interest in the destination array (in the case of an inverse 2d transform). If the value is negative, zero, or greater than the total number of rows, it is ig- nored. The parameter can be used to speed up 2d convolution/correlation when computing via DFT. See the example below. The function performs a forward or inverse transform of a 1D or 2D floating-point array: Forward Fourier transform of 1D vector of N elements: y = F(N)· x, whereF (N) jk = exp(−i · 2π · j · k/N) , i = sqrt(−1) Inverse Fourier transform of 1D vector of N elements: x0 = (F(N))−1 · y = conj(F(N)) · yx = (1/N)· x Forward Fourier transform of 2D vector of M × N elements: Y = F(M)·X·F(N) Inverse Fourier transform of 2D vector of M × N elements: X0 = conj(F(M))·Y· conj(F(N))X = (1/(M·N)) ·X0 In the case of real (single-channel) data, the packed format, borrowed from IPL, is used to represent the result of a forward Fourier transform or input for an inverse Fourier transform:   ReY0,0 ReY0,1 ImY0,1 ReY0,2 ImY0,2 ··· ReY0,N/2−1 ImY0,N/2−1 ReY0,N/2 ReY1,0 ReY1,1 ImY1,1 ReY1,2 ImY1,2 ··· ReY1,N/2−1 ImY1,N/2−1 ReY1,N/2 ImY1,0 ReY2,1 ImY2,1 ReY2,2 ImY2,2 ··· ReY2,N/2−1 ImY2,N/2−1 ImY1,N/2 .......................................................................................................... ReYM/2−1,0 ReYM−3,1 ImYM−3,1 .................... ReYM−3,N/2−1 ImYM−3,N/2−1 ReYM/2−1,N/2 ImYM/2−1,0 ReYM−2,1 ImYM−2,1 .................... ReYM−2,N/2−1 ImYM−2,N/2−1 ImYM/2−1,N/2 ReYM/2,0 ReYM−1,1 ImYM−1,1 .................... ReYM−1,N/2−1 ImYM−1,N/2−1 ReYM/2,N/2   Note: the last column is present if N is even, the last row is present if M is even. In the case of 1D real transform the result looks like the first row of the above matrix. Here is the example of how to compute 2D convolution using DFT. 78 CHAPTER 1. CORE. THE CORE FUNCTIONALITY CvMat* A = cvCreateMat(M1, N1, CVg32F); CvMat* B = cvCreateMat(M2, N2, A->type); // it is also possible to have only abs(M2-M1)+1 times abs(N2-N1)+1 // part of the full convolution result CvMat* conv = cvCreateMat(A->rows + B->rows - 1, A->cols + B->cols - 1, A->type); // initialize A and B ... int dftgM = cvGetOptimalDFTSize(A->rows + B->rows - 1); int dftgN = cvGetOptimalDFTSize(A->cols + B->cols - 1); CvMat* dftgA = cvCreateMat(dft\_M, dft\_N, A->type); CvMat* dftgB = cvCreateMat(dft\_M, dft\_N, B->type); CvMat tmp; // copy A to dftgA and pad dft\_A with zeros cvGetSubRect(dftgA, &tmp, cvRect(0,0,A->cols,A->rows)); cvCopy(A, &tmp); cvGetSubRect(dftgA, &tmp, cvRect(A->cols,0,dft\_A->cols - A->cols,A->rows)); cvZero(&tmp); // no need to pad bottom part of dftgA with zeros because of // use nonzerogrows parameter in cvDFT() call below cvDFT(dftgA, dft\_A, CV\_DXT\_FORWARD, A->rows); // repeat the same with the second array cvGetSubRect(dftgB, &tmp, cvRect(0,0,B->cols,B->rows)); cvCopy(B, &tmp); cvGetSubRect(dftgB, &tmp, cvRect(B->cols,0,dft\_B->cols - B->cols,B->rows)); cvZero(&tmp); // no need to pad bottom part of dftgB with zeros because of // use nonzerogrows parameter in cvDFT() call below cvDFT(dftgB, dft\_B, CV\_DXT\_FORWARD, B->rows); cvMulSpectrums(dftgA, dft\_B, dft\_A, 0 /* or CV\_DXT\_MUL\_CONJ to get correlation rather than convolution */); cvDFT(dftgA, dft\_A, CV\_DXT\_INV\_SCALE, conv->rows); // calculate only // the top part cvGetSubRect(dftgA, &tmp, cvRect(0,0,conv->cols,conv->rows)); 1.2. OPERATIONS ON ARRAYS 79 cvCopy(&tmp, conv); cvDecRefData (view/add comments) Decrements an array data reference counter. void cvDecRefData(CvArr* arr); arr Pointer to an array header The function decrements the data reference counter in a CvMat or CvMatND if the reference counter pointer is not NULL. If the counter reaches zero, the data is deallocated. In the current implementation the reference counter is not NULL only if the data was allocated using the cvCre- ateData function. The counter will be NULL in other cases such as: external data was assigned to the header using cvSetData, the matrix header is part of a larger matrix or image, or the header was converted from an image or n-dimensional matrix header. cvDet (view/add comments) Returns the determinant of a matrix. double cvDet(const CvArr* mat); mat The source matrix The function returns the determinant of the square matrix mat. The direct method is used for small matrices and Gaussian elimination is used for larger matrices. For symmetric positive- determined matrices, it is also possible to run cvSVD with U = V = 0 and then calculate the determinant as a product of the diagonal elements of W. cvDiv (view/add comments) Performs per-element division of two arrays. 80 CHAPTER 1. CORE. THE CORE FUNCTIONALITY void cvDiv(const CvArr* src1, const CvArr* src2, CvArr* dst, double scale=1); src1 The first source array. If the pointer is NULL, the array is assumed to be all 1’s. src2 The second source array dst The destination array scale Optional scale factor The function divides one array by another: dst(I) =  scale · src1(I)/src2(I) if src1 is not NULL scale/src2(I) otherwise All the arrays must have the same type and the same size (or ROI size). cvDotProduct (view/add comments) Calculates the dot product of two arrays in Euclidian metrics. double cvDotProduct(const CvArr* src1, const CvArr* src2); src1 The first source array src2 The second source array The function calculates and returns the Euclidean dot product of two arrays. src1 • src2 = X I (src1(I)src2(I)) In the case of multiple channel arrays, the results for all channels are accumulated. In par- ticular, cvDotProduct(a,a) where a is a complex vector, will return ||a||2. The function can process multi-dimensional arrays, row by row, layer by layer, and so on. 1.2. OPERATIONS ON ARRAYS 81 cvEigenVV (view/add comments) Computes eigenvalues and eigenvectors of a symmetric matrix. void cvEigenVV( CvArr* mat, CvArr* evects, CvArr* evals, double eps=0, int lowindex = -1, int highindex = -1); mat The input symmetric square matrix, modified during the processing evects The output matrix of eigenvectors, stored as subsequent rows evals The output vector of eigenvalues, stored in the descending order (order of eigenvalues and eigenvectors is syncronized, of course) eps Accuracy of diagonalization. Typically, DBL EPSILON (about 10−15) works well. THIS PA- RAMETER IS CURRENTLY IGNORED. lowindex Optional index of largest eigenvalue/-vector to calculate. (See below.) highindex Optional index of smallest eigenvalue/-vector to calculate. (See below.) The function computes the eigenvalues and eigenvectors of matrix A: mat*evects(i,:)’ = evals(i)*evects(i,:)’ (in MATLAB notation) If either low- or highindex is supplied the other is required, too. Indexing is 0-based. Example: To calculate the largest eigenvector/-value set lowindex=highindex=0. To calculate all the eigenvalues, leave lowindex=highindex=-1. For legacy reasons this function always returns a square matrix the same size as the source matrix with eigenvectors and a vector the length of the source matrix with eigenvalues. The selected eigenvectors/-values are always in the first highindex - lowindex + 1 rows. The contents of matrix A is destroyed by the function. Currently the function is slower than cvSVD yet less accurate, so if A is known to be positively- defined (for example, it is a covariance matrix)it is recommended to use cvSVD to find eigenvalues and eigenvectors of A, especially if eigenvectors are not required. 82 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvExp (view/add comments) Calculates the exponent of every array element. void cvExp(const CvArr* src, CvArr* dst); src The source array dst The destination array, it should have double type or the same type as the source The function calculates the exponent of every element of the input array: dst[I] = esrc(I) The maximum relative error is about 7 × 10−6. Currently, the function converts denormalized values to zeros on output. cvFastArctan (view/add comments) Calculates the angle of a 2D vector. float cvFastArctan(float y, float x); x x-coordinate of 2D vector y y-coordinate of 2D vector The function calculates the full-range angle of an input 2D vector. The angle is measured in degrees and varies from 0 degrees to 360 degrees. The accuracy is about 0.1 degrees. cvFlip (view/add comments) Flip a 2D array around vertical, horizontal or both axes. 1.2. OPERATIONS ON ARRAYS 83 void cvFlip(const CvArr* src, CvArr* dst=NULL, int flipMode=0); src Source array dst Destination array. If dst = NULL the flipping is done in place. flipMode Specifies how to flip the array: 0 means flipping around the x-axis, positive (e.g., 1) means flipping around y-axis, and negative (e.g., -1) means flipping around both axes. See also the discussion below for the formulas: The function flips the array in one of three different ways (row and column indices are 0-based): dst(i, j) =    src(rows(src) − i − 1, j) if flipMode = 0 src(i, cols(src) − j − 1) if flipMode > 0 src(rows(src) − i − 1, cols(src) − j − 1) if flipMode < 0 The example scenarios of function use are: • vertical flipping of the image (flipMode = 0) to switch between top-left and bottom-left image origin, which is a typical operation in video processing under Win32 systems. • horizontal flipping of the image with subsequent horizontal shift and absolute difference cal- culation to check for a vertical-axis symmetry (flipMode > 0) • simultaneous horizontal and vertical flipping of the image with subsequent shift and absolute difference calculation to check for a central symmetry (flipMode < 0) • reversing the order of 1d point arrays (flipMode ¿ 0) cvGEMM (view/add comments) Performs generalized matrix multiplication. void cvGEMM( const CvArr* src1, const CvArr* src2, double alpha, const CvArr* src3, double beta, 84 CHAPTER 1. CORE. THE CORE FUNCTIONALITY CvArr* dst, int tABC=0); #define cvMatMulAdd(src1, src2, src3, dst ) cvGEMM(src1, src2, 1, src3, 1, dst, 0 ) #define cvMatMul(src1, src2, dst ) cvMatMulAdd(src1, src2, 0, dst ) src1 The first source array src2 The second source array src3 The third source array (shift). Can be NULL, if there is no shift. dst The destination array tABC The operation flags that can be 0 or a combination of the following values CV GEMM AT transpose src1 CV GEMM BT transpose src2 CV GEMM CT transpose src3 For example, CV GEMM A T+CV GEMM CT corresponds to alpha src1T src2 + beta src3T The function performs generalized matrix multiplication: dst = alpha op(src1) op(src2) + beta op(src3) where op(X) is X or XT All the matrices should have the same data type and coordinated sizes. Real or complex floating-point matrices are supported. cvGet?D (view/add comments) Return a specific array element. CvScalar cvGet1D(const CvArr* arr, int idx0); CvScalar cvGet2D(const CvArr* arr, int idx0, int idx1); CvScalar cvGet3D(const CvArr* arr, int idx0, int idx1, int idx2); CvScalar cvGetND(const CvArr* arr, int* idx); 1.2. OPERATIONS ON ARRAYS 85 arr Input array idx0 The first zero-based component of the element index idx1 The second zero-based component of the element index idx2 The third zero-based component of the element index idx Array of the element indices The functions return a specific array element. In the case of a sparse array the functions return 0 if the requested node does not exist (no new node is created by the functions). cvGetCol(s) (view/add comments) Returns array column or column span. CvMat* cvGetCol(const CvArr* arr, CvMat* submat, int col); CvMat* cvGetCols(const CvArr* arr, CvMat* submat, int startCol, int endCol); arr Input array submat Pointer to the resulting sub-array header col Zero-based index of the selected column startCol Zero-based index of the starting column (inclusive) of the span endCol Zero-based index of the ending column (exclusive) of the span The functions GetCol and GetCols return the header, corresponding to a specified column span of the input array. GetCol is a shortcut for cvGetCols: cvGetCol(arr, submat, col); // ˜ cvGetCols(arr, submat, col, col + 1); 86 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvGetDiag (view/add comments) Returns one of array diagonals. CvMat* cvGetDiag(const CvArr* arr, CvMat* submat, int diag=0); arr Input array submat Pointer to the resulting sub-array header diag Array diagonal. Zero corresponds to the main diagonal, -1 corresponds to the diagonal above the main , 1 corresponds to the diagonal below the main, and so forth. The function returns the header, corresponding to a specified diagonal of the input array. cvGetDims, cvGetDimSize Return number of array dimensions and their sizes or the size of a particular dimension. int cvGetDims(const CvArr* arr, int* sizes=NULL); int cvGetDimSize(const CvArr* arr, int index); arr Input array sizes Optional output vector of the array dimension sizes. For 2d arrays the number of rows (height) goes first, number of columns (width) next. index Zero-based dimension index (for matrices 0 means number of rows, 1 means number of columns; for images 0 means height, 1 means width) 1.2. OPERATIONS ON ARRAYS 87 The function cvGetDims returns the array dimensionality and the array of dimension sizes. In the case of IplImage or CvMat it always returns 2 regardless of number of image/matrix rows. The function cvGetDimSize returns the particular dimension size (number of elements per that dimension). For example, the following code calculates total number of array elements in two ways: // via cvGetDims() int sizes[CV_MAX_DIM]; int i, total = 1; int dims = cvGetDims(arr, size); for(i = 0; i < dims; i++ ) total *= sizes[i]; // via cvGetDims() and cvGetDimSize() int i, total = 1; int dims = cvGetDims(arr); for(i = 0; i < dims; i++ ) total *= cvGetDimsSize(arr, i); cvGetElemType (view/add comments) Returns type of array elements. int cvGetElemType(const CvArr* arr); arr Input array The function returns type of the array elements as described in cvCreateMat discussion: CV 8UC1 ... CV 64FC4. cvGetImage (view/add comments) Returns image header for arbitrary array. IplImage* cvGetImage(const CvArr* arr, IplImage* imageHeader); 88 CHAPTER 1. CORE. THE CORE FUNCTIONALITY arr Input array imageHeader Pointer to IplImage structure used as a temporary buffer The function returns the image header for the input array that can be a matrix - CvMat , or an image - IplImage*. In the case of an image the function simply returns the input pointer. In the case of CvMat it initializes an imageHeader structure with the parameters of the input matrix. Note that if we transform IplImage to CvMat and then transform CvMat back to IplImage, we can get different headers if the ROI is set, and thus some IPL functions that calculate image stride from its width and align may fail on the resultant image. cvGetImageCOI (view/add comments) Returns the index of the channel of interest. int cvGetImageCOI(const IplImage* image); image A pointer to the image header Returns the channel of interest of in an IplImage. Returned values correspond to the coi in cvSetImageCOI. cvGetImageROI (view/add comments) Returns the image ROI. CvRect cvGetImageROI(const IplImage* image); image A pointer to the image header If there is no ROI set, cvRect(0,0,image->width,image->height) is returned. 1.2. OPERATIONS ON ARRAYS 89 cvGetMat (view/add comments) Returns matrix header for arbitrary array. CvMat* cvGetMat(const CvArr* arr, CvMat* header, int* coi=NULL, int allowND=0); arr Input array header Pointer to CvMat structure used as a temporary buffer coi Optional output parameter for storing COI allowND If non-zero, the function accepts multi-dimensional dense arrays (CvMatND*) and re- turns 2D (if CvMatND has two dimensions) or 1D matrix (when CvMatND has 1 dimension or more than 2 dimensions). The array must be continuous. The function returns a matrix header for the input array that can be a matrix - CvMat , an image - IplImage or a multi-dimensional dense array - CvMatND (latter case is allowed only if allowND != 0) . In the case of matrix the function simply returns the input pointer. In the case of IplImage* or CvMatND it initializes the header structure with parameters of the current image ROI and returns the pointer to this temporary structure. Because COI is not supported by CvMat , it is returned separately. The function provides an easy way to handle both types of arrays - IplImage and CvMat - using the same code. Reverse transform from CvMat to IplImage can be done using the cvGetImage function. Input array must have underlying data allocated or attached, otherwise the function fails. If the input array is IplImage with planar data layout and COI set, the function returns the pointer to the selected plane and COI = 0. It enables per-plane processing of multi-channel images with planar data layout using OpenCV functions. cvGetNextSparseNode (view/add comments) Returns the next sparse matrix element CvSparseNode* cvGetNextSparseNode(CvSparseMatIterator* matIterator); 90 CHAPTER 1. CORE. THE CORE FUNCTIONALITY matIterator Sparse array iterator The function moves iterator to the next sparse matrix element and returns pointer to it. In the current version there is no any particular order of the elements, because they are stored in the hash table. The sample below demonstrates how to iterate through the sparse matrix: Using cvInitSparseMatIterator and cvGetNextSparseNode to calculate sum of floating-point sparse array. double sum; int i, dims = cvGetDims(array); CvSparseMatIterator mat_iterator; CvSparseNode* node = cvInitSparseMatIterator(array, &mat_iterator); for(; node != 0; node = cvGetNextSparseNode(&mat_iterator )) { /* get pointer to the element indices */ int* idx = CV_NODE_IDX(array, node); /* get value of the element (assume that the type is CV_32FC1) */ float val = *(float*)CV_NODE_VAL(array, node); printf("("); for(i = 0; i < dims; i++ ) printf("%4d%s", idx[i], i < dims - 1 "," : "): "); printf("%g\n", val); sum += val; } printf("\nTotal sum = %g\n", sum); cvGetOptimalDFTSize (view/add comments) Returns optimal DFT size for a given vector size. int cvGetOptimalDFTSize(int size0); size0 Vector size The function returns the minimum number N that is greater than or equal to size0, such that the DFT of a vector of size N can be computed fast. In the current implementation N = 2p ×3q ×5r, for some p, q, r. The function returns a negative number if size0 is too large (very close to INT MAX) 1.2. OPERATIONS ON ARRAYS 91 cvGetRawData (view/add comments) Retrieves low-level information about the array. void cvGetRawData(const CvArr* arr, uchar** data, int* step=NULL, CvSize* roiSize=NULL); arr Array header data Output pointer to the whole image origin or ROI origin if ROI is set step Output full row length in bytes roiSize Output ROI size The function fills output variables with low-level information about the array data. All output parameters are optional, so some of the pointers may be set to NULL. If the array is IplImage with ROI set, the parameters of ROI are returned. The following example shows how to get access to array elements. GetRawData calculates the absolute value of the elements in a single-channel, floating-point array. float* data; int step; CvSize size; int x, y; cvGetRawData(array, (uchar**)&data, &step, &size); step /= sizeof(data[0]); for(y = 0; y < size.height; y++, data += step ) for(x = 0; x < size.width; x++ ) data[x] = (float)fabs(data[x]); cvGetReal1D (view/add comments) Return a specific element of single-channel 1D array. 92 CHAPTER 1. CORE. THE CORE FUNCTIONALITY double cvGetReal1D(const CvArr* arr, int idx0); arr Input array. Must have a single channel. idx0 The first zero-based component of the element index Returns a specific element of a single-channel array. If the array has multiple channels, a runtime error is raised. Note that cvGet function can be used safely for both single-channel and multiple-channel arrays though they are a bit slower. In the case of a sparse array the functions return 0 if the requested node does not exist (no new node is created by the functions). cvGetReal2D (view/add comments) Return a specific element of single-channel 2D array. double cvGetReal2D(const CvArr* arr, int idx0, int idx1); arr Input array. Must have a single channel. idx0 The first zero-based component of the element index idx1 The second zero-based component of the element index Returns a specific element of a single-channel array. If the array has multiple channels, a runtime error is raised. Note that cvGet function can be used safely for both single-channel and multiple-channel arrays though they are a bit slower. In the case of a sparse array the functions return 0 if the requested node does not exist (no new node is created by the functions). cvGetReal3D (view/add comments) Return a specific element of single-channel array. 1.2. OPERATIONS ON ARRAYS 93 double cvGetReal3D(const CvArr* arr, int idx0, int idx1, int idx2); arr Input array. Must have a single channel. idx0 The first zero-based component of the element index idx1 The second zero-based component of the element index idx2 The third zero-based component of the element index Returns a specific element of a single-channel array. If the array has multiple channels, a runtime error is raised. Note that cvGet function can be used safely for both single-channel and multiple-channel arrays though they are a bit slower. In the case of a sparse array the functions return 0 if the requested node does not exist (no new node is created by the functions). cvGetRealND (view/add comments) Return a specific element of single-channel array. double cvGetRealND(const CvArr* arr, int* idx)->float; arr Input array. Must have a single channel. idx Array of the element indices Returns a specific element of a single-channel array. If the array has multiple channels, a runtime error is raised. Note that cvGet function can be used safely for both single-channel and multiple-channel arrays though they are a bit slower. In the case of a sparse array the functions return 0 if the requested node does not exist (no new node is created by the functions). 94 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvGetRow(s) (view/add comments) Returns array row or row span. CvMat* cvGetRow(const CvArr* arr, CvMat* submat, int row); CvMat* cvGetRows(const CvArr* arr, CvMat* submat, int startRow, int endRow, int deltaRow=1); arr Input array submat Pointer to the resulting sub-array header row Zero-based index of the selected row startRow Zero-based index of the starting row (inclusive) of the span endRow Zero-based index of the ending row (exclusive) of the span deltaRow Index step in the row span. That is, the function extracts every deltaRow-th row from startRow and up to (but not including) endRow. The functions return the header, corresponding to a specified row/row span of the input array. Note that GetRow is a shortcut for cvGetRows: cvGetRow(arr, submat, row ) ˜ cvGetRows(arr, submat, row, row + 1, 1); cvGetSize (view/add comments) Returns size of matrix or image ROI. CvSize cvGetSize(const CvArr* arr); arr array header The function returns number of rows (CvSize::height) and number of columns (CvSize::width) of the input matrix or image. In the case of image the size of ROI is returned. 1.2. OPERATIONS ON ARRAYS 95 cvGetSubRect (view/add comments) Returns matrix header corresponding to the rectangular sub-array of input image or matrix. CvMat* cvGetSubRect(const CvArr* arr, CvMat* submat, CvRect rect); arr Input array submat Pointer to the resultant sub-array header rect Zero-based coordinates of the rectangle of interest The function returns header, corresponding to a specified rectangle of the input array. In other words, it allows the user to treat a rectangular part of input array as a stand-alone array. ROI is taken into account by the function so the sub-array of ROI is actually extracted. cvInRange (view/add comments) Checks that array elements lie between the elements of two other arrays. void cvInRange(const CvArr* src, const CvArr* lower, const CvArr* upper, CvArr* dst); src The first source array lower The inclusive lower boundary array upper The exclusive upper boundary array dst The destination array, must have 8u or 8s type The function does the range check for every element of the input array: dst(I) = lower(I)0 <= src(I)0 < upper(I)0 For single-channel arrays, 96 CHAPTER 1. CORE. THE CORE FUNCTIONALITY dst(I) = lower(I)0 <= src(I)0 < upper(I)0 ∧ lower(I)1 <= src(I)1 < upper(I)1 For two-channel arrays and so forth, dst(I) is set to 0xff (all 1-bits) if src(I) is within the range and 0 otherwise. All the arrays must have the same type, except the destination, and the same size (or ROI size). cvInRangeS (view/add comments) Checks that array elements lie between two scalars. void cvInRangeS(const CvArr* src, CvScalar lower, CvScalar upper, CvArr* dst); src The first source array lower The inclusive lower boundary upper The exclusive upper boundary dst The destination array, must have 8u or 8s type The function does the range check for every element of the input array: dst(I) = lower0 <= src(I)0 < upper0 For single-channel arrays, dst(I) = lower0 <= src(I)0 < upper0 ∧ lower1 <= src(I)1 < upper1 For two-channel arrays nd so forth, ’dst(I)’ is set to 0xff (all 1-bits) if ’src(I)’ is within the range and 0 otherwise. All the arrays must have the same size (or ROI size). cvIncRefData (view/add comments) Increments array data reference counter. 1.2. OPERATIONS ON ARRAYS 97 int cvIncRefData(CvArr* arr); arr Array header The function increments CvMat or CvMatND data reference counter and returns the new counter value if the reference counter pointer is not NULL, otherwise it returns zero. cvInitImageHeader (view/add comments) Initializes an image header that was previously allocated. IplImage* cvInitImageHeader( IplImage* image, CvSize size, int depth, int channels, int origin=0, int align=4); image Image header to initialize size Image width and height depth Image depth (see cvCreateImage) channels Number of channels (see cvCreateImage) origin Top-left IPL ORIGIN TL or bottom-left IPL ORIGIN BL align Alignment for image rows, typically 4 or 8 bytes The returned IplImage* points to the initialized header. 98 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvInitMatHeader (view/add comments) Initializes a pre-allocated matrix header. CvMat* cvInitMatHeader( CvMat* mat, int rows, int cols, int type, void* data=NULL, int step=CV AUTOSTEP); mat A pointer to the matrix header to be initialized rows Number of rows in the matrix cols Number of columns in the matrix type Type of the matrix elements, see cvCreateMat. data Optional: data pointer assigned to the matrix header step Optional: full row width in bytes of the assigned data. By default, the minimal possible step is used which assumes there are no gaps between subsequent rows of the matrix. This function is often used to process raw data with OpenCV matrix functions. For example, the following code computes the matrix product of two matrices, stored as ordinary arrays: double a[] = { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 }; double b[] = { 1, 5, 9, 2, 6, 10, 3, 7, 11, 4, 8, 12 }; double c[9]; CvMat Ma, Mb, Mc ; cvInitMatHeader(&Ma, 3, 4, CV_64FC1, a); 1.2. OPERATIONS ON ARRAYS 99 cvInitMatHeader(&Mb, 4, 3, CV_64FC1, b); cvInitMatHeader(&Mc, 3, 3, CV_64FC1, c); cvMatMulAdd(&Ma, &Mb, 0, &Mc); // the c array now contains the product of a (3x4) and b (4x3) cvInitMatNDHeader (view/add comments) Initializes a pre-allocated multi-dimensional array header. CvMatND* cvInitMatNDHeader( CvMatND* mat, int dims, const int* sizes, int type, void* data=NULL); mat A pointer to the array header to be initialized dims The number of array dimensions sizes An array of dimension sizes type Type of array elements, see cvCreateMat data Optional data pointer assigned to the matrix header cvInitSparseMatIterator (view/add comments) Initializes sparse array elements iterator. CvSparseNode* cvInitSparseMatIterator(const CvSparseMat* mat, CvSparseMatIterator* matIterator); mat Input array 100 CHAPTER 1. CORE. THE CORE FUNCTIONALITY matIterator Initialized iterator The function initializes iterator of sparse array elements and returns pointer to the first element, or NULL if the array is empty. cvInvSqrt (view/add comments) Calculates the inverse square root. float cvInvSqrt(float value); value The input floating-point value The function calculates the inverse square root of the argument, and normally it is faster than 1./sqrt(value). If the argument is zero or negative, the result is not determined. Special values (±∞ , NaN) are not handled. cvInv (view/add comments) Synonym for Invert cvInvert (view/add comments) Finds the inverse or pseudo-inverse of a matrix. double cvInvert(const CvArr* src, CvArr* dst, int method=CV LU); src The source matrix dst The destination matrix method Inversion method CV LU Gaussian elimination with optimal pivot element chosen CV SVD Singular value decomposition (SVD) method 1.2. OPERATIONS ON ARRAYS 101 CV SVD SYM SVD method for a symmetric positively-defined matrix The function inverts matrix src1 and stores the result in src2. In the case of LU method, the function returns the src1 determinant (src1 must be square). If it is 0, the matrix is not inverted and src2 is filled with zeros. In the case of SVD methods, the function returns the inversed condition of src1 (ratio of the smallest singular value to the largest singular value) and 0 if src1 is all zeros. The SVD methods calculate a pseudo-inverse matrix if src1 is singular. cvIsInf (view/add comments) Determines if the argument is Infinity. int cvIsInf(double value); value The input floating-point value The function returns 1 if the argument is ±∞ (as defined by IEEE754 standard), 0 otherwise. cvIsNaN (view/add comments) Determines if the argument is Not A Number. int cvIsNaN(double value); value The input floating-point value The function returns 1 if the argument is Not A Number (as defined by IEEE754 standard), 0 otherwise. cvLUT (view/add comments) Performs a look-up table transform of an array. 102 CHAPTER 1. CORE. THE CORE FUNCTIONALITY void cvLUT(const CvArr* src, CvArr* dst, const CvArr* lut); src Source array of 8-bit elements dst Destination array of a given depth and of the same number of channels as the source array lut Look-up table of 256 elements; should have the same depth as the destination array. In the case of multi-channel source and destination arrays, the table should either have a single- channel (in this case the same table is used for all channels) or the same number of channels as the source/destination array. The function fills the destination array with values from the look-up table. Indices of the entries are taken from the source array. That is, the function processes each element of src as follows: dsti ← lutsrci+d where d =  0 if src has depth CV 8U 128 if src has depth CV 8S cvLog (view/add comments) Calculates the natural logarithm of every array element’s absolute value. void cvLog(const CvArr* src, CvArr* dst); src The source array dst The destination array, it should have double type or the same type as the source The function calculates the natural logarithm of the absolute value of every element of the input array: dst[I] =  log |src(I) if src[I] 6= 0 C otherwise Where C is a large negative number (about -700 in the current implementation). 1.2. OPERATIONS ON ARRAYS 103 cvMahalanobis (view/add comments) Calculates the Mahalanobis distance between two vectors. double cvMahalanobis( const CvArr* vec1, const CvArr* vec2, CvArr* mat); vec1 The first 1D source vector vec2 The second 1D source vector mat The inverse covariance matrix The function calculates and returns the weighted distance between two vectors: d(vec1, vec2) = sX i,j icovar(i,j) ·(vec1(I) − vec2(I)) ·(vec1(j) − vec2(j)) The covariance matrix may be calculated using the cvCalcCovarMatrix function and further inverted using the cvInvert function (CV SVD method is the prefered one because the matrix might be singular). cvMat (view/add comments) Initializes matrix header (lightweight variant). CvMat cvMat( int rows, int cols, int type, void* data=NULL); rows Number of rows in the matrix 104 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cols Number of columns in the matrix type Type of the matrix elements - see cvCreateMat data Optional data pointer assigned to the matrix header Initializes a matrix header and assigns data to it. The matrix is filled row-wise (the first cols elements of data form the first row of the matrix, etc.) This function is a fast inline substitution for cvInitMatHeader. Namely, it is equivalent to: CvMat mat; cvInitMatHeader(&mat, rows, cols, type, data, CV\_AUTOSTEP); cvMax (view/add comments) Finds per-element maximum of two arrays. void cvMax(const CvArr* src1, const CvArr* src2, CvArr* dst); src1 The first source array src2 The second source array dst The destination array The function calculates per-element maximum of two arrays: dst(I) = max(src1(I), src2(I)) All the arrays must have a single channel, the same data type and the same size (or ROI size). cvMaxS (view/add comments) Finds per-element maximum of array and scalar. void cvMaxS(const CvArr* src, double value, CvArr* dst); 1.2. OPERATIONS ON ARRAYS 105 src The first source array value The scalar value dst The destination array The function calculates per-element maximum of array and scalar: dst(I) = max(src(I), value) All the arrays must have a single channel, the same data type and the same size (or ROI size). cvMerge (view/add comments) Composes a multi-channel array from several single-channel arrays or inserts a single channel into the array. void cvMerge(const CvArr* src0, const CvArr* src1, const CvArr* src2, const CvArr* src3, CvArr* dst); #define cvCvtPlaneToPix cvMerge src0 Input channel 0 src1 Input channel 1 src2 Input channel 2 src3 Input channel 3 dst Destination array The function is the opposite to cvSplit. If the destination array has N channels then if the first N input channels are not NULL, they all are copied to the destination array; if only a single source channel of the first N is not NULL, this particular channel is copied into the destination array; otherwise an error is raised. The rest of the source channels (beyond the first N) must always be NULL. For IplImage cvCopy with COI set can be also used to insert a single channel into the image. 106 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvMin (view/add comments) Finds per-element minimum of two arrays. void cvMin(const CvArr* src1, const CvArr* src2, CvArr* dst); src1 The first source array src2 The second source array dst The destination array The function calculates per-element minimum of two arrays: dst(I) = min(src1(I), src2(I)) All the arrays must have a single channel, the same data type and the same size (or ROI size). cvMinMaxLoc (view/add comments) Finds global minimum and maximum in array or subarray. void cvMinMaxLoc(const CvArr* arr, double* minVal, double* maxVal, CvPoint* minLoc=NULL, CvPoint* maxLoc=NULL, const CvArr* mask=NULL); arr The source array, single-channel or multi-channel with COI set minVal Pointer to returned minimum value maxVal Pointer to returned maximum value minLoc Pointer to returned minimum location maxLoc Pointer to returned maximum location mask The optional mask used to select a subarray 1.2. OPERATIONS ON ARRAYS 107 The function finds minimum and maximum element values and their positions. The extremums are searched across the whole array, selected ROI (in the case of IplImage) or, if mask is not NULL, in the specified array region. If the array has more than one channel, it must be IplImage with COI set. In the case of multi-dimensional arrays, minLoc->x and maxLoc->x will contain raw (linear) positions of the extremums. cvMinS (view/add comments) Finds per-element minimum of an array and a scalar. void cvMinS(const CvArr* src, double value, CvArr* dst); src The first source array value The scalar value dst The destination array The function calculates minimum of an array and a scalar: dst(I) = min(src(I), value) All the arrays must have a single channel, the same data type and the same size (or ROI size). Mirror Synonym for Flip. cvMixChannels (view/add comments) Copies several channels from input arrays to certain channels of output arrays void cvMixChannels(const CvArr** src, int srcCount, CvArr** dst, int dstCount, const int* fromTo, int pairCount); 108 CHAPTER 1. CORE. THE CORE FUNCTIONALITY src Input arrays srcCount The number of input arrays. dst Destination arrays dstCount The number of output arrays. fromTo The array of pairs of indices of the planes copied. fromTo[k*2] is the 0-based in- dex of the input channel in src and fromTo[k*2+1] is the index of the output channel in dst. Here the continuous channel numbering is used, that is, the first input image channels are indexed from 0 to channels(src[0])-1, the second input image channels are in- dexed from channels(src[0]) to channels(src[0]) + channels(src[1])-1 etc., and the same scheme is used for the output image channels. As a special case, when fromTo[k*2] is negative, the corresponding output channel is filled with zero. The function is a generalized form of cvcvSplit and cvMerge and some forms of CvtColor. It can be used to change the order of the planes, add/remove alpha channel, extract or insert a single plane or multiple planes etc. As an example, this code splits a 4-channel RGBA image into a 3-channel BGR (i.e. with R and B swapped) and separate alpha channel image: CvMat* rgba = cvCreateMat(100, 100, CV_8UC4); CvMat* bgr = cvCreateMat(rgba->rows, rgba->cols, CV_8UC3); CvMat* alpha = cvCreateMat(rgba->rows, rgba->cols, CV_8UC1); cvSet(rgba, cvScalar(1,2,3,4)); CvArr* out[] = { bgr, alpha }; int from_to[] = { 0,2, 1,1, 2,0, 3,3 }; cvMixChannels(&bgra, 1, out, 2, from_to, 4); MulAddS Synonym for ScaleAdd. cvMul (view/add comments) Calculates the per-element product of two arrays. void cvMul(const CvArr* src1, const CvArr* src2, CvArr* dst, double scale=1); 1.2. OPERATIONS ON ARRAYS 109 src1 The first source array src2 The second source array dst The destination array scale Optional scale factor The function calculates the per-element product of two arrays: dst(I) = scale · src1(I)· src2(I) All the arrays must have the same type and the same size (or ROI size). For types that have limited range this operation is saturating. cvMulSpectrums (view/add comments) Performs per-element multiplication of two Fourier spectrums. void cvMulSpectrums( const CvArr* src1, const CvArr* src2, CvArr* dst, int flags); src1 The first source array src2 The second source array dst The destination array of the same type and the same size as the source arrays flags A combination of the following values; CV DXT ROWS treats each row of the arrays as a separate spectrum (see cvDFT parameters description). CV DXT MUL CONJ conjugate the second source array before the multiplication. The function performs per-element multiplication of the two CCS-packed or complex matrices that are results of a real or complex Fourier transform. The function, together with cvDFT, may be used to calculate convolution of two arrays rapidly. 110 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvMulTransposed (view/add comments) Calculates the product of an array and a transposed array. void cvMulTransposed(const CvArr* src, CvArr* dst, int order, const CvArr* delta=NULL, double scale=1.0); src The source matrix dst The destination matrix. Must be CV 32F or CV 64F. order Order of multipliers delta An optional array, subtracted from src before multiplication scale An optional scaling The function calculates the product of src and its transposition: dst = scale(src − delta)(src − delta)T if order = 0, and dst = scale(src − delta)T(src − delta) otherwise. cvNorm (view/add comments) Calculates absolute array norm, absolute difference norm, or relative difference norm. double cvNorm(const CvArr* arr1, const CvArr* arr2=NULL, int normType=CV L2, const CvArr* mask=NULL); arr1 The first source image arr2 The second source image. If it is NULL, the absolute norm of arr1 is calculated, otherwise the absolute or relative norm of arr1-arr2 is calculated. 1.2. OPERATIONS ON ARRAYS 111 normType Type of norm, see the discussion mask The optional operation mask The function calculates the absolute norm of arr1 if arr2 is NULL: norm =    ||arr1||C = maxI |arr1(I)| if normType = CV C ||arr1||L1 = P I |arr1(I)| if normType = CV L1 ||arr1||L2 = pP I arr1(I)2 if normType = CV L2 or the absolute difference norm if arr2 is not NULL: norm =    ||arr1 − arr2||C = maxI |arr1(I) − arr2(I)| if normType = CV C ||arr1 − arr2||L1 = P I |arr1(I) − arr2(I)| if normType = CV L1 ||arr1 − arr2||L2 = pP I(arr1(I) − arr2(I))2 if normType = CV L2 or the relative difference norm if arr2 is not NULL and (normType & CV RELATIVE) != 0: norm =    ||arr1−arr2||C ||arr2||C if normType = CV RELATIVE C ||arr1−arr2||L1 ||arr2||L1 if normType = CV RELATIVE L1 ||arr1−arr2||L2 ||arr2||L2 if normType = CV RELATIVE L2 The function returns the calculated norm. A multiple-channel array is treated as a single- channel, that is, the results for all channels are combined. cvNot (view/add comments) Performs per-element bit-wise inversion of array elements. void cvNot(const CvArr* src, CvArr* dst); src The source array dst The destination array The function Not inverses every bit of every array element: dst(I)=˜src(I) 112 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvOr (view/add comments) Calculates per-element bit-wise disjunction of two arrays. void cvOr(const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL); src1 The first source array src2 The second source array dst The destination array mask Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed The function calculates per-element bit-wise disjunction of two arrays: dst(I)=src1(I)|src2(I) In the case of floating-point arrays their bit representations are used for the operation. All the arrays must have the same type, except the mask, and the same size. cvOrS (view/add comments) Calculates a per-element bit-wise disjunction of an array and a scalar. void cvOrS(const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL); src The source array value Scalar to use in the operation dst The destination array mask Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed 1.2. OPERATIONS ON ARRAYS 113 The function OrS calculates per-element bit-wise disjunction of an array and a scalar: dst(I)=src(I)|value if mask(I)!=0 Prior to the actual operation, the scalar is converted to the same type as that of the array(s). In the case of floating-point arrays their bit representations are used for the operation. All the arrays must have the same type, except the mask, and the same size. cvPerspectiveTransform (view/add comments) Performs perspective matrix transformation of a vector array. void cvPerspectiveTransform(const CvArr* src, CvArr* dst, const CvMat* mat); src The source three-channel floating-point array dst The destination three-channel floating-point array mat 3 × 3 or 4 × 4 transformation matrix The function transforms every element of src (by treating it as 2D or 3D vector) in the following way: (x, y, z) → (x0/w, y0/w, z0/w) where (x0, y0, z0, w0) = mat · x y z 1 and w =  w0 if w0 6= 0 ∞ otherwise cvPolarToCart (view/add comments) Calculates Cartesian coordinates of 2d vectors represented in polar form. 114 CHAPTER 1. CORE. THE CORE FUNCTIONALITY void cvPolarToCart( const CvArr* magnitude, const CvArr* angle, CvArr* x, CvArr* y, int angleInDegrees=0); magnitude The array of magnitudes. If it is NULL, the magnitudes are assumed to be all 1’s. angle The array of angles, whether in radians or degrees x The destination array of x-coordinates, may be set to NULL if it is not needed y The destination array of y-coordinates, mau be set to NULL if it is not needed angleInDegrees The flag indicating whether the angles are measured in radians, which is de- fault mode, or in degrees The function calculates either the x-coodinate, y-coordinate or both of every vector magnitude(I)*exp(angle(I)*j), j=sqrt(-1): x(I)=magnitude(I)*cos(angle(I)), y(I)=magnitude(I)*sin(angle(I)) cvPow (view/add comments) Raises every array element to a power. void cvPow( const CvArr* src, CvArr* dst, double power); src The source array dst The destination array, should be the same type as the source 1.2. OPERATIONS ON ARRAYS 115 power The exponent of power The function raises every element of the input array to p: dst[I] =  src(I)p if p is integer |src(I)p| otherwise That is, for a non-integer power exponent the absolute values of input array elements are used. However, it is possible to get true values for negative values using some extra operations, as the following example, computing the cube root of array elements, shows: CvSize size = cvGetSize(src); CvMat* mask = cvCreateMat(size.height, size.width, CV_8UC1); cvCmpS(src, 0, mask, CV_CMP_LT); /* find negative elements */ cvPow(src, dst, 1./3); cvSubRS(dst, cvScalarAll(0), dst, mask); /* negate the results of negative inputs */ cvReleaseMat(&mask); For some values of power, such as integer values, 0.5, and -0.5, specialized faster algorithms are used. cvPtr?D (view/add comments) Return pointer to a particular array element. uchar* cvPtr1D(const CvArr* arr, int idx0, int* type=NULL); uchar* cvPtr2D(const CvArr* arr, int idx0, int idx1, int* type=NULL); uchar* cvPtr3D(const CvArr* arr, int idx0, int idx1, int idx2, int* type=NULL); uchar* cvPtrND(const CvArr* arr, int* idx, int* type=NULL, int createNode=1, unsigned* precalcHashval=NULL); arr Input array idx0 The first zero-based component of the element index idx1 The second zero-based component of the element index idx2 The third zero-based component of the element index idx Array of the element indices 116 CHAPTER 1. CORE. THE CORE FUNCTIONALITY type Optional output parameter: type of matrix elements createNode Optional input parameter for sparse matrices. Non-zero value of the parameter means that the requested element is created if it does not exist already. precalcHashval Optional input parameter for sparse matrices. If the pointer is not NULL, the function does not recalculate the node hash value, but takes it from the specified location. It is useful for speeding up pair-wise operations (TODO: provide an example) The functions return a pointer to a specific array element. Number of array dimension should match to the number of indices passed to the function except for cvPtr1D function that can be used for sequential access to 1D, 2D or nD dense arrays. The functions can be used for sparse arrays as well - if the requested node does not exist they create it and set it to zero. All these as well as other functions accessing array elements ( cvGet, cvGetReal, cvSet, cvSetReal) raise an error in case if the element index is out of range. cvRNG (view/add comments) Initializes a random number generator state. CvRNG cvRNG(int64 seed=-1); seed 64-bit value used to initiate a random sequence The function initializes a random number generator and returns the state. The pointer to the state can be then passed to the cvRandInt, cvRandReal and cvRandArr functions. In the current implementation a multiply-with-carry generator is used. cvRandArr (view/add comments) Fills an array with random numbers and updates the RNG state. void cvRandArr( CvRNG* rng, CvArr* arr, 1.2. OPERATIONS ON ARRAYS 117 int distType, CvScalar param1, CvScalar param2); rng RNG state initialized by cvRNG arr The destination array distType Distribution type CV RAND UNI uniform distribution CV RAND NORMAL normal or Gaussian distribution param1 The first parameter of the distribution. In the case of a uniform distribution it is the inclu- sive lower boundary of the random numbers range. In the case of a normal distribution it is the mean value of the random numbers. param2 The second parameter of the distribution. In the case of a uniform distribution it is the exclusive upper boundary of the random numbers range. In the case of a normal distribution it is the standard deviation of the random numbers. The function fills the destination array with uniformly or normally distributed random numbers. In the example below, the function is used to add a few normally distributed floating-point numbers to random locations within a 2d array. /* let noisy_screen be the floating-point 2d array that is to be "crapped" */ CvRNG rng_state = cvRNG(0xffffffff); int i, pointCount = 1000; /* allocate the array of coordinates of points */ CvMat* locations = cvCreateMat(pointCount, 1, CV_32SC2); /* arr of random point values */ CvMat* values = cvCreateMat(pointCount, 1, CV_32FC1); CvSize size = cvGetSize(noisy_screen); /* initialize the locations */ cvRandArr(&rng_state, locations, CV_RAND_UNI, cvScalar(0,0,0,0), cvScalar(size.width,size.height,0,0)); /* generate values */ cvRandArr(&rng_state, values, CV_RAND_NORMAL, cvRealScalar(100), // average intensity cvRealScalar(30) // deviation of the intensity 118 CHAPTER 1. CORE. THE CORE FUNCTIONALITY ); /* set the points */ for(i = 0; i < pointCount; i++ ) { CvPoint pt = *(CvPoint*)cvPtr1D(locations, i, 0); float value = *(float*)cvPtr1D(values, i, 0); *((float*)cvPtr2D(noisy_screen, pt.y, pt.x, 0 )) += value; } /* not to forget to release the temporary arrays */ cvReleaseMat(&locations); cvReleaseMat(&values); /* RNG state does not need to be deallocated */ cvRandInt (view/add comments) Returns a 32-bit unsigned integer and updates RNG. unsigned cvRandInt(CvRNG* rng); rng RNG state initialized by RandInit and, optionally, customized by RandSetRange (though, the latter function does not affect the discussed function outcome) The function returns a uniformly-distributed random 32-bit unsigned integer and updates the RNG state. It is similar to the rand() function from the C runtime library, but it always generates a 32-bit number whereas rand() returns a number in between 0 and RAND MAX which is 216 or 232, depending on the platform. The function is useful for generating scalar random numbers, such as points, patch sizes, table indices, etc., where integer numbers of a certain range can be generated using a modulo operation and floating-point numbers can be generated by scaling from 0 to 1 or any other specific range. Here is the example from the previous function discussion rewritten using cvRandInt: /* the input and the task is the same as in the previous sample. */ CvRNG rnggstate = cvRNG(0xffffffff); int i, pointCount = 1000; /*... - no arrays are allocated here */ CvSize size = cvGetSize(noisygscreen); 1.2. OPERATIONS ON ARRAYS 119 /* make a buffer for normally distributed numbers to reduce call overhead */ #define bufferSize 16 float normalValueBuffer[bufferSize]; CvMat normalValueMat = cvMat(bufferSize, 1, CVg32F, normalValueBuffer); int valuesLeft = 0; for(i = 0; i < pointCount; i++ ) { CvPoint pt; /* generate random point */ pt.x = cvRandInt(&rnggstate ) % size.width; pt.y = cvRandInt(&rnggstate ) % size.height; if(valuesLeft <= 0 ) { /* fulfill the buffer with normally distributed numbers if the buffer is empty */ cvRandArr(&rnggstate, &normalValueMat, CV\_RAND\_NORMAL, cvRealScalar(100), cvRealScalar(30)); valuesLeft = bufferSize; } *((float*)cvPtr2D(noisygscreen, pt.y, pt.x, 0 ) = normalValueBuffer[--valuesLeft]; } /* there is no need to deallocate normalValueMat because we have both the matrix header and the data on stack. It is a common and efficient practice of working with small, fixed-size matrices */ cvRandReal (view/add comments) Returns a floating-point random number and updates RNG. double cvRandReal(CvRNG* rng); rng RNG state initialized by cvRNG The function returns a uniformly-distributed random floating-point number between 0 and 1 (1 is not included). 120 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvReduce (view/add comments) Reduces a matrix to a vector. void cvReduce(const CvArr* src, CvArr* dst, int dim = -1, int op=CV REDUCE SUM); src The input matrix. dst The output single-row/single-column vector that accumulates somehow all the matrix rows/- columns. dim The dimension index along which the matrix is reduced. 0 means that the matrix is reduced to a single row, 1 means that the matrix is reduced to a single column and -1 means that the dimension is chosen automatically by analysing the dst size. op The reduction operation. It can take of the following values: CV REDUCE SUM The output is the sum of all of the matrix’s rows/columns. CV REDUCE AVG The output is the mean vector of all of the matrix’s rows/columns. CV REDUCE MAX The output is the maximum (column/row-wise) of all of the matrix’s rows/- columns. CV REDUCE MIN The output is the minimum (column/row-wise) of all of the matrix’s rows/- columns. The function reduces matrix to a vector by treating the matrix rows/columns as a set of 1D vectors and performing the specified operation on the vectors until a single row/column is obtained. For example, the function can be used to compute horizontal and vertical projections of an raster image. In the case of CV REDUCE SUM and CV REDUCE AVG the output may have a larger element bit-depth to preserve accuracy. And multi-channel arrays are also supported in these two reduction modes. cvReleaseData (view/add comments) Releases array data. 1.2. OPERATIONS ON ARRAYS 121 void cvReleaseData(CvArr* arr); arr Array header The function releases the array data. In the case of CvMat or CvMatND it simply calls cvDecRefData(), that is the function can not deallocate external data. See also the note to cvCre- ateData. cvReleaseImage (view/add comments) Deallocates the image header and the image data. void cvReleaseImage(IplImage** image); image Double pointer to the image header This call is a shortened form of if(*image ) { cvReleaseData(*image); cvReleaseImageHeader(image); } cvReleaseImageHeader (view/add comments) Deallocates an image header. void cvReleaseImageHeader(IplImage** image); image Double pointer to the image header 122 CHAPTER 1. CORE. THE CORE FUNCTIONALITY This call is an analogue of if(image ) { iplDeallocate(*image, IPL_IMAGE_HEADER | IPL_IMAGE_ROI); *image = 0; } but it does not use IPL functions by default (see the CV TURN ON IPL COMPATIBILITY macro). cvReleaseMat (view/add comments) Deallocates a matrix. void cvReleaseMat(CvMat** mat); mat Double pointer to the matrix The function decrements the matrix data reference counter and deallocates matrix header. If the data reference counter is 0, it also deallocates the data. if(*mat ) cvDecRefData(*mat); cvFree((void**)mat); cvReleaseMatND (view/add comments) Deallocates a multi-dimensional array. void cvReleaseMatND(CvMatND** mat); mat Double pointer to the array The function decrements the array data reference counter and releases the array header. If the reference counter reaches 0, it also deallocates the data. if(*mat ) cvDecRefData(*mat); cvFree((void**)mat); 1.2. OPERATIONS ON ARRAYS 123 cvReleaseSparseMat (view/add comments) Deallocates sparse array. void cvReleaseSparseMat(CvSparseMat** mat); mat Double pointer to the array The function releases the sparse array and clears the array pointer upon exit. cvRepeat (view/add comments) Fill the destination array with repeated copies of the source array. void cvRepeat(const CvArr* src, CvArr* dst); src Source array, image or matrix dst Destination array, image or matrix The function fills the destination array with repeated copies of the source array: dst(i,j)=src(i mod rows(src), j mod cols(src)) So the destination array may be as larger as well as smaller than the source array. cvResetImageROI (view/add comments) Resets the image ROI to include the entire image and releases the ROI structure. void cvResetImageROI(IplImage* image); image A pointer to the image header 124 CHAPTER 1. CORE. THE CORE FUNCTIONALITY This produces a similar result to the following , but in addition it releases the ROI structure. cvSetImageROI(image, cvRect(0, 0, image->width, image->height )); cvSetImageCOI(image, 0); cvReshape (view/add comments) Changes shape of matrix/image without copying data. CvMat* cvReshape(const CvArr* arr, CvMat* header, int newCn, int newRows=0); arr Input array header Output header to be filled newCn New number of channels. ’newCn = 0’ means that the number of channels remains un- changed. newRows New number of rows. ’newRows = 0’ means that the number of rows remains un- changed unless it needs to be changed according to newCn value. The function initializes the CvMat header so that it points to the same data as the original array but has a different shape - different number of channels, different number of rows, or both. The following example code creates one image buffer and two image headers, the first is for a 320x240x3 image and the second is for a 960x240x1 image: IplImage* color_img = cvCreateImage(cvSize(320,240), IPL_DEPTH_8U, 3); CvMat gray_mat_hdr; IplImage gray_img_hdr, *gray_img; cvReshape(color_img, &gray_mat_hdr, 1); gray_img = cvGetImage(&gray_mat_hdr, &gray_img_hdr); And the next example converts a 3x3 matrix to a single 1x9 vector: CvMat* mat = cvCreateMat(3, 3, CV_32F); CvMat row_header, *row; row = cvReshape(mat, &row_header, 0, 1); 1.2. OPERATIONS ON ARRAYS 125 cvReshapeMatND (view/add comments) Changes the shape of a multi-dimensional array without copying the data. CvArr* cvReshapeMatND(const CvArr* arr, int sizeofHeader, CvArr* header, int newCn, int newDims, int* newSizes); #define cvReshapeND(arr, header, newCn, newDims, newSizes ) \ cvReshapeMatND((arr), sizeof(*(header)), (header), \ (newCn), (newDims), (newSizes)) arr Input array sizeofHeader Size of output header to distinguish between IplImage, CvMat and CvMatND output headers header Output header to be filled newCn New number of channels. newCn = 0 means that the number of channels remains un- changed. newDims New number of dimensions. newDims = 0 means that the number of dimensions remains the same. newSizes Array of new dimension sizes. Only newDims − 1 values are used, because the total number of elements must remain the same. Thus, if newDims = 1, newSizes array is not used. The function is an advanced version of cvReshape that can work with multi-dimensional ar- rays as well (though it can work with ordinary images and matrices) and change the number of dimensions. Below are the two samples from the cvReshape description rewritten using cvReshape- MatND: IplImage* color_img = cvCreateImage(cvSize(320,240), IPL_DEPTH_8U, 3); IplImage gray_img_hdr, *gray_img; gray_img = (IplImage*)cvReshapeND(color_img, &gray_img_hdr, 1, 0, 0); ... 126 CHAPTER 1. CORE. THE CORE FUNCTIONALITY /* second example is modified to convert 2x2x2 array to 8x1 vector */ int size[] = { 2, 2, 2 }; CvMatND* mat = cvCreateMatND(3, size, CV_32F); CvMat row_header, *row; row = (CvMat*)cvReshapeND(mat, &row_header, 0, 1, 0); cvRound, cvFloor, cvCeil (view/add comments) Converts a floating-point number to an integer. int cvRound(double value); int cvFloor(double value); int cvCeil(double value); value The input floating-point value The functions convert the input floating-point number to an integer using one of the rounding modes. Round returns the nearest integer value to the argument. Floor returns the maximum integer value that is not larger than the argument. Ceil returns the minimum integer value that is not smaller than the argument. On some architectures the functions work much faster than the standard cast operations in C. If the absolute value of the argument is greater than 231, the result is not determined. Special values (±∞ , NaN) are not handled. cvScaleAdd (view/add comments) Calculates the sum of a scaled array and another array. void cvScaleAdd(const CvArr* src1, CvScalar scale, const CvArr* src2, CvArr* dst); src1 The first source array scale Scale factor for the first array src2 The second source array 1.2. OPERATIONS ON ARRAYS 127 dst The destination array The function calculates the sum of a scaled array and another array: dst(I) = scale src1(I) + src2(I) All array parameters should have the same type and the same size. cvSet (view/add comments) Sets every element of an array to a given value. void cvSet(CvArr* arr, CvScalar value, const CvArr* mask=NULL); arr The destination array value Fill value mask Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed The function copies the scalar value to every selected element of the destination array: arr(I) = value if mask(I) 6= 0 If array arr is of IplImage type, then is ROI used, but COI must not be set. cvSet?D (view/add comments) Change the particular array element. void cvSet1D(CvArr* arr, int idx0, CvScalar value); void cvSet2D(CvArr* arr, int idx0, int idx1, CvScalar value); void cvSet3D(CvArr* arr, int idx0, int idx1, int idx2, CvScalar value); void cvSetND(CvArr* arr, int* idx, CvScalar value); 128 CHAPTER 1. CORE. THE CORE FUNCTIONALITY arr Input array idx0 The first zero-based component of the element index idx1 The second zero-based component of the element index idx2 The third zero-based component of the element index idx Array of the element indices value The assigned value The functions assign the new value to a particular array element. In the case of a sparse array the functions create the node if it does not exist yet. cvSetData (view/add comments) Assigns user data to the array header. void cvSetData(CvArr* arr, void* data, int step); arr Array header data User data step Full row length in bytes The function assigns user data to the array header. Header should be initialized before using cvCreate*Header, cvInit*Header or cvMat (in the case of matrix) function. cvSetIdentity (view/add comments) Initializes a scaled identity matrix. void cvSetIdentity(CvArr* mat, CvScalar value=cvRealScalar(1)); mat The matrix to initialize (not necesserily square) 1.2. OPERATIONS ON ARRAYS 129 value The value to assign to the diagonal elements The function initializes a scaled identity matrix: arr(i, j) =  value if i = j 0 otherwise cvSetImageCOI (view/add comments) Sets the channel of interest in an IplImage. void cvSetImageCOI( IplImage* image, int coi); image A pointer to the image header coi The channel of interest. 0 - all channels are selected, 1 - first channel is selected, etc. Note that the channel indices become 1-based. If the ROI is set to NULL and the coi is not 0, the ROI is allocated. Most OpenCV functions do not support the COI setting, so to process an individual image/matrix channel one may copy (via cvCopy or cvSplit) the channel to a separate image/matrix, process it and then copy the result back (via cvCopy or cvMerge) if needed. cvSetImageROI (view/add comments) Sets an image Region Of Interest (ROI) for a given rectangle. void cvSetImageROI( IplImage* image, CvRect rect); image A pointer to the image header 130 CHAPTER 1. CORE. THE CORE FUNCTIONALITY rect The ROI rectangle If the original image ROI was NULL and the rect is not the whole image, the ROI structure is allocated. Most OpenCV functions support the use of ROI and treat the image rectangle as a separate image. For example, all of the pixel coordinates are counted from the top-left (or bottom-left) corner of the ROI, not the original image. cvSetReal?D (view/add comments) Change a specific array element. void cvSetReal1D(CvArr* arr, int idx0, double value); void cvSetReal2D(CvArr* arr, int idx0, int idx1, double value); void cvSetReal3D(CvArr* arr, int idx0, int idx1, int idx2, double value); void cvSetRealND(CvArr* arr, int* idx, double value); arr Input array idx0 The first zero-based component of the element index idx1 The second zero-based component of the element index idx2 The third zero-based component of the element index idx Array of the element indices value The assigned value The functions assign a new value to a specific element of a single-channel array. If the array has multiple channels, a runtime error is raised. Note that the cvSet*D function can be used safely for both single-channel and multiple-channel arrays, though they are a bit slower. In the case of a sparse array the functions create the node if it does not yet exist. cvSetZero (view/add comments) Clears the array. 1.2. OPERATIONS ON ARRAYS 131 void cvSetZero(CvArr* arr); #define cvZero cvSetZero arr Array to be cleared The function clears the array. In the case of dense arrays (CvMat, CvMatND or IplImage), cvZero(array) is equivalent to cvSet(array,cvScalarAll(0),0). In the case of sparse arrays all the elements are removed. cvSolve (view/add comments) Solves a linear system or least-squares problem. int cvSolve(const CvArr* src1, const CvArr* src2, CvArr* dst, int method=CV LU); A The source matrix B The right-hand part of the linear system X The output solution method The solution (matrix inversion) method CV LU Gaussian elimination with optimal pivot element chosen CV SVD Singular value decomposition (SVD) method CV SVD SYM SVD method for a symmetric positively-defined matrix. The function solves a linear system or least-squares problem (the latter is possible with SVD methods): dst = argminX||src1 X − src2|| If CV LU method is used, the function returns 1 if src1 is non-singular and 0 otherwise; in the latter case dst is not valid. 132 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvSolveCubic (view/add comments) Finds the real roots of a cubic equation. void cvSolveCubic(const CvArr* coeffs, CvArr* roots); coeffs The equation coefficients, an array of 3 or 4 elements roots The output array of real roots which should have 3 elements The function finds the real roots of a cubic equation: If coeffs is a 4-element vector: coeffs[0]x3 + coeffs[1]x2 + coeffs[2]x + coeffs[3] = 0 or if coeffs is 3-element vector: x3 + coeffs[0]x2 + coeffs[1]x + coeffs[2] = 0 The function returns the number of real roots found. The roots are stored to root array, which is padded with zeros if there is only one root. cvSplit (view/add comments) Divides multi-channel array into several single-channel arrays or extracts a single channel from the array. void cvSplit(const CvArr* src, CvArr* dst0, CvArr* dst1, CvArr* dst2, CvArr* dst3); src Source array dst0 Destination channel 0 dst1 Destination channel 1 dst2 Destination channel 2 1.2. OPERATIONS ON ARRAYS 133 dst3 Destination channel 3 The function divides a multi-channel array into separate single-channel arrays. Two modes are available for the operation. If the source array has N channels then if the first N destination channels are not NULL, they all are extracted from the source array; if only a single destination channel of the first N is not NULL, this particular channel is extracted; otherwise an error is raised. The rest of the destination channels (beyond the first N) must always be NULL. For IplImage cvCopy with COI set can be also used to extract a single channel from the image. cvSqrt (view/add comments) Calculates the square root. float cvSqrt(float value); value The input floating-point value The function calculates the square root of the argument. If the argument is negative, the result is not determined. cvSub (view/add comments) Computes the per-element difference between two arrays. void cvSub(const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL); src1 The first source array src2 The second source array dst The destination array mask Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed 134 CHAPTER 1. CORE. THE CORE FUNCTIONALITY The function subtracts one array from another one: dst(I)=src1(I)-src2(I) if mask(I)!=0 All the arrays must have the same type, except the mask, and the same size (or ROI size). For types that have limited range this operation is saturating. cvSubRS (view/add comments) Computes the difference between a scalar and an array. void cvSubRS(const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL); src The first source array value Scalar to subtract from dst The destination array mask Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed The function subtracts every element of source array from a scalar: dst(I)=value-src(I) if mask(I)!=0 All the arrays must have the same type, except the mask, and the same size (or ROI size). For types that have limited range this operation is saturating. cvSubS (view/add comments) Computes the difference between an array and a scalar. void cvSubS(const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL); src The source array 1.2. OPERATIONS ON ARRAYS 135 value Subtracted scalar dst The destination array mask Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed The function subtracts a scalar from every element of the source array: dst(I)=src(I)-value if mask(I)!=0 All the arrays must have the same type, except the mask, and the same size (or ROI size). For types that have limited range this operation is saturating. cvSum (view/add comments) Adds up array elements. CvScalar cvSum(const CvArr* arr); arr The array The function calculates the sum S of array elements, independently for each channel: X I arr(I)c If the array is IplImage and COI is set, the function processes the selected channel only and stores the sum to the first scalar component. cvSVBkSb (view/add comments) Performs singular value back substitution. void cvSVBkSb( const CvArr* W, const CvArr* U, const CvArr* V, 136 CHAPTER 1. CORE. THE CORE FUNCTIONALITY const CvArr* B, CvArr* X, int flags); W Matrix or vector of singular values U Left orthogonal matrix (tranposed, perhaps) V Right orthogonal matrix (tranposed, perhaps) B The matrix to multiply the pseudo-inverse of the original matrix A by. This is an optional param- eter. If it is omitted then it is assumed to be an identity matrix of an appropriate size (so that X will be the reconstructed pseudo-inverse of A). X The destination matrix: result of back substitution flags Operation flags, should match exactly to the flags passed to cvSVD The function calculates back substitution for decomposed matrix A(see cvSVD description) and matrix B: X = VW−1UTB where W −1 (i,i) =  1/W(i,i) if W(i,i) >  P i W(i,i) 0 otherwise and  is a small number that depends on the matrix data type. This function together with cvSVD is used inside cvInvert and cvSolve, and the possible reason to use these (svd and bksb) ”low-level” function, is to avoid allocation of temporary matrices inside the high-level counterparts (inv and solve). cvSVD (view/add comments) Performs singular value decomposition of a real floating-point matrix. 1.2. OPERATIONS ON ARRAYS 137 void cvSVD( CvArr* A, CvArr* W, CvArr* U=NULL, CvArr* V=NULL, int flags=0); A Source M × N matrix W Resulting singular value diagonal matrix (M × N or min(M,N) × min(M,N)) or min(M,N) × 1 vector of the singular values U Optional left orthogonal matrix, M × min(M,N)(when CV SVD UT is not set), or min(M,N) × M (when CV SVD UT is set), or M × M(regardless of CV SVD UT flag). V Optional right orthogonal matrix, N × min(M,N)(when CV SVD VT is not set), or min(M,N) × N (when CV SVD VT is set), or N × N(regardless of CV SVD VT flag). flags Operation flags; can be 0 or a combination of the following values: CV SVD MODIFY A enables modification of matrix A during the operation. It speeds up the processing. CV SVD UT means that the transposed matrix U is returned. Specifying the flag speeds up the processing. CV SVD VT means that the transposed matrix V is returned. Specifying the flag speeds up the processing. The function decomposes matrix A into the product of a diagonal matrix and two orthogonal matrices: A = UWVT where W is a diagonal matrix of singular values that can be coded as a 1D vector of singular values and U and V. All the singular values are non-negative and sorted (together with U and V columns) in descending order. An SVD algorithm is numerically robust and its typical applications include: • accurate eigenvalue problem solution when matrix A is a square, symmetric, and positively defined matrix, for example, when it is a covariance matrix. W in this case will be a vector/- matrix of the eigenvalues, and U = V will be a matrix of the eigenvectors. 138 CHAPTER 1. CORE. THE CORE FUNCTIONALITY • accurate solution of a poor-conditioned linear system. • least-squares solution of an overdetermined linear system. This and the preceeding is done by using the cvSolve function with the CV SVD method. • accurate calculation of different matrix characteristics such as the matrix rank (the number of non-zero singular values), condition number (ratio of the largest singular value to the smallest one), and determinant (absolute value of the determinant is equal to the product of singular values). cvTrace (view/add comments) Returns the trace of a matrix. CvScalar cvTrace(const CvArr* mat); mat The source matrix The function returns the sum of the diagonal elements of the matrix src1. tr(mat) = X i mat(i, i) cvTransform (view/add comments) Performs matrix transformation of every array element. void cvTransform(const CvArr* src, CvArr* dst, const CvMat* transmat, const CvMat* shiftvec=NULL); src The first source array dst The destination array transmat Transformation matrix 1.2. OPERATIONS ON ARRAYS 139 shiftvec Optional shift vector The function performs matrix transformation of every element of array src and stores the results in dst: dst(I) = transmat · src(I) + shiftvec That is, every element of an N-channel array src is considered as an N-element vector which is transformed using a M × N matrix transmat and shift vector shiftvec into an element of M-channel array dst. There is an option to embedd shiftvec into transmat. In this case transmat should be a M × (N + 1) matrix and the rightmost column is treated as the shift vector. Both source and destination arrays should have the same depth and the same size or selected ROI size. transmat and shiftvec should be real floating-point matrices. The function may be used for geometrical transformation of n dimensional point set, arbitrary linear color space transformation, shuffling the channels and so forth. cvTranspose (view/add comments) Transposes a matrix. void cvTranspose(const CvArr* src, CvArr* dst); src The source matrix dst The destination matrix The function transposes matrix src1: dst(i, j) = src(j, i) Note that no complex conjugation is done in the case of a complex matrix. Conjugation should be done separately: look at the sample code in cvXorS for an example. cvXor (view/add comments) Performs per-element bit-wise ”exclusive or” operation on two arrays. 140 CHAPTER 1. CORE. THE CORE FUNCTIONALITY void cvXor(const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL); src1 The first source array src2 The second source array dst The destination array mask Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed The function calculates per-element bit-wise logical conjunction of two arrays: dst(I)=src1(I)ˆsrc2(I) if mask(I)!=0 In the case of floating-point arrays their bit representations are used for the operation. All the arrays must have the same type, except the mask, and the same size. cvXorS (view/add comments) Performs per-element bit-wise ”exclusive or” operation on an array and a scalar. void cvXorS(const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL); src The source array value Scalar to use in the operation dst The destination array mask Operation mask, 8-bit single channel array; specifies elements of the destination array to be changed The function XorS calculates per-element bit-wise conjunction of an array and a scalar: dst(I)=src(I)ˆvalue if mask(I)!=0 1.2. OPERATIONS ON ARRAYS 141 Prior to the actual operation, the scalar is converted to the same type as that of the array(s). In the case of floating-point arrays their bit representations are used for the operation. All the arrays must have the same type, except the mask, and the same size The following sample demonstrates how to conjugate complex vector by switching the most- significant bit of imaging part: float a[] = { 1, 0, 0, 1, -1, 0, 0, -1 }; /* 1, j, -1, -j */ CvMat A = cvMat(4, 1, CV\_32FC2, &a); int i, negMask = 0x80000000; cvXorS(&A, cvScalar(0, *(float*)&negMask, 0, 0 ), &A, 0); for(i = 0; i < 4; i++ ) printf("(\%.1f, \%.1f) ", a[i*2], a[i*2+1]); The code should print: (1.0,0.0) (0.0,-1.0) (-1.0,0.0) (0.0,1.0) cvmGet (view/add comments) Returns the particular element of single-channel floating-point matrix. double cvmGet(const CvMat* mat, int row, int col); mat Input matrix row The zero-based index of row col The zero-based index of column The function is a fast replacement for cvGetReal2D in the case of single-channel floating-point matrices. It is faster because it is inline, it does fewer checks for array type and array element type, and it checks for the row and column ranges only in debug mode. cvmSet (view/add comments) Returns a specific element of a single-channel floating-point matrix. 142 CHAPTER 1. CORE. THE CORE FUNCTIONALITY void cvmSet(CvMat* mat, int row, int col, double value); mat The matrix row The zero-based index of row col The zero-based index of column value The new value of the matrix element The function is a fast replacement for cvSetReal2D in the case of single-channel floating-point matrices. It is faster because it is inline, it does fewer checks for array type and array element type, and it checks for the row and column ranges only in debug mode. 1.3 Dynamic Structures CvMemStorage (view/add comments) Growing memory storage. typedef struct CvMemStorage { struct CvMemBlock* bottom;/* first allocated block */ struct CvMemBlock* top; /* the current memory block - top of the stack */ struct CvMemStorage* parent; /* borrows new blocks from */ int block\_size; /* block size */ int free\_space; /* free space in the \texttt{top} block (in bytes) */ } CvMemStorage; Memory storage is a low-level structure used to store dynamicly growing data structures such as sequences, contours, graphs, subdivisions, etc. It is organized as a list of memory blocks of equal size - bottom field is the beginning of the list of blocks and top is the currently used block, but not necessarily the last block of the list. All blocks between bottom and top, not including the latter, are considered fully occupied; all blocks between top and the last block, not including top, are considered free and top itself is partly ocupied - free space contains the number of free bytes left in the end of top. A new memory buffer that may be allocated explicitly by cvMemStorageAlloc function or im- plicitly by higher-level functions, such as cvSeqPush, cvGraphAddEdge, etc., always starts in the end of the current block if it fits there. After allocation, free space is decremented by the 1.3. DYNAMIC STRUCTURES 143 size of the allocated buffer plus some padding to keep the proper alignment. When the allocated buffer does not fit into the available portion of top, the next storage block from the list is taken as top and free space is reset to the whole block size prior to the allocation. If there are no more free blocks, a new block is allocated (or borrowed from the parent, see cvCreateChildMemStorage) and added to the end of list. Thus, the storage behaves as a stack with bottom indicating bottom of the stack and the pair (top, free space) indicating top of the stack. The stack top may be saved via cvSaveMemStoragePos, restored via cvRestoreMemStor- agePos, or reset via cvClearStorage. CvMemBlock (view/add comments) Memory storage block. typedef struct CvMemBlock { struct CvMemBlock* prev; struct CvMemBlock* next; } CvMemBlock; The structure CvMemBlock represents a single block of memory storage. The actual data in the memory blocks follows the header, that is, the ith byte of the memory block can be retrieved with the expression ((char*)(mem block ptr+1))[i]. However, there is normally no need to access the storage structure fields directly. CvMemStoragePos (view/add comments) Memory storage position. typedef struct CvMemStoragePos { CvMemBlock* top; int free\_space; } CvMemStoragePos; The structure described above stores the position of the stack top that can be saved via cvSaveMemStoragePos and restored via cvRestoreMemStoragePos. CvSeq (view/add comments) Growable sequence of elements. #define CV_SEQUENCE\_FIELDS() \ int flags; /* micsellaneous flags */\ 144 CHAPTER 1. CORE. THE CORE FUNCTIONALITY int header_size; /* size of sequence header */\ struct CvSeq* h_prev; /* previous sequence */\ struct CvSeq* h_next; /* next sequence */\ struct CvSeq* v_prev; /* 2nd previous sequence */\ struct CvSeq* v_next; /* 2nd next sequence */\ int total; /* total number of elements */\ int elem_size;/* size of sequence element in bytes */\ char* block_max;/* maximal bound of the last block */\ char* ptr; /* current write pointer */\ int delta_elems; /* how many elements allocated when the sequence grows (sequence granularity) */\ CvMemStorage* storage; /* where the seq is stored */\ CvSeqBlock* free_blocks; /* free blocks list */\ CvSeqBlock* first; /* pointer to the first sequence block */ typedef struct CvSeq { CV_SEQUENCE_FIELDS() } CvSeq; The structure CvSeq is a base for all of OpenCV dynamic data structures. Such an unusual definition via a helper macro simplifies the extension of the structure CvSeq with additional parameters. To extend CvSeq the user may define a new structure and put user- defined fields after all CvSeq fields that are included via the macro CV SEQUENCE FIELDS(). There are two types of sequences - dense and sparse. The base type for dense sequences is CvSeq and such sequences are used to represent growable 1d arrays - vectors, stacks, queues, and deques. They have no gaps in the middle - if an element is removed from the middle or inserted into the middle of the sequence, the elements from the closer end are shifted. Sparse sequences have CvSet as a base class and they are discussed later in more detail. They are sequences of nodes; each may be either occupied or free as indicated by the node flag. Such sequences are used for unordered data structures such as sets of elements, graphs, hash tables and so forth. The field header size contains the actual size of the sequence header and should be greater than or equal to sizeof(CvSeq). The fields h prev, h next, v prev, v next can be used to create hierarchical structures from separate sequences. The fields h prev and h next point to the previous and the next sequences on the same hierarchical level, while the fields v prev and v next point to the previous and the next sequences in the vertical direction, that is, the parent and its first child. But these are just names and the pointers can be used in a different way. The field first points to the first sequence block, whose structure is described below. The field total contains the actual number of dense sequence elements and number of allo- cated nodes in a sparse sequence. 1.3. DYNAMIC STRUCTURES 145 The field flags contains the particular dynamic type signature (CV SEQ MAGIC VAL for dense sequences and CV SET MAGIC VAL for sparse sequences) in the highest 16 bits and miscella- neous information about the sequence. The lowest CV SEQ ELTYPE BITS bits contain the ID of the element type. Most of sequence processing functions do not use element type but rather el- ement size stored in elem size. If a sequence contains the numeric data for one of the CvMat type then the element type matches to the corresponding CvMat element type, e.g., CV 32SC2 may be used for a sequence of 2D points, CV 32FC1 for sequences of floating-point values, etc. A CV SEQ ELTYPE(seq header ptr) macro retrieves the type of sequence elements. Processing functions that work with numerical sequences check that elem size is equal to that calculated from the type element size. Besides CvMat compatible types, there are few extra element types defined in the cvtypes.h header: Standard Types of Sequence Elements #define CV_SEQ_ELTYPE_POINT CV_32SC2 /*(x,y) */ #define CV_SEQ_ELTYPE_CODE CV_8UC1 /* freeman code: 0..7 */ #define CV_SEQ_ELTYPE_GENERIC 0 /* unspecified type of sequence elements */ #define CV_SEQ_ELTYPE_PTR CV_USRTYPE1 /* =6 */ #define CV_SEQ_ELTYPE_PPOINT CV_SEQ_ELTYPE_PTR /*&elem: pointer to element of other sequence */ #define CV_SEQ_ELTYPE_INDEX CV_32SC1 /*#elem: index of element of some other sequence */ #define CV_SEQ_ELTYPE_GRAPH_EDGE CV_SEQ_ELTYPE_GENERIC /*&next_o, &next_d, &vtx_o, &vtx_d */ #define CV_SEQ_ELTYPE_GRAPH_VERTEX CV_SEQ_ELTYPE_GENERIC /* first_edge, &(x,y) */ #define CV_SEQ_ELTYPE_TRIAN_ATR CV_SEQ_ELTYPE_GENERIC /* vertex of the binary tree */ #define CV_SEQ_ELTYPE_CONNECTED_COMP CV_SEQ_ELTYPE_GENERIC /* connected component */ #define CV_SEQ_ELTYPE_POINT3D CV_32FC3 /*(x,y,z) */ The next CV SEQ KIND BITS bits specify the kind of sequence: Standard Kinds of Sequences /* generic (unspecified) kind of sequence */ #define CV_SEQ_KIND_GENERIC (0 << CV_SEQ_ELTYPE_BITS) /* dense sequence suntypes */ #define CV_SEQ_KIND_CURVE (1 << CV_SEQ_ELTYPE_BITS) #define CV_SEQ_KIND_BIN_TREE (2 << CV_SEQ_ELTYPE_BITS) /* sparse sequence (or set) subtypes */ 146 CHAPTER 1. CORE. THE CORE FUNCTIONALITY #define CV_SEQ_KIND_GRAPH (3 << CV_SEQ_ELTYPE_BITS) #define CV_SEQ_KIND_SUBDIV2D (4 << CV_SEQ_ELTYPE_BITS) The remaining bits are used to identify different features specific to certain sequence kinds and element types. For example, curves made of points (CV SEQ KIND CURVE|CV SEQ ELTYPE POINT), together with the flag CV SEQ FLAG CLOSED, belong to the type CV SEQ POLYGON or, if other flags are used, to its subtype. Many contour processing functions check the type of the input sequence and report an error if they do not support this type. The file cvtypes.h stores the complete list of all supported predefined sequence types and helper macros designed to get the sequence type of other properties. The definition of the building blocks of sequences can be found below. CvSeqBlock (view/add comments) Continuous sequence block. typedef struct CvSeqBlock { struct CvSeqBlock* prev; /* previous sequence block */ struct CvSeqBlock* next; /* next sequence block */ int start_index; /* index of the first element in the block + sequence->first->start_index */ int count; /* number of elements in the block */ char* data; /* pointer to the first element of the block */ } CvSeqBlock; Sequence blocks make up a circular double-linked list, so the pointers prev and next are never NULL and point to the previous and the next sequence blocks within the sequence. It means that next of the last block is the first block and prev of the first block is the last block. The fields startIndex and count help to track the block location within the sequence. For example, if the sequence consists of 10 elements and splits into three blocks of 3, 5, and 2 elements, and the first block has the parameter startIndex = 2, then pairs (startIndex, count) for the sequence blocks are (2,3), (5, 5), and (10, 2) correspondingly. The parameter startIndex of the first block is usually 0 unless some elements have been inserted at the beginning of the sequence. CvSlice (view/add comments) A sequence slice. typedef struct CvSlice { int start_index; int end_index; } CvSlice; 1.3. DYNAMIC STRUCTURES 147 inline CvSlice cvSlice( int start, int end ); #define CV_WHOLE_SEQ_END_INDEX 0x3fffffff #define CV_WHOLE_SEQ cvSlice(0, CV_WHOLE_SEQ_END_INDEX) /* calculates the sequence slice length */ int cvSliceLength( CvSlice slice, const CvSeq* seq ); Some of functions that operate on sequences take a CvSlice slice parameter that is of- ten set to the whole sequence (CV WHOLE SEQ) by default. Either of the startIndex and endIndex may be negative or exceed the sequence length, startIndex is inclusive, and endIndex is an exclusive boundary. If they are equal, the slice is considered empty (i.e., contains no ele- ments). Because sequences are treated as circular structures, the slice may select a few elements in the end of a sequence followed by a few elements at the beginning of the sequence. For ex- ample, cvSlice(-2, 3) in the case of a 10-element sequence will select a 5-element slice, containing the pre-last (8th), last (9th), the very first (0th), second (1th) and third (2nd) elements. The functions normalize the slice argument in the following way: first, cvSliceLength is called to determine the length of the slice, then, startIndex of the slice is normalized similarly to the ar- gument of cvGetSeqElem (i.e., negative indices are allowed). The actual slice to process starts at the normalized startIndex and lasts cvSliceLength elements (again, assuming the sequence is a circular structure). If a function does not accept a slice argument, but you want to process only a part of the sequence, the sub-sequence may be extracted using the cvSeqSlice function, or stored into a continuous buffer with CvtSeqToArray (optionally, followed by cvMakeSeqHeaderForArray). CvSet (view/add comments) Collection of nodes. typedef struct CvSetElem { int flags; /* it is negative if the node is free and zero or positive otherwise */ struct CvSetElem* next_free; /* if the node is free, the field is a pointer to next free node */ } CvSetElem; #define CV_SET_FIELDS() \ CV_SEQUENCE_FIELDS() /* inherits from [#CvSeq CvSeq] */\ struct CvSetElem* free_elems; /* list of free nodes */ typedef struct CvSet { 148 CHAPTER 1. CORE. THE CORE FUNCTIONALITY CV_SET_FIELDS() } CvSet; The structure CvSet is a base for OpenCV sparse data structures. As follows from the above declaration, CvSet inherits from CvSeq and it adds the free elems field, which is a list of free nodes, to it. Every set node, whether free or not, is an element of the underlying sequence. While there are no restrictions on elements of dense sequences, the set (and derived structures) elements must start with an integer field and be able to fit CvSetElem structure, because these two fields (an integer followed by a pointer) are required for the orga- nization of a node set with the list of free nodes. If a node is free, the flags field is negative (the most-significant bit, or MSB, of the field is set), and the next free points to the next free node (the first free node is referenced by the free elems field of CvSet ). And if a node is occupied, the flags field is positive and contains the node index that may be retrieved using the (set elem->flags & CV SET ELEM IDX MASK) expressions, the rest of the node content is determined by the user. In particular, the occupied nodes are not linked as the free nodes are, so the second field can be used for such a link as well as for some different purpose. The macro CV IS SET ELEM(set elem ptr) can be used to determined whether the specified node is occupied or not. Initially the set and the list are empty. When a new node is requested from the set, it is taken from the list of free nodes, which is then updated. If the list appears to be empty, a new sequence block is allocated and all the nodes within the block are joined in the list of free nodes. Thus, the total field of the set is the total number of nodes both occupied and free. When an occupied node is released, it is added to the list of free nodes. The node released last will be occupied first. In OpenCV CvSet is used for representing graphs ( CvGraph ), sparse multi-dimensional arrays ( CvSparseMat ), and planar subdivisions CvSubdiv2D. CvGraph (view/add comments) Oriented or unoriented weighted graph. #define CV_GRAPH_VERTEX_FIELDS() \ int flags; /* vertex flags */\ struct CvGraphEdge* first; /* the first incident edge */ typedef struct CvGraphVtx { CV_GRAPH_VERTEX_FIELDS() } CvGraphVtx; #define CV_GRAPH_EDGE_FIELDS() \ int flags; /* edge flags */\ 1.3. DYNAMIC STRUCTURES 149 float weight; /* edge weight */\ struct CvGraphEdge* next[2]; /* the next edges in the incidence lists for staring (0) */\ /* and ending (1) vertices */\ struct CvGraphVtx* vtx[2]; /* the starting (0) and ending (1) vertices */ typedef struct CvGraphEdge { CV_GRAPH_EDGE_FIELDS() } CvGraphEdge; #define CV_GRAPH_FIELDS() \ CV_SET_FIELDS() /* set of vertices */\ CvSet* edges; /* set of edges */ typedef struct CvGraph { CV_GRAPH_FIELDS() } CvGraph; The structure CvGraph is a base for graphs used in OpenCV. The graph structure inherits from CvSet - which describes common graph properties and the graph vertices, and contains another set as a member - which describes the graph edges. The vertex, edge, and the graph header structures are declared using the same technique as other extendible OpenCV structures - via macros, which simplify extension and customization of the structures. While the vertex and edge structures do not inherit from CvSetElem explicitly, they satisfy both conditions of the set elements: having an integer field in the beginning and fitting within the CvSetElem structure. The flags fields are used as for indicating occupied vertices and edges as well as for other purposes, for example, for graph traversal (see cvCreateGraphScanner et al.), so it is better not to use them directly. The graph is represented as a set of edges each of which has a list of incident edges. The incidence lists for different vertices are interleaved to avoid information duplication as much as posssible. The graph may be oriented or unoriented. In the latter case there is no distiction between the edge connecting vertex A with vertex B and the edge connecting vertex B with vertex A- only one of them can exist in the graph at the same moment and it represents both A → B and B → A edges. CvGraphScanner (view/add comments) Graph traversal state. 150 CHAPTER 1. CORE. THE CORE FUNCTIONALITY typedef struct CvGraphScanner { CvGraphVtx* vtx; /* current graph vertex (or current edge origin) */ CvGraphVtx* dst; /* current graph edge destination vertex */ CvGraphEdge* edge; /* current edge */ CvGraph* graph; /* the graph */ CvSeq* stack; /* the graph vertex stack */ int index; /* the lower bound of certainly visited vertices */ int mask; /* event mask */ } CvGraphScanner; The structure CvGraphScanner is used for depth-first graph traversal. See discussion of the functions below. CV TREE NODE FIELDS (view/add comments) Helper macro for a tree node type declaration. The macro CV TREE NODE FIELDS() is used to declare structures that can be organized into hierarchical strucutures (trees), such as CvSeq - the basic type for all dynamic structures. The trees created with nodes declared using this macro can be processed using the functions described below in this section. CvTreeNodeIterator (view/add comments) Opens existing or creates new file storage. typedef struct CvTreeNodeIterator { const void* node; int level; int max_level; } CvTreeNodeIterator; #define CV_TREE_NODE_FIELDS(node_type) \ int flags; /* micsellaneous flags */\ int header_size; /* size of sequence header */\ struct node_type* h_prev; /* previous sequence */\ struct node_type* h_next; /* next sequence */\ struct node_type* v_prev; /* 2nd previous sequence */\ struct node_type* v_next; /* 2nd next sequence */ 1.3. DYNAMIC STRUCTURES 151 The structure CvTreeNodeIterator is used to traverse trees. Each tree node should start with the certain fields which are defined by CV TREE NODE FIELDS(...) macro. In C++ terms, each tree node should be a structure ”derived” from struct _BaseTreeNode { CV_TREE_NODE_FIELDS(_BaseTreeNode); } CvSeq, CvSet, CvGraph and other dynamic structures derived from CvSeq comply with the requirement. cvClearGraph (view/add comments) Clears a graph. void cvClearGraph( CvGraph* graph ); graph Graph The function removes all vertices and edges from a graph. The function has O(1) time com- plexity. cvClearMemStorage (view/add comments) Clears memory storage. void cvClearMemStorage( CvMemStorage* storage ); storage Memory storage The function resets the top (free space boundary) of the storage to the very beginning. This function does not deallocate any memory. If the storage has a parent, the function returns all blocks to the parent. 152 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvClearSeq (view/add comments) Clears a sequence. void cvClearSeq( CvSeq* seq ); seq Sequence The function removes all elements from a sequence. The function does not return the mem- ory to the storage block, but this memory is reused later when new elements are added to the sequence. The function has ’O(1)’ time complexity. cvClearSet (view/add comments) Clears a set. void cvClearSet( CvSet* setHeader ); setHeader Cleared set The function removes all elements from set. It has O(1) time complexity. cvCloneGraph (view/add comments) Clones a graph. CvGraph* cvCloneGraph( const CvGraph* graph, CvMemStorage* storage ); graph The graph to copy 1.3. DYNAMIC STRUCTURES 153 storage Container for the copy The function creates a full copy of the specified graph. If the graph vertices or edges have pointers to some external data, it can still be shared between the copies. The vertex and edge indices in the new graph may be different from the original because the function defragments the vertex and edge sets. cvCloneSeq (view/add comments) Creates a copy of a sequence. CvSeq* cvCloneSeq( const CvSeq* seq, CvMemStorage* storage=NULL ); seq Sequence storage The destination storage block to hold the new sequence header and the copied data, if any. If it is NULL, the function uses the storage block containing the input sequence. The function makes a complete copy of the input sequence and returns it. The call cvCloneSeq( seq, storage ) is equivalent to cvSeqSlice( seq, CV_WHOLE_SEQ, storage, 1 ) cvCreateChildMemStorage (view/add comments) Creates child memory storage. CvMemStorage* cvCreateChildMemStorage(CvMemStorage* parent); parent Parent memory storage 154 CHAPTER 1. CORE. THE CORE FUNCTIONALITY The function creates a child memory storage that is similar to simple memory storage except for the differences in the memory allocation/deallocation mechanism. When a child storage needs a new block to add to the block list, it tries to get this block from the parent. The first unoccupied parent block available is taken and excluded from the parent block list. If no blocks are available, the parent either allocates a block or borrows one from its own parent, if any. In other words, the chain, or a more complex structure, of memory storages where every storage is a child/parent of another is possible. When a child storage is released or even cleared, it returns all blocks to the parent. In other aspects, child storage is the same as simple storage. Child storage is useful in the following situation. Imagine that the user needs to process dy- namic data residing in a given storage area and put the result back to that same storage area. With the simplest approach, when temporary data is resided in the same storage area as the input and output data, the storage area will look as follows after processing: Dynamic data processing without using child storage That is, garbage appears in the middle of the storage. However, if one creates a child memory storage at the beginning of processing, writes temporary data there, and releases the child storage at the end, no garbage will appear in the source/destination storage: Dynamic data processing using a child storage 1.3. DYNAMIC STRUCTURES 155 cvCreateGraph (view/add comments) Creates an empty graph. CvGraph* cvCreateGraph( int graph flags, int header size, int vtx size, int edge size, CvMemStorage* storage ); graph flags Type of the created graph. Usually, it is either CV SEQ KIND GRAPH for generic unoriented graphs and CV SEQ KIND GRAPH | CV GRAPH FLAG ORIENTED for generic ori- ented graphs. header size Graph header size; may not be less than sizeof(CvGraph) vtx size Graph vertex size; the custom vertex structure must start with CvGraphVtx (use CV GRAPH VERTEX FIELDS()) edge size Graph edge size; the custom edge structure must start with CvGraphEdge (use CV GRAPH EDGE FIELDS()) storage The graph container The function creates an empty graph and returns a pointer to it. cvCreateGraphScanner (view/add comments) Creates structure for depth-first graph traversal. CvGraphScanner* cvCreateGraphScanner( CvGraph* graph, CvGraphVtx* vtx=NULL, int mask=CV GRAPH ALL ITEMS ); 156 CHAPTER 1. CORE. THE CORE FUNCTIONALITY graph Graph vtx Initial vertex to start from. If NULL, the traversal starts from the first vertex (a vertex with the minimal index in the sequence of vertices). mask Event mask indicating which events are of interest to the user (where cvNextGraphItem function returns control to the user) It can be CV GRAPH ALL ITEMS (all events are of inter- est) or a combination of the following flags: CV GRAPH VERTEX stop at the graph vertices visited for the first time CV GRAPH TREE EDGE stop at tree edges (tree edge is the edge connecting the last vis- ited vertex and the vertex to be visited next) CV GRAPH BACK EDGE stop at back edges (back edge is an edge connecting the last vis- ited vertex with some of its ancestors in the search tree) CV GRAPH FORWARD EDGE stop at forward edges (forward edge is an edge conecting the last visited vertex with some of its descendants in the search tree. The forward edges are only possible during oriented graph traversal) CV GRAPH CROSS EDGE stop at cross edges (cross edge is an edge connecting different search trees or branches of the same tree. The cross edges are only possible during oriented graph traversal) CV GRAPH ANY EDGE stop at any edge (tree, back, forward, and cross edges) CV GRAPH NEW TREE stop in the beginning of every new search tree. When the traversal procedure visits all vertices and edges reachable from the initial vertex (the visited vertices together with tree edges make up a tree), it searches for some unvisited vertex in the graph and resumes the traversal process from that vertex. Before starting a new tree (including the very first tree when cvNextGraphItem is called for the first time) it generates a CV GRAPH NEW TREE event. For unoriented graphs, each search tree corresponds to a connected component of the graph. CV GRAPH BACKTRACKING stop at every already visited vertex during backtracking - return- ing to already visited vertexes of the traversal tree. The function creates a structure for depth-first graph traversal/search. The initialized structure is used in the cvNextGraphItem function - the incremental traversal procedure. cvCreateMemStorage (view/add comments) Creates memory storage. 1.3. DYNAMIC STRUCTURES 157 CvMemStorage* cvCreateMemStorage( int blockSize=0 ); blockSize Size of the storage blocks in bytes. If it is 0, the block size is set to a default value - currently it is about 64K. The function creates an empty memory storage. See CvMemStorage description. cvCreateSeq (view/add comments) Creates a sequence. CvSeq* cvCreateSeq( int seqFlags, int headerSize, int elemSize, CvMemStorage* storage); seqFlags Flags of the created sequence. If the sequence is not passed to any function work- ing with a specific type of sequences, the sequence value may be set to 0, otherwise the appropriate type must be selected from the list of predefined sequence types. headerSize Size of the sequence header; must be greater than or equal to sizeof(CvSeq). If a specific type or its extension is indicated, this type must fit the base type header. elemSize Size of the sequence elements in bytes. The size must be consistent with the se- quence type. For example, for a sequence of points to be created, the element type CV SEQ ELTYPE POINT should be specified and the parameter elemSize must be equal to sizeof(CvPoint). storage Sequence location The function creates a sequence and returns the pointer to it. The function allocates the se- quence header in the storage block as one continuous chunk and sets the structure fields flags, elemSize, headerSize, and storage to passed values, sets delta elems to the default value (that may be reassigned using the cvSetSeqBlockSize function), and clears other header fields, including the space following the first sizeof(CvSeq) bytes. 158 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvCreateSet (view/add comments) Creates an empty set. CvSet* cvCreateSet( int set flags, int header size, int elem size, CvMemStorage* storage ); set flags Type of the created set header size Set header size; may not be less than sizeof(CvSet) elem size Set element size; may not be less than CvSetElem storage Container for the set The function creates an empty set with a specified header size and element size, and returns the pointer to the set. This function is just a thin layer on top of cvCreateSeq. cvCvtSeqToArray (view/add comments) Copies a sequence to one continuous block of memory. void* cvCvtSeqToArray( const CvSeq* seq, void* elements, CvSlice slice=CV WHOLE SEQ ); seq Sequence elements Pointer to the destination array that must be large enough. It should be a pointer to data, not a matrix header. slice The sequence portion to copy to the array The function copies the entire sequence or subsequence to the specified buffer and returns the pointer to the buffer. 1.3. DYNAMIC STRUCTURES 159 cvEndWriteSeq (view/add comments) Finishes the process of writing a sequence. CvSeq* cvEndWriteSeq( CvSeqWriter* writer ); writer Writer state The function finishes the writing process and returns the pointer to the written sequence. The function also truncates the last incomplete sequence block to return the remaining part of the block to memory storage. After that, the sequence can be read and modified safely. See cvcvS- tartWriteSeq and cvcvStartAppendToSeq cvFindGraphEdge (view/add comments) Finds an edge in a graph. CvGraphEdge* cvFindGraphEdge( const CvGraph* graph, int start idx, int end idx ); #define cvGraphFindEdge cvFindGraphEdge graph Graph start idx Index of the starting vertex of the edge end idx Index of the ending vertex of the edge. For an unoriented graph, the order of the vertex parameters does not matter. The function finds the graph edge connecting two specified vertices and returns a pointer to it or NULL if the edge does not exist. 160 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvFindGraphEdgeByPtr (view/add comments) Finds an edge in a graph by using its pointer. CvGraphEdge* cvFindGraphEdgeByPtr( const CvGraph* graph, const CvGraphVtx* startVtx, const CvGraphVtx* endVtx ); #define cvGraphFindEdgeByPtr cvFindGraphEdgeByPtr graph Graph startVtx Pointer to the starting vertex of the edge endVtx Pointer to the ending vertex of the edge. For an unoriented graph, the order of the vertex parameters does not matter. The function finds the graph edge connecting two specified vertices and returns pointer to it or NULL if the edge does not exists. cvFlushSeqWriter (view/add comments) Updates sequence headers from the writer. void cvFlushSeqWriter( CvSeqWriter* writer ); writer Writer state The function is intended to enable the user to read sequence elements, whenever required, during the writing process, e.g., in order to check specific conditions. The function updates the sequence headers to make reading from the sequence possible. The writer is not closed, however, so that the writing process can be continued at any time. If an algorithm requires frequent flushes, consider using cvSeqPush instead. 1.3. DYNAMIC STRUCTURES 161 cvGetGraphVtx (view/add comments) Finds a graph vertex by using its index. CvGraphVtx* cvGetGraphVtx( CvGraph* graph, int vtx idx ); graph Graph vtx idx Index of the vertex The function finds the graph vertex by using its index and returns the pointer to it or NULL if the vertex does not belong to the graph. cvGetSeqElem (view/add comments) Returns a pointer to a sequence element according to its index. char* cvGetSeqElem( const CvSeq* seq, int index ); #define CV_GET_SEQ_ELEM( TYPE, seq, index ) (TYPE*)cvGetSeqElem( (CvSeq*)(seq), (index) ) seq Sequence index Index of element The function finds the element with the given index in the sequence and returns the pointer to it. If the element is not found, the function returns 0. The function supports negative indices, where -1 stands for the last sequence element, -2 stands for the one before last, etc. If the sequence is most likely to consist of a single sequence block or the desired element is likely to be located in the first block, then the macro CV GET SEQ ELEM( elemType, seq, index ) should be used, where the parameter elemType is the type of sequence elements ( CvPoint for example), the parameter seq is a sequence, and the parameter index is the index of the desired element. The macro checks first whether the desired element belongs to the first block of the sequence and returns it if it does; otherwise the macro calls the main function GetSeqElem. Negative indices always cause the cvGetSeqElem call. The function has O(1) time complexity assuming that the number of blocks is much smaller than the number of elements. 162 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvGetSeqReaderPos (view/add comments) Returns the current reader position. int cvGetSeqReaderPos( CvSeqReader* reader ); reader Reader state The function returns the current reader position (within 0 ... reader->seq->total - 1). cvGetSetElem (view/add comments) Finds a set element by its index. CvSetElem* cvGetSetElem( const CvSet* setHeader, int index ); setHeader Set index Index of the set element within a sequence The function finds a set element by its index. The function returns the pointer to it or 0 if the index is invalid or the corresponding node is free. The function supports negative indices as it uses cvGetSeqElem to locate the node. cvGraphAddEdge (view/add comments) Adds an edge to a graph. int cvGraphAddEdge( CvGraph* graph, int start idx, 1.3. DYNAMIC STRUCTURES 163 int end idx, const CvGraphEdge* edge=NULL, CvGraphEdge** inserted edge=NULL ); graph Graph start idx Index of the starting vertex of the edge end idx Index of the ending vertex of the edge. For an unoriented graph, the order of the vertex parameters does not matter. edge Optional input parameter, initialization data for the edge inserted edge Optional output parameter to contain the address of the inserted edge The function connects two specified vertices. The function returns 1 if the edge has been added successfully, 0 if the edge connecting the two vertices exists already and -1 if either of the vertices was not found, the starting and the ending vertex are the same, or there is some other critical situation. In the latter case (i.e., when the result is negative), the function also reports an error by default. cvGraphAddEdgeByPtr (view/add comments) Adds an edge to a graph by using its pointer. int cvGraphAddEdgeByPtr( CvGraph* graph, CvGraphVtx* start vtx, CvGraphVtx* end vtx, const CvGraphEdge* edge=NULL, CvGraphEdge** inserted edge=NULL ); graph Graph start vtx Pointer to the starting vertex of the edge end vtx Pointer to the ending vertex of the edge. For an unoriented graph, the order of the vertex parameters does not matter. 164 CHAPTER 1. CORE. THE CORE FUNCTIONALITY edge Optional input parameter, initialization data for the edge inserted edge Optional output parameter to contain the address of the inserted edge within the edge set The function connects two specified vertices. The function returns 1 if the edge has been added successfully, 0 if the edge connecting the two vertices exists already, and -1 if either of the vertices was not found, the starting and the ending vertex are the same or there is some other critical situation. In the latter case (i.e., when the result is negative), the function also reports an error by default. cvGraphAddVtx (view/add comments) Adds a vertex to a graph. int cvGraphAddVtx( CvGraph* graph, const CvGraphVtx* vtx=NULL, CvGraphVtx** inserted vtx=NULL ); graph Graph vtx Optional input argument used to initialize the added vertex (only user-defined fields beyond sizeof(CvGraphVtx) are copied) inserted vertex Optional output argument. If not NULL, the address of the new vertex is written here. The function adds a vertex to the graph and returns the vertex index. cvGraphEdgeIdx (view/add comments) Returns the index of a graph edge. int cvGraphEdgeIdx( CvGraph* graph, CvGraphEdge* edge ); 1.3. DYNAMIC STRUCTURES 165 graph Graph edge Pointer to the graph edge The function returns the index of a graph edge. cvGraphRemoveEdge (view/add comments) Removes an edge from a graph. void cvGraphRemoveEdge( CvGraph* graph, int start idx, int end idx ); graph Graph start idx Index of the starting vertex of the edge end idx Index of the ending vertex of the edge. For an unoriented graph, the order of the vertex parameters does not matter. The function removes the edge connecting two specified vertices. If the vertices are not con- nected [in that order], the function does nothing. cvGraphRemoveEdgeByPtr (view/add comments) Removes an edge from a graph by using its pointer. void cvGraphRemoveEdgeByPtr( CvGraph* graph, CvGraphVtx* start vtx, CvGraphVtx* end vtx ); graph Graph 166 CHAPTER 1. CORE. THE CORE FUNCTIONALITY start vtx Pointer to the starting vertex of the edge end vtx Pointer to the ending vertex of the edge. For an unoriented graph, the order of the vertex parameters does not matter. The function removes the edge connecting two specified vertices. If the vertices are not con- nected [in that order], the function does nothing. cvGraphRemoveVtx (view/add comments) Removes a vertex from a graph. int cvGraphRemoveVtx( CvGraph* graph, int index ); graph Graph vtx idx Index of the removed vertex The function removes a vertex from a graph together with all the edges incident to it. The function reports an error if the input vertex does not belong to the graph. The return value is the number of edges deleted, or -1 if the vertex does not belong to the graph. cvGraphRemoveVtxByPtr (view/add comments) Removes a vertex from a graph by using its pointer. int cvGraphRemoveVtxByPtr( CvGraph* graph, CvGraphVtx* vtx ); graph Graph vtx Pointer to the removed vertex 1.3. DYNAMIC STRUCTURES 167 The function removes a vertex from the graph by using its pointer together with all the edges incident to it. The function reports an error if the vertex does not belong to the graph. The return value is the number of edges deleted, or -1 if the vertex does not belong to the graph. cvGraphVtxDegree (view/add comments) Counts the number of edges indicent to the vertex. int cvGraphVtxDegree( const CvGraph* graph, int vtxIdx ); graph Graph vtxIdx Index of the graph vertex The function returns the number of edges incident to the specified vertex, both incoming and outgoing. To count the edges, the following code is used: CvGraphEdge* edge = vertex->first; int count = 0; while( edge ) { edge = CV_NEXT_GRAPH_EDGE( edge, vertex ); count++; } The macro CV NEXT GRAPH EDGE( edge, vertex ) returns the edge incident to vertex that follows after edge. cvGraphVtxDegreeByPtr (view/add comments) Finds an edge in a graph. int cvGraphVtxDegreeByPtr( const CvGraph* graph, const CvGraphVtx* vtx ); graph Graph 168 CHAPTER 1. CORE. THE CORE FUNCTIONALITY vtx Pointer to the graph vertex The function returns the number of edges incident to the specified vertex, both incoming and outcoming. cvGraphVtxIdx (view/add comments) Returns the index of a graph vertex. int cvGraphVtxIdx( CvGraph* graph, CvGraphVtx* vtx ); graph Graph vtx Pointer to the graph vertex The function returns the index of a graph vertex. cvInitTreeNodeIterator (view/add comments) Initializes the tree node iterator. void cvInitTreeNodeIterator( CvTreeNodeIterator* tree iterator, const void* first, int max level ); tree iterator Tree iterator initialized by the function first The initial node to start traversing from max level The maximal level of the tree (first node assumed to be at the first level) to traverse up to. For example, 1 means that only nodes at the same level as first should be visited, 2 means that the nodes on the same level as first and their direct children should be visited, and so forth. The function initializes the tree iterator. The tree is traversed in depth-first order. 1.3. DYNAMIC STRUCTURES 169 cvInsertNodeIntoTree (view/add comments) Adds a new node to a tree. void cvInsertNodeIntoTree( void* node, void* parent, void* frame ); node The inserted node parent The parent node that is already in the tree frame The top level node. If parent and frame are the same, the v prev field of node is set to NULL rather than parent. The function adds another node into tree. The function does not allocate any memory, it can only modify links of the tree nodes. cvMakeSeqHeaderForArray (view/add comments) Constructs a sequence header for an array. CvSeq* cvMakeSeqHeaderForArray( int seq type, int header size, int elem size, void* elements, int total, CvSeq* seq, CvSeqBlock* block ); seq type Type of the created sequence header size Size of the header of the sequence. Parameter sequence must point to the struc- ture of that size or greater 170 CHAPTER 1. CORE. THE CORE FUNCTIONALITY elem size Size of the sequence elements elements Elements that will form a sequence total Total number of elements in the sequence. The number of array elements must be equal to the value of this parameter. seq Pointer to the local variable that is used as the sequence header block Pointer to the local variable that is the header of the single sequence block The function initializes a sequence header for an array. The sequence header as well as the sequence block are allocated by the user (for example, on stack). No data is copied by the function. The resultant sequence will consists of a single block and have NULL storage pointer; thus, it is possible to read its elements, but the attempts to add elements to the sequence will raise an error in most cases. cvMemStorageAlloc (view/add comments) Allocates a memory buffer in a storage block. void* cvMemStorageAlloc( CvMemStorage* storage, size t size ); storage Memory storage size Buffer size The function allocates a memory buffer in a storage block. The buffer size must not exceed the storage block size, otherwise a runtime error is raised. The buffer address is aligned by CV STRUCT ALIGN=sizeof(double) (for the moment) bytes. cvMemStorageAllocString (view/add comments) Allocates a text string in a storage block. 1.3. DYNAMIC STRUCTURES 171 CvString cvMemStorageAllocString(CvMemStorage* storage, const char* ptr, int len=-1); typedef struct CvString { int len; char* ptr; } CvString; storage Memory storage ptr The string len Length of the string (not counting the ending NUL) . If the parameter is negative, the function computes the length. The function creates copy of the string in memory storage. It returns the structure that contains user-passed or computed length of the string and pointer to the copied string. cvNextGraphItem (view/add comments) Executes one or more steps of the graph traversal procedure. int cvNextGraphItem( CvGraphScanner* scanner ); scanner Graph traversal state. It is updated by this function. The function traverses through the graph until an event of interest to the user (that is, an event, specified in the mask in the cvCreateGraphScanner call) is met or the traversal is completed. In the first case, it returns one of the events listed in the description of the mask parameter above and with the next call it resumes the traversal. In the latter case, it returns CV GRAPH OVER (-1). When the event is CV GRAPH VERTEX, CV GRAPH BACKTRACKING, or CV GRAPH NEW TREE, the currently observed vertex is stored in scanner->vtx. And if the event is edge-related, the edge itself is stored at scanner->edge, the previously visited vertex - at scanner->vtx and the other ending vertex of the edge - at scanner->dst. 172 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvNextTreeNode (view/add comments) Returns the currently observed node and moves the iterator toward the next node. void* cvNextTreeNode( CvTreeNodeIterator* tree iterator ); tree iterator Tree iterator initialized by the function The function returns the currently observed node and then updates the iterator - moving it toward the next node. In other words, the function behavior is similar to the *p++ expression on a typical C pointer or C++ collection iterator. The function returns NULL if there are no more nodes. cvPrevTreeNode (view/add comments) Returns the currently observed node and moves the iterator toward the previous node. void* cvPrevTreeNode( CvTreeNodeIterator* tree iterator ); tree iterator Tree iterator initialized by the function The function returns the currently observed node and then updates the iterator - moving it toward the previous node. In other words, the function behavior is similar to the *p-- expression on a typical C pointer or C++ collection iterator. The function returns NULL if there are no more nodes. cvReleaseGraphScanner (view/add comments) Completes the graph traversal procedure. void cvReleaseGraphScanner( CvGraphScanner** scanner ); scanner Double pointer to graph traverser The function completes the graph traversal procedure and releases the traverser state. 1.3. DYNAMIC STRUCTURES 173 cvReleaseMemStorage (view/add comments) Releases memory storage. void cvReleaseMemStorage( CvMemStorage** storage ); storage Pointer to the released storage The function deallocates all storage memory blocks or returns them to the parent, if any. Then it deallocates the storage header and clears the pointer to the storage. All child storage associated with a given parent storage block must be released before the parent storage block is released. cvRestoreMemStoragePos (view/add comments) Restores memory storage position. void cvRestoreMemStoragePos( CvMemStorage* storage, CvMemStoragePos* pos); storage Memory storage pos New storage top position The function restores the position of the storage top from the parameter pos. This function and the function cvClearMemStorage are the only methods to release memory occupied in memory blocks. Note again that there is no way to free memory in the middle of an occupied portion of a storage block. cvSaveMemStoragePos (view/add comments) Saves memory storage position. 174 CHAPTER 1. CORE. THE CORE FUNCTIONALITY void cvSaveMemStoragePos( const CvMemStorage* storage, CvMemStoragePos* pos); storage Memory storage pos The output position of the storage top The function saves the current position of the storage top to the parameter pos. The function cvRestoreMemStoragePos can further retrieve this position. cvSeqElemIdx (view/add comments) Returns the index of a specific sequence element. int cvSeqElemIdx( const CvSeq* seq, const void* element, CvSeqBlock** block=NULL ); seq Sequence element Pointer to the element within the sequence block Optional argument. If the pointer is not NULL, the address of the sequence block that contains the element is stored in this location. The function returns the index of a sequence element or a negative number if the element is not found. cvSeqInsert (view/add comments) Inserts an element in the middle of a sequence. 1.3. DYNAMIC STRUCTURES 175 char* cvSeqInsert( CvSeq* seq, int beforeIndex, void* element=NULL ); seq Sequence beforeIndex Index before which the element is inserted. Inserting before 0 (the minimal allowed value of the parameter) is equal to cvSeqPushFront and inserting before seq->total (the maximal allowed value of the parameter) is equal to cvSeqPush. element Inserted element The function shifts the sequence elements from the inserted position to the nearest end of the sequence and copies the element content there if the pointer is not NULL. The function returns a pointer to the inserted element. cvSeqInsertSlice (view/add comments) Inserts an array in the middle of a sequence. void cvSeqInsertSlice( CvSeq* seq, int beforeIndex, const CvArr* fromArr ); seq Sequence slice The part of the sequence to remove fromArr The array to take elements from The function inserts all fromArr array elements at the specified position of the sequence. The array fromArr can be a matrix or another sequence. 176 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvSeqInvert (view/add comments) Reverses the order of sequence elements. void cvSeqInvert( CvSeq* seq ); seq Sequence The function reverses the sequence in-place - makes the first element go last, the last element go first and so forth. cvSeqPop (view/add comments) Removes an element from the end of a sequence. void cvSeqPop( CvSeq* seq, void* element=NULL ); seq Sequence element Optional parameter . If the pointer is not zero, the function copies the removed element to this location. The function removes an element from a sequence. The function reports an error if the se- quence is already empty. The function has O(1) complexity. cvSeqPopFront (view/add comments) Removes an element from the beginning of a sequence. 1.3. DYNAMIC STRUCTURES 177 void cvSeqPopFront( CvSeq* seq, void* element=NULL ); seq Sequence element Optional parameter. If the pointer is not zero, the function copies the removed element to this location. The function removes an element from the beginning of a sequence. The function reports an error if the sequence is already empty. The function has O(1) complexity. cvSeqPopMulti (view/add comments) Removes several elements from either end of a sequence. void cvSeqPopMulti( CvSeq* seq, void* elements, int count, int in front=0 ); seq Sequence elements Removed elements count Number of elements to pop in front The flags specifying which end of the modified sequence. CV BACK the elements are added to the end of the sequence CV FRONT the elements are added to the beginning of the sequence The function removes several elements from either end of the sequence. If the number of the elements to be removed exceeds the total number of elements in the sequence, the function removes as many elements as possible. 178 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvSeqPush (view/add comments) Adds an element to the end of a sequence. char* cvSeqPush( CvSeq* seq, void* element=NULL ); seq Sequence element Added element The function adds an element to the end of a sequence and returns a pointer to the allo- cated element. If the input element is NULL, the function simply allocates a space for one more element. The following code demonstrates how to create a new sequence using this function: CvMemStorage* storage = cvCreateMemStorage(0); CvSeq* seq = cvCreateSeq( CV_32SC1, /* sequence of integer elements */ sizeof(CvSeq), /* header size - no extra fields */ sizeof(int), /* element size */ storage /* the container storage */ ); int i; for( i = 0; i < 100; i++ ) { int* added = (int*)cvSeqPush( seq, &i ); printf( "%d is added\n", *added ); } ... /* release memory storage in the end */ cvReleaseMemStorage( &storage ); The function has O(1) complexity, but there is a faster method for writing large sequences (see cvStartWriteSeq and related functions). cvSeqPushFront (view/add comments) Adds an element to the beginning of a sequence. 1.3. DYNAMIC STRUCTURES 179 char* cvSeqPushFront( CvSeq* seq, void* element=NULL ); seq Sequence element Added element The function is similar to cvSeqPush but it adds the new element to the beginning of the sequence. The function has O(1) complexity. cvSeqPushMulti (view/add comments) Pushes several elements to either end of a sequence. void cvSeqPushMulti( CvSeq* seq, void* elements, int count, int in front=0 ); seq Sequence elements Added elements count Number of elements to push in front The flags specifying which end of the modified sequence. CV BACK the elements are added to the end of the sequence CV FRONT the elements are added to the beginning of the sequence The function adds several elements to either end of a sequence. The elements are added to the sequence in the same order as they are arranged in the input array but they can fall into different sequence blocks. 180 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvSeqRemove (view/add comments) Removes an element from the middle of a sequence. void cvSeqRemove( CvSeq* seq, int index ); seq Sequence index Index of removed element The function removes elements with the given index. If the index is out of range the function reports an error. An attempt to remove an element from an empty sequence is a special case of this situation. The function removes an element by shifting the sequence elements between the nearest end of the sequence and the index-th position, not counting the latter. cvSeqRemoveSlice (view/add comments) Removes a sequence slice. void cvSeqRemoveSlice( CvSeq* seq, CvSlice slice ); seq Sequence slice The part of the sequence to remove The function removes a slice from the sequence. cvSeqSearch (view/add comments) Searches for an element in a sequence. 1.3. DYNAMIC STRUCTURES 181 char* cvSeqSearch( CvSeq* seq, const void* elem, CvCmpFunc func, int is sorted, int* elem idx, void* userdata=NULL ); seq The sequence elem The element to look for func The comparison function that returns negative, zero or positive value depending on the relationships among the elements (see also cvSeqSort) is sorted Whether the sequence is sorted or not elem idx Output parameter; index of the found element userdata The user parameter passed to the compasion function; helps to avoid global variables in some cases /* a < b ? -1 : a > b ? 1 : 0 */ typedef int (CV_CDECL* CvCmpFunc)(const void* a, const void* b, void* userdata); The function searches for the element in the sequence. If the sequence is sorted, a binary O(log(N)) search is used; otherwise, a simple linear search is used. If the element is not found, the function returns a NULL pointer and the index is set to the number of sequence elements if a linear search is used, or to the smallest index i, seq(i)>elem. cvSeqSlice (view/add comments) Makes a separate header for a sequence slice. CvSeq* cvSeqSlice( const CvSeq* seq, CvSlice slice, CvMemStorage* storage=NULL, int copy data=0 ); seq Sequence 182 CHAPTER 1. CORE. THE CORE FUNCTIONALITY slice The part of the sequence to be extracted storage The destination storage block to hold the new sequence header and the copied data, if any. If it is NULL, the function uses the storage block containing the input sequence. copy data The flag that indicates whether to copy the elements of the extracted slice (copy data!=0) or not (copy data=0) The function creates a sequence that represents the specified slice of the input sequence. The new sequence either shares the elements with the original sequence or has its own copy of the elements. So if one needs to process a part of sequence but the processing function does not have a slice parameter, the required sub-sequence may be extracted using this function. cvSeqSort (view/add comments) Sorts sequence element using the specified comparison function. void cvSeqSort( CvSeq* seq, CvCmpFunc func, void* userdata=NULL ); /* a < b ? -1 : a > b ? 1 : 0 */ typedef int (CV_CDECL* CvCmpFunc)(const void* a, const void* b, void* userdata); seq The sequence to sort func The comparison function that returns a negative, zero, or positive value depending on the relationships among the elements (see the above declaration and the example below) - a similar function is used by qsort from C runline except that in the latter, userdata is not used userdata The user parameter passed to the compasion function; helps to avoid global variables in some cases The function sorts the sequence in-place using the specified criteria. Below is an example of using this function: /* Sort 2d points in top-to-bottom left-to-right order */ static int cmp_func( const void*_a, const void*_b, void* userdata ) { CvPoint* a = (CvPoint*)_a; 1.3. DYNAMIC STRUCTURES 183 CvPoint* b = (CvPoint*)_b; int y_diff = a->y - b->y; int x_diff = a->x - b->x; return y_diff ? y_diff : x_diff; } ... CvMemStorage* storage = cvCreateMemStorage(0); CvSeq* seq = cvCreateSeq( CV_32SC2, sizeof(CvSeq), sizeof(CvPoint), storage ); int i; for( i = 0; i < 10; i++ ) { CvPoint pt; pt.x = rand() % 1000; pt.y = rand() % 1000; cvSeqPush( seq, &pt ); } cvSeqSort( seq, cmp_func, 0 /* userdata is not used here */ ); /* print out the sorted sequence */ for( i = 0; i < seq->total; i++ ) { CvPoint* pt = (CvPoint*)cvSeqElem( seq, i ); printf( "(%d,%d)\n", pt->x, pt->y ); } cvReleaseMemStorage( &storage ); cvSetAdd (view/add comments) Occupies a node in the set. int cvSetAdd( CvSet* setHeader, CvSetElem* elem=NULL, CvSetElem** inserted elem=NULL ); 184 CHAPTER 1. CORE. THE CORE FUNCTIONALITY setHeader Set elem Optional input argument, an inserted element. If not NULL, the function copies the data to the allocated node (the MSB of the first integer field is cleared after copying). inserted elem Optional output argument; the pointer to the allocated cell The function allocates a new node, optionally copies input element data to it, and returns the pointer and the index to the node. The index value is taken from the lower bits of the flags field of the node. The function has O(1) complexity; however, there exists a faster function for allocating set nodes (see cvSetNew). cvSetNew (view/add comments) Adds an element to a set (fast variant). CvSetElem* cvSetNew( CvSet* setHeader ); setHeader Set The function is an inline lightweight variant of cvSetAdd. It occupies a new node and returns a pointer to it rather than an index. cvSetRemove (view/add comments) Removes an element from a set. void cvSetRemove( CvSet* setHeader, int index ); setHeader Set index Index of the removed element The function removes an element with a specified index from the set. If the node at the spec- ified location is not occupied, the function does nothing. The function has O(1) complexity; how- ever, cvSetRemoveByPtr provides a quicker way to remove a set element if it is located already. 1.3. DYNAMIC STRUCTURES 185 cvSetRemoveByPtr (view/add comments) Removes a set element based on its pointer. void cvSetRemoveByPtr( CvSet* setHeader, void* elem ); setHeader Set elem Removed element The function is an inline lightweight variant of cvSetRemove that requires an element pointer. The function does not check whether the node is occupied or not - the user should take care of that. cvSetSeqBlockSize (view/add comments) Sets up sequence block size. void cvSetSeqBlockSize( CvSeq* seq, int deltaElems ); seq Sequence deltaElems Desirable sequence block size for elements The function affects memory allocation granularity. When the free space in the sequence buffers has run out, the function allocates the space for deltaElems sequence elements. If this block immediately follows the one previously allocated, the two blocks are concatenated; other- wise, a new sequence block is created. Therefore, the bigger the parameter is, the lower the possible sequence fragmentation, but the more space in the storage block is wasted. When the sequence is created, the parameter deltaElems is set to the default value of about 1K. The function can be called any time after the sequence is created and affects future allocations. The function can modify the passed value of the parameter to meet memory storage constraints. 186 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvSetSeqReaderPos (view/add comments) Moves the reader to the specified position. void cvSetSeqReaderPos( CvSeqReader* reader, int index, int is relative=0 ); reader Reader state index The destination position. If the positioning mode is used (see the next parameter), the actual position will be index mod reader->seq->total. is relative If it is not zero, then index is a relative to the current position The function moves the read position to an absolute position or relative to the current position. cvStartAppendToSeq (view/add comments) Initializes the process of writing data to a sequence. void cvStartAppendToSeq( CvSeq* seq, CvSeqWriter* writer ); seq Pointer to the sequence writer Writer state; initialized by the function The function initializes the process of writing data to a sequence. Written elements are added to the end of the sequence by using the CV WRITE SEQ ELEM( written elem, writer ) macro. Note that during the writing process, other operations on the sequence may yield an incorrect result or even corrupt the sequence (see description of cvFlushSeqWriter, which helps to avoid some of these problems). 1.3. DYNAMIC STRUCTURES 187 cvStartReadSeq (view/add comments) Initializes the process of sequential reading from a sequence. void cvStartReadSeq( const CvSeq* seq, CvSeqReader* reader, int reverse=0 ); seq Sequence reader Reader state; initialized by the function reverse Determines the direction of the sequence traversal. If reverse is 0, the reader is positioned at the first sequence element; otherwise it is positioned at the last element. The function initializes the reader state. After that, all the sequence elements from the first one down to the last one can be read by subsequent calls of the macro CV READ SEQ ELEM( read elem, reader ) in the case of forward reading and by using CV REV READ SEQ ELEM( read elem, reader ) in the case of reverse reading. Both macros put the sequence element to read elem and move the reading pointer toward the next element. A circular structure of sequence blocks is used for the reading process, that is, after the last element has been read by the macro CV READ SEQ ELEM, the first element is read when the macro is called again. The same applies to CV REV READ SEQ ELEM. There is no function to finish the reading process, since it neither changes the sequence nor creates any temporary buffers. The reader field ptr points to the current element of the sequence that is to be read next. The code below demonstrates how to use the sequence writer and reader. CvMemStorage* storage = cvCreateMemStorage(0); CvSeq* seq = cvCreateSeq( CV_32SC1, sizeof(CvSeq), sizeof(int), storage ); CvSeqWriter writer; CvSeqReader reader; int i; cvStartAppendToSeq( seq, &writer ); for( i = 0; i < 10; i++ ) { int val = rand()%100; CV_WRITE_SEQ_ELEM( val, writer ); printf("%d is written\n", val ); 188 CHAPTER 1. CORE. THE CORE FUNCTIONALITY } cvEndWriteSeq( &writer ); cvStartReadSeq( seq, &reader, 0 ); for( i = 0; i < seq->total; i++ ) { int val; #if 1 CV_READ_SEQ_ELEM( val, reader ); printf("%d is read\n", val ); #else /* alternative way, that is prefferable if sequence elements are large, or their size/type is unknown at compile time */ printf("%d is read\n", *(int*)reader.ptr ); CV_NEXT_SEQ_ELEM( seq->elem_size, reader ); #endif } ... cvReleaseStorage( &storage ); cvStartWriteSeq (view/add comments) Creates a new sequence and initializes a writer for it. void cvStartWriteSeq( int seq flags, int header size, int elem size, CvMemStorage* storage, CvSeqWriter* writer ); seq flags Flags of the created sequence. If the sequence is not passed to any function working with a specific type of sequences, the sequence value may be equal to 0; otherwise the appropriate type must be selected from the list of predefined sequence types. header size Size of the sequence header. The parameter value may not be less than sizeof(CvSeq). If a certain type or extension is specified, it must fit within the base type header. 1.4. DRAWING FUNCTIONS 189 elem size Size of the sequence elements in bytes; must be consistent with the sequence type. For example, if a sequence of points is created (element type CV SEQ ELTYPE POINT ), then the parameter elem size must be equal to sizeof(CvPoint). storage Sequence location writer Writer state; initialized by the function The function is a combination of cvCreateSeq and cvStartAppendToSeq. The pointer to the created sequence is stored at writer->seq and is also returned by the cvEndWriteSeq function that should be called at the end. cvTreeToNodeSeq (view/add comments) Gathers all node pointers to a single sequence. CvSeq* cvTreeToNodeSeq( const void* first, int header size, CvMemStorage* storage ); first The initial tree node header size Header size of the created sequence (sizeof(CvSeq) is the most frequently used value) storage Container for the sequence The function puts pointers of all nodes reacheable from first into a single sequence. The pointers are written sequentially in the depth-first order. 1.4 Drawing Functions Drawing functions work with matrices/images of arbitrary depth. The boundaries of the shapes can be rendered with antialiasing (implemented only for 8-bit images for now). All the functions include the parameter color that uses a rgb value (that may be constructed with CV RGB macro or the cv function ) for color images and brightness for grayscale images. For color images the 190 CHAPTER 1. CORE. THE CORE FUNCTIONALITY order channel is normally Blue, Green, Red, this is what cv, cv and cv expect , so if you form a color using cv, it should look like: cvScalar(blue component, green component, red component[, alpha component]) If you are using your own image rendering and I/O functions, you can use any channel ordering, the drawing functions process each channel independently and do not depend on the channel order or even on the color space used. The whole image can be converted from BGR to RGB or to a different color space using cv. If a drawn figure is partially or completely outside the image, the drawing functions clip it. Also, many drawing functions can handle pixel coordinates specified with sub-pixel accuracy, that is, the coordinates can be passed as fixed-point numbers, encoded as integers. The number of fractional bits is specified by the shift parameter and the real point coordinates are calculated as Point(x, y) → Point2f(x∗2−shift, y∗2−shift). This feature is especially effective wehn rendering antialiased shapes. Also, note that the functions do not support alpha-transparency - when the target image is 4-channnel, then the color[3] is simply copied to the repainted pixels. Thus, if you want to paint semi-transparent shapes, you can paint them in a separate buffer and then blend it with the main image. cvCircle (view/add comments) Draws a circle. void cvCircle( CvArr* img, CvPoint center, int radius, CvScalar color, int thickness=1, int lineType=8, int shift=0 ); img Image where the circle is drawn center Center of the circle radius Radius of the circle 1.4. DRAWING FUNCTIONS 191 color Circle color thickness Thickness of the circle outline if positive, otherwise this indicates that a filled circle is to be drawn lineType Type of the circle boundary, see Line description shift Number of fractional bits in the center coordinates and radius value The function draws a simple or filled circle with a given center and radius. cvClipLine (view/add comments) Clips the line against the image rectangle. int cvClipLine( CvSize imgSize, CvPoint* pt1, CvPoint* pt2 ); imgSize Size of the image pt1 First ending point of the line segment. It is modified by the function. pt2 Second ending point of the line segment. It is modified by the function. The function calculates a part of the line segment which is entirely within the image. It returns 0 if the line segment is completely outside the image and 1 otherwise. cvDrawContours (view/add comments) Draws contour outlines or interiors in an image. void cvDrawContours( CvArr *img, CvSeq* contour, CvScalar external color, 192 CHAPTER 1. CORE. THE CORE FUNCTIONALITY CvScalar hole color, int max level, int thickness=1, int lineType=8 ); img Image where the contours are to be drawn. As with any other drawing function, the contours are clipped with the ROI. contour Pointer to the first contour external color Color of the external contours hole color Color of internal contours (holes) max level Maximal level for drawn contours. If 0, only contour is drawn. If 1, the contour and all contours following it on the same level are drawn. If 2, all contours following and all contours one level below the contours are drawn, and so forth. If the value is negative, the function does not draw the contours following after contour but draws the child contours of contour up to the |max level| − 1 level. thickness Thickness of lines the contours are drawn with. If it is negative (For example, =CV FILLED), the contour interiors are drawn. lineType Type of the contour segments, see Line description The function draws contour outlines in the image if thickness ≥ 0 or fills the area bounded by the contours if thickness < 0. Example: Connected component detection via contour functions #include "cv.h" #include "highgui.h" int main( int argc, char** argv ) { IplImage* src; // the first command line parameter must be file name of binary // (black-n-white) image if( argc == 2 && (src=cvLoadImage(argv[1], 0))!= 0) { IplImage* dst = cvCreateImage( cvGetSize(src), 8, 3 ); CvMemStorage* storage = cvCreateMemStorage(0); CvSeq* contour = 0; 1.4. DRAWING FUNCTIONS 193 cvThreshold( src, src, 1, 255, CV_THRESH_BINARY ); cvNamedWindow( "Source", 1 ); cvShowImage( "Source", src ); cvFindContours( src, storage, &contour, sizeof(CvContour), CV_RETR_CCOMP, CV_CHAIN_APPROX_SIMPLE ); cvZero( dst ); for( ; contour != 0; contour = contour->h_next ) { CvScalar color = CV_RGB( rand()&255, rand()&255, rand()&255 ); /* replace CV_FILLED with 1 to see the outlines */ cvDrawContours( dst, contour, color, color, -1, CV_FILLED, 8 ); } cvNamedWindow( "Components", 1 ); cvShowImage( "Components", dst ); cvWaitKey(0); } } cvEllipse (view/add comments) Draws a simple or thick elliptic arc or an fills ellipse sector. void cvEllipse( CvArr* img, CvPoint center, CvSize axes, double angle, double start angle, double end angle, CvScalar color, int thickness=1, int lineType=8, int shift=0 ); img The image 194 CHAPTER 1. CORE. THE CORE FUNCTIONALITY center Center of the ellipse axes Length of the ellipse axes angle Rotation angle start angle Starting angle of the elliptic arc end angle Ending angle of the elliptic arc. color Ellipse color thickness Thickness of the ellipse arc outline if positive, otherwise this indicates that a filled ellipse sector is to be drawn lineType Type of the ellipse boundary, see Line description shift Number of fractional bits in the center coordinates and axes’ values The function draws a simple or thick elliptic arc or fills an ellipse sector. The arc is clipped by the ROI rectangle. A piecewise-linear approximation is used for antialiased arcs and thick arcs. All the angles are given in degrees. The picture below explains the meaning of the parameters. Parameters of Elliptic Arc cvEllipseBox (view/add comments) Draws a simple or thick elliptic arc or fills an ellipse sector. 1.4. DRAWING FUNCTIONS 195 void cvEllipseBox( CvArr* img, CvBox2D box, CvScalar color, int thickness=1, int lineType=8, int shift=0 ); img Image box The enclosing box of the ellipse drawn thickness Thickness of the ellipse boundary lineType Type of the ellipse boundary, see Line description shift Number of fractional bits in the box vertex coordinates The function draws a simple or thick ellipse outline, or fills an ellipse. The functions provides a convenient way to draw an ellipse approximating some shape; that is what CamShift and FitEllipse do. The ellipse drawn is clipped by ROI rectangle. A piecewise-linear approximation is used for antialiased arcs and thick arcs. cvFillConvexPoly (view/add comments) Fills a convex polygon. void cvFillConvexPoly( CvArr* img, CvPoint* pts, int npts, CvScalar color, int lineType=8, int shift=0 ); img Image 196 CHAPTER 1. CORE. THE CORE FUNCTIONALITY pts Array of pointers to a single polygon npts Polygon vertex counter color Polygon color lineType Type of the polygon boundaries, see Line description shift Number of fractional bits in the vertex coordinates The function fills a convex polygon’s interior. This function is much faster than the function cvFillPoly and can fill not only convex polygons but any monotonic polygon, i.e., a polygon whose contour intersects every horizontal line (scan line) twice at the most. cvFillPoly (view/add comments) Fills a polygon’s interior. void cvFillPoly( CvArr* img, CvPoint** pts, int* npts, int contours, CvScalar color, int lineType=8, int shift=0 ); img Image pts Array of pointers to polygons npts Array of polygon vertex counters contours Number of contours that bind the filled region color Polygon color lineType Type of the polygon boundaries, see Line description shift Number of fractional bits in the vertex coordinates The function fills an area bounded by several polygonal contours. The function fills complex areas, for example, areas with holes, contour self-intersection, and so forth. 1.4. DRAWING FUNCTIONS 197 cvGetTextSize (view/add comments) Retrieves the width and height of a text string. void cvGetTextSize( const char* textString, const CvFont* font, CvSize* textSize, int* baseline ); font Pointer to the font structure textString Input string textSize Resultant size of the text string. Height of the text does not include the height of character parts that are below the baseline. baseline y-coordinate of the baseline relative to the bottom-most text point The function calculates the dimensions of a rectangle to enclose a text string when a specified font is used. cvInitFont (view/add comments) Initializes font structure. void cvInitFont( CvFont* font, int fontFace, double hscale, double vscale, double shear=0, int thickness=1, int lineType=8 ); font Pointer to the font structure initialized by the function 198 CHAPTER 1. CORE. THE CORE FUNCTIONALITY fontFace Font name identifier. Only a subset of Hershey fonts http://sources.isc.org/ utils/misc/hershey-font.txt are supported now: CV FONT HERSHEY SIMPLEX normal size sans-serif font CV FONT HERSHEY PLAIN small size sans-serif font CV FONT HERSHEY DUPLEX normal size sans-serif font (more complex than CV FONT HERSHEY SIMPLEX) CV FONT HERSHEY COMPLEX normal size serif font CV FONT HERSHEY TRIPLEX normal size serif font (more complex than CV FONT HERSHEY COMPLEX) CV FONT HERSHEY COMPLEX SMALL smaller version of CV FONT HERSHEY COMPLEX CV FONT HERSHEY SCRIPT SIMPLEX hand-writing style font CV FONT HERSHEY SCRIPT COMPLEX more complex variant of CV FONT HERSHEY SCRIPT SIMPLEX The parameter can be composited from one of the values above and an optional CV FONT ITALIC flag, which indicates italic or oblique font. hscale Horizontal scale. If equal to 1.0f, the characters have the original width depending on the font type. If equal to 0.5f, the characters are of half the original width. vscale Vertical scale. If equal to 1.0f, the characters have the original height depending on the font type. If equal to 0.5f, the characters are of half the original height. shear Approximate tangent of the character slope relative to the vertical line. A zero value means a non-italic font, 1.0f means about a 45 degree slope, etc. thickness Thickness of the text strokes lineType Type of the strokes, see Line description The function initializes the font structure that can be passed to text rendering functions. cvInitLineIterator (view/add comments) Initializes the line iterator. int cvInitLineIterator( const CvArr* image, CvPoint pt1, 1.4. DRAWING FUNCTIONS 199 CvPoint pt2, CvLineIterator* line iterator, int connectivity=8, int left to right=0 ); image Image to sample the line from pt1 First ending point of the line segment pt2 Second ending point of the line segment line iterator Pointer to the line iterator state structure connectivity The scanned line connectivity, 4 or 8. left to right If (left to right = 0 ) then the line is scanned in the specified order, from pt1 to pt2. If (left to right 6= 0) the line is scanned from left-most point to right-most. The function initializes the line iterator and returns the number of pixels between the two end points. Both points must be inside the image. After the iterator has been initialized, all the points on the raster line that connects the two ending points may be retrieved by successive calls of CV NEXT LINE POINT point. The points on the line are calculated one by one using a 4-connected or 8-connected Bresen- ham algorithm. Example: Using line iterator to calculate the sum of pixel values along the color line. CvScalar sum_line_pixels( IplImage* image, CvPoint pt1, CvPoint pt2 ) { CvLineIterator iterator; int blue_sum = 0, green_sum = 0, red_sum = 0; int count = cvInitLineIterator( image, pt1, pt2, &iterator, 8, 0 ); for( int i = 0; i < count; i++ ){ blue_sum += iterator.ptr[0]; green_sum += iterator.ptr[1]; red_sum += iterator.ptr[2]; CV_NEXT_LINE_POINT(iterator); /* print the pixel coordinates: demonstrates how to calculate the coordinates */ { 200 CHAPTER 1. CORE. THE CORE FUNCTIONALITY int offset, x, y; /* assume that ROI is not set, otherwise need to take it into account. */ offset = iterator.ptr - (uchar*)(image->imageData); y = offset/image->widthStep; x = (offset - y*image->widthStep)/(3*sizeof(uchar) /* size of pixel */); printf("(%d,%d)\n", x, y ); } } return cvScalar( blue_sum, green_sum, red_sum ); } cvLine (view/add comments) Draws a line segment connecting two points. void cvLine( CvArr* img, CvPoint pt1, CvPoint pt2, CvScalar color, int thickness=1, int lineType=8, int shift=0 ); img The image pt1 First point of the line segment pt2 Second point of the line segment color Line color thickness Line thickness lineType Type of the line: 8 (or omitted) 8-connected line. 4 4-connected line. 1.4. DRAWING FUNCTIONS 201 CV AA antialiased line. shift Number of fractional bits in the point coordinates The function draws the line segment between pt1 and pt2 points in the image. The line is clipped by the image or ROI rectangle. For non-antialiased lines with integer coordinates the 8-connected or 4-connected Bresenham algorithm is used. Thick lines are drawn with rounding endings. Antialiased lines are drawn using Gaussian filtering. To specify the line color, the user may use the macro CV RGB( r, g, b ). cvPolyLine (view/add comments) Draws simple or thick polygons. void cvPolyLine( CvArr* img, CvPoint** pts, int* npts, int contours, int is closed, CvScalar color, int thickness=1, int lineType=8, int shift=0 ); pts Array of pointers to polygons npts Array of polygon vertex counters contours Number of contours that bind the filled region img Image is closed Indicates whether the polylines must be drawn closed. If closed, the function draws the line from the last vertex of every contour to the first vertex. color Polyline color thickness Thickness of the polyline edges 202 CHAPTER 1. CORE. THE CORE FUNCTIONALITY lineType Type of the line segments, see Line description shift Number of fractional bits in the vertex coordinates The function draws single or multiple polygonal curves. cvPutText (view/add comments) Draws a text string. void cvPutText( CvArr* img, const char* text, CvPoint org, const CvFont* font, CvScalar color ); img Input image text String to print org Coordinates of the bottom-left corner of the first letter font Pointer to the font structure color Text color The function renders the text in the image with the specified font and color. The printed text is clipped by the ROI rectangle. Symbols that do not belong to the specified font are replaced with the symbol for a rectangle. cvRectangle (view/add comments) Draws a simple, thick, or filled rectangle. 1.4. DRAWING FUNCTIONS 203 void cvRectangle( CvArr* img, CvPoint pt1, CvPoint pt2, CvScalar color, int thickness=1, int lineType=8, int shift=0 ); img Image pt1 One of the rectangle’s vertices pt2 Opposite rectangle vertex color Line color (RGB) or brightness (grayscale image) thickness Thickness of lines that make up the rectangle. Negative values, e.g., CV FILLED, cause the function to draw a filled rectangle. lineType Type of the line, see Line description shift Number of fractional bits in the point coordinates The function draws a rectangle with two opposite corners pt1 and pt2. CV RGB (view/add comments) Constructs a color value. #define CV RGB( r, g, b ) cvScalar( (b), (g), (r) ) red Red component grn Green component blu Blue component 204 CHAPTER 1. CORE. THE CORE FUNCTIONALITY 1.5 XML/YAML Persistence CvFileStorage (view/add comments) File Storage. typedef struct CvFileStorage { ... // hidden fields } CvFileStorage; The structure CvFileStorage is a ”black box” representation of the file storage associated with a file on disk. Several functions that are described below take CvFileStorage as inputs and allow theuser to save or to load hierarchical collections that consist of scalar values, standard CXCore objects (such as matrices, sequences, graphs), and user-defined objects. CXCore can read and write data in XML (http://www.w3c.org/XML) or YAML (http://www.yaml.org) formats. Below is an example of 3 × 3 floating-point identity matrix A, stored in XML and YAML files using CXCore functions: XML: 3 3
f
1. 0. 0. 0. 1. 0. 0. 0. 1.
YAML: %YAML:1.0 A: !!opencv-matrix rows: 3 cols: 3 dt: f data: [ 1., 0., 0., 0., 1., 0., 0., 0., 1.] As it can be seen from the examples, XML uses nested tags to represent hierarchy, while YAML uses indentation for that purpose (similar to the Python programming language). The same CXCore functions can read and write data in both formats; the particular format is determined by the extension of the opened file, .xml for XML files and .yml or .yaml for YAML. 1.5. XML/YAML PERSISTENCE 205 CvFileNode (view/add comments) File Storage Node. /* file node type */ #define CV_NODE_NONE 0 #define CV_NODE_INT 1 #define CV_NODE_INTEGER CV_NODE_INT #define CV_NODE_REAL 2 #define CV_NODE_FLOAT CV_NODE_REAL #define CV_NODE_STR 3 #define CV_NODE_STRING CV_NODE_STR #define CV_NODE_REF 4 /* not used */ #define CV_NODE_SEQ 5 #define CV_NODE_MAP 6 #define CV_NODE_TYPE_MASK 7 /* optional flags */ #define CV_NODE_USER 16 #define CV_NODE_EMPTY 32 #define CV_NODE_NAMED 64 #define CV_NODE_TYPE(tag) ((tag) & CV_NODE_TYPE_MASK) #define CV_NODE_IS_INT(tag) (CV_NODE_TYPE(tag) == CV_NODE_INT) #define CV_NODE_IS_REAL(tag) (CV_NODE_TYPE(tag) == CV_NODE_REAL) #define CV_NODE_IS_STRING(tag) (CV_NODE_TYPE(tag) == CV_NODE_STRING) #define CV_NODE_IS_SEQ(tag) (CV_NODE_TYPE(tag) == CV_NODE_SEQ) #define CV_NODE_IS_MAP(tag) (CV_NODE_TYPE(tag) == CV_NODE_MAP) #define CV_NODE_IS_COLLECTION(tag) (CV_NODE_TYPE(tag) >= CV_NODE_SEQ) #define CV_NODE_IS_FLOW(tag) (((tag) & CV_NODE_FLOW) != 0) #define CV_NODE_IS_EMPTY(tag) (((tag) & CV_NODE_EMPTY) != 0) #define CV_NODE_IS_USER(tag) (((tag) & CV_NODE_USER) != 0) #define CV_NODE_HAS_NAME(tag) (((tag) & CV_NODE_NAMED) != 0) #define CV_NODE_SEQ_SIMPLE 256 #define CV_NODE_SEQ_IS_SIMPLE(seq) (((seq)->flags & CV_NODE_SEQ_SIMPLE) != 0) typedef struct CvString { int len; char* ptr; } CvString; 206 CHAPTER 1. CORE. THE CORE FUNCTIONALITY /* all the keys (names) of elements in the readed file storage are stored in the hash to speed up the lookup operations */ typedef struct CvStringHashNode { unsigned hashval; CvString str; struct CvStringHashNode* next; } CvStringHashNode; /* basic element of the file storage - scalar or collection */ typedef struct CvFileNode { int tag; struct CvTypeInfo* info; /* type information (only for user-defined object, for others it is 0) */ union { double f; /* scalar floating-point number */ int i; /* scalar integer number */ CvString str; /* text string */ CvSeq* seq; /* sequence (ordered collection of file nodes) */ struct CvMap* map; /* map (collection of named file nodes) */ } data; } CvFileNode; The structure is used only for retrieving data from file storage (i.e., for loading data from the file). When data is written to a file, it is done sequentially, with minimal buffering. No data is stored in the file storage. In opposite, when data is read from a file, the whole file is parsed and represented in memory as a tree. Every node of the tree is represented by CvFileNode . The type of file node N can be retrieved as CV NODE TYPE(N->tag). Some file nodes (leaves) are scalars: text strings, integers, or floating-point numbers. Other file nodes are collections of file nodes, which can be scalars or collections in their turn. There are two types of collections: sequences and maps (we use YAML notation, however, the same is true for XML streams). Sequences (do not mix them with CvSeq ) are ordered collections of unnamed file nodes; maps are unordered collections of named file nodes. Thus, elements of sequences are accessed by index ( GetSeqElem ), while elements of maps are accessed by name ( GetFileNodeByName ). The table below describes the different types of file nodes: 1.5. XML/YAML PERSISTENCE 207 Type CV NODE TYPE(node->tag) Value Integer CV NODE INT node->data.i Floating-point CV NODE REAL node->data.f Text string CV NODE STR node->data.str.ptr Sequence CV NODE SEQ node->data.seq Map CV NODE MAP node->data.map (see below) There is no need to access the map field directly (by the way, CvMap is a hidden structure). The elements of the map can be retrieved with the GetFileNodeByName function that takes a pointer to the ”map” file node. A user (custom) object is an instance of either one of the standard CxCore types, such as CvMat, CvSeq etc., or any type registered with RegisterTypeInfo . Such an object is initially rep- resented in a file as a map (as shown in XML and YAML example files above) after the file storage has been opened and parsed. Then the object can be decoded (coverted to native representation) by request - when a user calls the Read or ReadByName functions. CvAttrList (view/add comments) List of attributes. typedef struct CvAttrList { const char** attr; /* NULL-terminated array of (attribute\_name,attribute\_value) pairs */ struct CvAttrList* next; /* pointer to next chunk of the attributes list */ } CvAttrList; /* initializes CvAttrList structure */ inline CvAttrList cvAttrList( const char** attr=NULL, CvAttrList* next=NULL ); /* returns attribute value or 0 (NULL) if there is no such attribute */ const char* cvAttrValue( const CvAttrList* attr, const char* attr\_name ); In the current implementation, attributes are used to pass extra parameters when writing user objects (see Write ). XML attributes inside tags are not supported, aside from the object type specification (type id attribute). CvTypeInfo (view/add comments) Type information. typedef int (CV_CDECL *CvIsInstanceFunc)( const void* structPtr ); typedef void (CV_CDECL *CvReleaseFunc)( void** structDblPtr ); typedef void*(CV_CDECL *CvReadFunc)( CvFileStorage* storage, CvFileNode* node ); 208 CHAPTER 1. CORE. THE CORE FUNCTIONALITY typedef void (CV_CDECL *CvWriteFunc)( CvFileStorage* storage, const char* name, const void* structPtr, CvAttrList attributes ); typedef void*(CV_CDECL *CvCloneFunc)( const void* structPtr ); typedef struct CvTypeInfo { int flags; /* not used */ int header_size; /* sizeof(CvTypeInfo) */ struct CvTypeInfo* prev; /* previous registered type in the list */ struct CvTypeInfo* next; /* next registered type in the list */ const char* type_name; /* type name, written to file storage */ /* methods */ CvIsInstanceFunc is_instance; /* checks if the passed object belongs to the type */ CvReleaseFunc release; /* releases object (memory etc.) */ CvReadFunc read; /* reads object from file storage */ CvWriteFunc write; /* writes object to file storage */ CvCloneFunc clone; /* creates a copy of the object */ } CvTypeInfo; The structure CvTypeInfo contains information about one of the standard or user-defined types. Instances of the type may or may not contain a pointer to the corresponding CvTypeInfo structure. In any case, there is a way to find the type info structure for a given object using the TypeOf function. Aternatively, type info can be found by type name using FindType , which is used when an object is read from file storage. The user can register a new type with RegisterType that adds the type information structure into the beginning of the type list. Thus, it is possible to create specialized types from generic standard types and override the basic methods. cvClone (view/add comments) Makes a clone of an object. void* cvClone( const void* structPtr ); structPtr The object to clone The function finds the type of a given object and calls clone with the passed object. 1.5. XML/YAML PERSISTENCE 209 cvEndWriteStruct (view/add comments) Ends the writing of a structure. void cvEndWriteStruct(CvFileStorage* fs); fs File storage The function finishes the currently written structure. cvFindType (view/add comments) Finds a type by its name. CvTypeInfo* cvFindType(const char* typeName); typeName Type name The function finds a registered type by its name. It returns NULL if there is no type with the specified name. cvFirstType (view/add comments) Returns the beginning of a type list. CvTypeInfo* cvFirstType(void); The function returns the first type in the list of registered types. Navigation through the list can be done via the prev and next fields of the CvTypeInfo structure. 210 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvGetFileNode (view/add comments) Finds a node in a map or file storage. CvFileNode* cvGetFileNode( CvFileStorage* fs, CvFileNode* map, const CvStringHashNode* key, int createMissing=0 ); fs File storage map The parent map. If it is NULL, the function searches a top-level node. If both map and key are NULLs, the function returns the root file node - a map that contains top-level nodes. key Unique pointer to the node name, retrieved with GetHashedKey createMissing Flag that specifies whether an absent node should be added to the map The function finds a file node. It is a faster version of GetFileNodeByName (see GetHashed- Key discussion). Also, the function can insert a new node, if it is not in the map yet. cvGetFileNodeByName (view/add comments) Finds a node in a map or file storage. CvFileNode* cvGetFileNodeByName( const CvFileStorage* fs, const CvFileNode* map, const char* name); fs File storage map The parent map. If it is NULL, the function searches in all the top-level nodes (streams), starting with the first one. 1.5. XML/YAML PERSISTENCE 211 name The file node name The function finds a file node by name. The node is searched either in map or, if the pointer is NULL, among the top-level file storage nodes. Using this function for maps and GetSeqElem (or sequence reader) for sequences, it is possible to nagivate through the file storage. To speed up multiple queries for a certain key (e.g., in the case of an array of structures) one may use a combination of GetHashedKey and GetFileNode. cvGetFileNodeName (view/add comments) Returns the name of a file node. const char* cvGetFileNodeName( const CvFileNode* node ); node File node The function returns the name of a file node or NULL, if the file node does not have a name or if node is NULL. cvGetHashedKey (view/add comments) Returns a unique pointer for a given name. CvStringHashNode* cvGetHashedKey( CvFileStorage* fs, const char* name, int len=-1, int createMissing=0 ); fs File storage name Literal node name len Length of the name (if it is known apriori), or -1 if it needs to be calculated createMissing Flag that specifies, whether an absent key should be added into the hash table 212 CHAPTER 1. CORE. THE CORE FUNCTIONALITY The function returns a unique pointer for each particular file node name. This pointer can be then passed to the GetFileNode function that is faster than GetFileNodeByName because it compares text strings by comparing pointers rather than the strings’ content. Consider the following example where an array of points is encoded as a sequence of 2-entry maps: %YAML:1.0 points: - { x: 10, y: 10 } - { x: 20, y: 20 } - { x: 30, y: 30 } # ... Then, it is possible to get hashed ”x” and ”y” pointers to speed up decoding of the points. #include "cxcore.h" int main( int argc, char** argv ) { CvFileStorage* fs = cvOpenFileStorage( "points.yml", 0, CV\_STORAGE\_READ ); CvStringHashNode* x\_key = cvGetHashedNode( fs, "x", -1, 1 ); CvStringHashNode* y\_key = cvGetHashedNode( fs, "y", -1, 1 ); CvFileNode* points = cvGetFileNodeByName( fs, 0, "points" ); if( CV\_NODE\_IS\_SEQ(points->tag) ) { CvSeq* seq = points->data.seq; int i, total = seq->total; CvSeqReader reader; cvStartReadSeq( seq, &reader, 0 ); for( i = 0; i < total; i++ ) { CvFileNode* pt = (CvFileNode*)reader.ptr; #if 1 /* faster variant */ CvFileNode* xnode = cvGetFileNode( fs, pt, x\_key, 0 ); CvFileNode* ynode = cvGetFileNode( fs, pt, y\_key, 0 ); assert( xnode && CV\_NODE\_IS\_INT(xnode->tag) && ynode && CV\_NODE\_IS\_INT(ynode->tag)); int x = xnode->data.i; // or x = cvReadInt( xnode, 0 ); int y = ynode->data.i; // or y = cvReadInt( ynode, 0 ); #elif 1 /* slower variant; does not use x\_key & y\_key */ CvFileNode* xnode = cvGetFileNodeByName( fs, pt, "x" ); CvFileNode* ynode = cvGetFileNodeByName( fs, pt, "y" ); assert( xnode && CV\_NODE\_IS\_INT(xnode->tag) && 1.5. XML/YAML PERSISTENCE 213 ynode && CV\_NODE\_IS\_INT(ynode->tag)); int x = xnode->data.i; // or x = cvReadInt( xnode, 0 ); int y = ynode->data.i; // or y = cvReadInt( ynode, 0 ); #else /* the slowest yet the easiest to use variant */ int x = cvReadIntByName( fs, pt, "x", 0 /* default value */ ); int y = cvReadIntByName( fs, pt, "y", 0 /* default value */ ); #endif CV\_NEXT\_SEQ\_ELEM( seq->elem\_size, reader ); printf("%d: (%d, %d)\n", i, x, y ); } } cvReleaseFileStorage( &fs ); return 0; } Please note that whatever method of accessing a map you are using, it is still much slower than using plain sequences; for example, in the above example, it is more efficient to encode the points as pairs of integers in a single numeric sequence. cvGetRootFileNode (view/add comments) Retrieves one of the top-level nodes of the file storage. CvFileNode* cvGetRootFileNode( const CvFileStorage* fs, int stream index=0 ); fs File storage stream index Zero-based index of the stream. See StartNextStream . In most cases, there is only one stream in the file; however, there can be several. The function returns one of the top-level file nodes. The top-level nodes do not have a name, they correspond to the streams that are stored one after another in the file storage. If the index is out of range, the function returns a NULL pointer, so all the top-level nodes may be iterated by subsequent calls to the function with stream index=0,1,..., until the NULL pointer is returned. This function may be used as a base for recursive traversal of the file storage. 214 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvLoad (view/add comments) Loads an object from a file. void* cvLoad( const char* filename, CvMemStorage* storage=NULL, const char* name=NULL, const char** realName=NULL ); filename File name storage Memory storage for dynamic structures, such as CvSeq or CvGraph . It is not used for matrices or images. name Optional object name. If it is NULL, the first top-level object in the storage will be loaded. realName Optional output parameter that will contain the name of the loaded object (useful if name=NULL) The function loads an object from a file. It provides a simple interface to cvRead. After the object is loaded, the file storage is closed and all the temporary buffers are deleted. Thus, to load a dynamic structure, such as a sequence, contour, or graph, one should pass a valid memory storage destination to the function. cvOpenFileStorage (view/add comments) Opens file storage for reading or writing data. CvFileStorage* cvOpenFileStorage( const char* filename, CvMemStorage* memstorage, int flags); filename Name of the file associated with the storage 1.5. XML/YAML PERSISTENCE 215 memstorage Memory storage used for temporary data and for storing dynamic structures, such as CvSeq or CvGraph . If it is NULL, a temporary memory storage is created and used. flags Can be one of the following: CV STORAGE READ the storage is open for reading CV STORAGE WRITE the storage is open for writing The function opens file storage for reading or writing data. In the latter case, a new file is created or an existing file is rewritten. The type of the read or written file is determined by the filename extension: .xml for XML and .yml or .yaml for YAML. The function returns a pointer to the CvFileStorage structure. cvRead (view/add comments) Decodes an object and returns a pointer to it. void* cvRead( CvFileStorage* fs, CvFileNode* node, CvAttrList* attributes=NULL ); fs File storage node The root object node attributes Unused parameter The function decodes a user object (creates an object in a native representation from the file storage subtree) and returns it. The object to be decoded must be an instance of a registered type that supports the read method (see CvTypeInfo ). The type of the object is determined by the type name that is encoded in the file. If the object is a dynamic structure, it is created either in memory storage and passed to OpenFileStorage or, if a NULL pointer was passed, in temporary memory storage, which is released when ReleaseFileStorage is called. Otherwise, if the object is not a dynamic structure, it is created in a heap and should be released with a specialized function or by using the generic Release. 216 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvReadByName (view/add comments) Finds an object by name and decodes it. void* cvReadByName( CvFileStorage* fs, const CvFileNode* map, const char* name, CvAttrList* attributes=NULL ); fs File storage map The parent map. If it is NULL, the function searches a top-level node. name The node name attributes Unused parameter The function is a simple superposition of GetFileNodeByName and Read. cvReadInt (view/add comments) Retrieves an integer value from a file node. int cvReadInt( const CvFileNode* node, int defaultValue=0 ); node File node defaultValue The value that is returned if node is NULL The function returns an integer that is represented by the file node. If the file node is NULL, the defaultValue is returned (thus, it is convenient to call the function right after GetFileNode without checking for a NULL pointer). If the file node has type CV NODE INT, then node->data.i is returned. If the file node has type CV NODE REAL, then node->data.f is converted to an integer and returned. Otherwise the result is not determined. 1.5. XML/YAML PERSISTENCE 217 cvReadIntByName (view/add comments) Finds a file node and returns its value. int cvReadIntByName( const CvFileStorage* fs, const CvFileNode* map, const char* name, int defaultValue=0 ); fs File storage map The parent map. If it is NULL, the function searches a top-level node. name The node name defaultValue The value that is returned if the file node is not found The function is a simple superposition of GetFileNodeByName and ReadInt. cvReadRawData (view/add comments) Reads multiple numbers. void cvReadRawData( const CvFileStorage* fs, const CvFileNode* src, void* dst, const char* dt); fs File storage src The file node (a sequence) to read numbers from dst Pointer to the destination array dt Specification of each array element. It has the same format as in WriteRawData. The function reads elements from a file node that represents a sequence of scalars. 218 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvReadRawDataSlice (view/add comments) Initializes file node sequence reader. void cvReadRawDataSlice( const CvFileStorage* fs, CvSeqReader* reader, int count, void* dst, const char* dt ); fs File storage reader The sequence reader. Initialize it with StartReadRawData. count The number of elements to read dst Pointer to the destination array dt Specification of each array element. It has the same format as in WriteRawData. The function reads one or more elements from the file node, representing a sequence, to a user-specified array. The total number of read sequence elements is a product of total and the number of components in each array element. For example, if dt=2if, the function will read total × 3 sequence elements. As with any sequence, some parts of the file node sequence may be skipped or read repeatedly by repositioning the reader using SetSeqReaderPos. cvReadReal (view/add comments) Retrieves a floating-point value from a file node. double cvReadReal( const CvFileNode* node, double defaultValue=0. ); node File node 1.5. XML/YAML PERSISTENCE 219 defaultValue The value that is returned if node is NULL The function returns a floating-point value that is represented by the file node. If the file node is NULL, the defaultValue is returned (thus, it is convenient to call the function right after GetFileNode without checking for a NULL pointer). If the file node has type CV NODE REAL, then node->data.f is returned. If the file node has type CV NODE INT, then node->data.f is converted to floating-point and returned. Otherwise the result is not determined. cvReadRealByName (view/add comments) Finds a file node and returns its value. double cvReadRealByName( const CvFileStorage* fs, const CvFileNode* map, const char* name, double defaultValue=0.); fs File storage map The parent map. If it is NULL, the function searches a top-level node. name The node name defaultValue The value that is returned if the file node is not found The function is a simple superposition of GetFileNodeByName and ReadReal. cvReadString (view/add comments) Retrieves a text string from a file node. const char* cvReadString( const CvFileNode* node, const char* defaultValue=NULL ); 220 CHAPTER 1. CORE. THE CORE FUNCTIONALITY node File node defaultValue The value that is returned if node is NULL The function returns a text string that is represented by the file node. If the file node is NULL, the defaultValue is returned (thus, it is convenient to call the function right after Get- FileNode without checking for a NULL pointer). If the file node has type CV NODE STR, then node->data.str.ptr is returned. Otherwise the result is not determined. cvReadStringByName (view/add comments) Finds a file node by its name and returns its value. const char* cvReadStringByName( const CvFileStorage* fs, const CvFileNode* map, const char* name, const char* defaultValue=NULL ); fs File storage map The parent map. If it is NULL, the function searches a top-level node. name The node name defaultValue The value that is returned if the file node is not found The function is a simple superposition of GetFileNodeByName and ReadString. cvRegisterType (view/add comments) Registers a new type. void cvRegisterType(const CvTypeInfo* info); info Type info structure The function registers a new type, which is described by info. The function creates a copy of the structure, so the user should delete it after calling the function. 1.5. XML/YAML PERSISTENCE 221 cvRelease (view/add comments) Releases an object. void cvRelease( void** structPtr ); structPtr Double pointer to the object The function finds the type of a given object and calls release with the double pointer. cvReleaseFileStorage (view/add comments) Releases file storage. void cvReleaseFileStorage(CvFileStorage** fs); fs Double pointer to the released file storage The function closes the file associated with the storage and releases all the temporary struc- tures. It must be called after all I/O operations with the storage are finished. cvSave (view/add comments) Saves an object to a file. void cvSave( const char* filename, const void* structPtr, const char* name=NULL, const char* comment=NULL, CvAttrList attributes=cvAttrList()); 222 CHAPTER 1. CORE. THE CORE FUNCTIONALITY filename File name structPtr Object to save name Optional object name. If it is NULL, the name will be formed from filename. comment Optional comment to put in the beginning of the file attributes Optional attributes passed to Write The function saves an object to a file. It provides a simple interface to Write. cvStartNextStream (view/add comments) Starts the next stream. void cvStartNextStream(CvFileStorage* fs); fs File storage The function starts the next stream in file storage. Both YAML and XML support multiple ”streams.” This is useful for concatenating files or for resuming the writing process. cvStartReadRawData (view/add comments) Initializes the file node sequence reader. void cvStartReadRawData( const CvFileStorage* fs, const CvFileNode* src, CvSeqReader* reader); fs File storage src The file node (a sequence) to read numbers from reader Pointer to the sequence reader The function initializes the sequence reader to read data from a file node. The initialized reader can be then passed to ReadRawDataSlice. 1.5. XML/YAML PERSISTENCE 223 cvStartWriteStruct (view/add comments) Starts writing a new structure. void cvStartWriteStruct( CvFileStorage* fs, const char* name, int struct flags, const char* typeName=NULL, CvAttrList attributes=cvAttrList( )); fs File storage name Name of the written structure. The structure can be accessed by this name when the storage is read. struct flags A combination one of the following values: CV NODE SEQ the written structure is a sequence (see discussion of CvFileStorage ), that is, its elements do not have a name. CV NODE MAP the written structure is a map (see discussion of CvFileStorage ), that is, all its elements have names. One and only one of the two above flags must be specified CV NODE FLOW the optional flag that makes sense only for YAML streams. It means that the structure is written as a flow (not as a block), which is more compact. It is recommended to use this flag for structures or arrays whose elements are all scalars. typeName Optional parameter - the object type name. In case of XML it is written as a type id attribute of the structure opening tag. In the case of YAML it is written after a colon following the structure name (see the example in CvFileStorage description). Mainly it is used with user objects. When the storage is read, the encoded type name is used to determine the object type (see CvTypeInfo and FindTypeInfo). attributes This parameter is not used in the current implementation The function starts writing a compound structure (collection) that can be a sequence or a map. After all the structure fields, which can be scalars or structures, are written, EndWriteStruct should be called. The function can be used to group some objects or to implement the write function for a some user object (see CvTypeInfo). 224 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvTypeOf (view/add comments) Returns the type of an object. CvTypeInfo* cvTypeOf( const void* structPtr ); structPtr The object pointer The function finds the type of a given object. It iterates through the list of registered types and calls the is instance function/method for every type info structure with that object until one of them returns non-zero or until the whole list has been traversed. In the latter case, the function returns NULL. cvUnregisterType (view/add comments) Unregisters the type. void cvUnregisterType( const char* typeName ); typeName Name of an unregistered type The function unregisters a type with a specified name. If the name is unknown, it is possible to locate the type info by an instance of the type using TypeOf or by iterating the type list, starting from FirstType , and then calling cvUnregisterType(info->typeName). cvWrite (view/add comments) Writes a user object. void cvWrite( CvFileStorage* fs, const char* name, const void* ptr, CvAttrList attributes=cvAttrList( ) ); 1.5. XML/YAML PERSISTENCE 225 fs File storage name Name of the written object. Should be NULL if and only if the parent structure is a sequence. ptr Pointer to the object attributes The attributes of the object. They are specific for each particular type (see the dicsussion below). The function writes an object to file storage. First, the appropriate type info is found using TypeOf . Then, the write method associated with the type info is called. Attributes are used to customize the writing procedure. The standard types support the follow- ing attributes (all the *dt attributes have the same format as in WriteRawData): 1. CvSeq header dt description of user fields of the sequence header that follow CvSeq, or CvChain (if the sequence is a Freeman chain) or CvContour (if the sequence is a contour or point sequence) dt description of the sequence elements. recursive if the attribute is present and is not equal to ”0” or ”false”, the whole tree of sequences (contours) is stored. 2. Cvgraph header dt description of user fields of the graph header that follows CvGraph; vertex dt description of user fields of graph vertices edge dt description of user fields of graph edges (note that the edge weight is always written, so there is no need to specify it explicitly) Below is the code that creates the YAML file shown in the CvFileStorage description: #include "cxcore.h" int main( int argc, char** argv ) { CvMat* mat = cvCreateMat( 3, 3, CV\_32F ); CvFileStorage* fs = cvOpenFileStorage( "example.yml", 0, CV\_STORAGE\_WRITE ); cvSetIdentity( mat ); cvWrite( fs, "A", mat, cvAttrList(0,0) ); cvReleaseFileStorage( &fs ); 226 CHAPTER 1. CORE. THE CORE FUNCTIONALITY cvReleaseMat( &mat ); return 0; } cvWriteComment (view/add comments) Writes a comment. void cvWriteComment( CvFileStorage* fs, const char* comment, int eolComment); fs File storage comment The written comment, single-line or multi-line eolComment If non-zero, the function tries to put the comment at the end of current line. If the flag is zero, if the comment is multi-line, or if it does not fit at the end of the current line, the comment starts a new line. The function writes a comment into file storage. The comments are skipped when the storage is read, so they may be used only for debugging or descriptive purposes. cvWriteFileNode (view/add comments) Writes a file node to another file storage. void cvWriteFileNode( CvFileStorage* fs, const char* new node name, const CvFileNode* node, int embed ); fs Destination file storage 1.5. XML/YAML PERSISTENCE 227 new file node New name of the file node in the destination file storage. To keep the existing name, use cvGetFileNodeName node The written node embed If the written node is a collection and this parameter is not zero, no extra level of hiararchy is created. Instead, all the elements of node are written into the currently written structure. Of course, map elements may be written only to a map, and sequence elements may be written only to a sequence. The function writes a copy of a file node to file storage. Possible applications of the function are merging several file storages into one and conversion between XML and YAML formats. cvWriteInt (view/add comments) Writes an integer value. void cvWriteInt( CvFileStorage* fs, const char* name, int value); fs File storage name Name of the written value. Should be NULL if and only if the parent structure is a sequence. value The written value The function writes a single integer value (with or without a name) to the file storage. cvWriteRawData (view/add comments) Writes multiple numbers. 228 CHAPTER 1. CORE. THE CORE FUNCTIONALITY void cvWriteRawData( CvFileStorage* fs, const void* src, int len, const char* dt ); fs File storage src Pointer to the written array len Number of the array elements to write dt Specification of each array element that has the following format ([count]{’u’|’c’|’w’|’s’|’i’|’f’|’d’})... where the characters correspond to fundamental C types: u 8-bit unsigned number c 8-bit signed number w 16-bit unsigned number s 16-bit signed number i 32-bit signed number f single precision floating-point number d double precision floating-point number r pointer, 32 lower bits of which are written as a signed integer. The type can be used to store structures with links between the elements. count is the optional counter of val- ues of a given type. For example, 2if means that each array element is a structure of 2 integers, followed by a single-precision floating-point number. The equivalent notations of the above specification are ’iif’, ’2i1f’ and so forth. Other examples: u means that the array consists of bytes, and 2d means the array consists of pairs of doubles. The function writes an array, whose elements consist of single or multiple numbers. The func- tion call can be replaced with a loop containing a few WriteInt and WriteReal calls, but a single call is more efficient. Note that because none of the elements have a name, they should be written to a sequence rather than a map. 1.5. XML/YAML PERSISTENCE 229 cvWriteReal (view/add comments) Writes a floating-point value. void cvWriteReal( CvFileStorage* fs, const char* name, double value ); fs File storage name Name of the written value. Should be NULL if and only if the parent structure is a sequence. value The written value The function writes a single floating-point value (with or without a name) to file storage. Special values are encoded as follows: NaN (Not A Number) as .NaN, ±∞ as +.Inf (-.Inf). The following example shows how to use the low-level writing functions to store custom struc- tures, such as termination criteria, without registering a new type. void write_termcriteria( CvFileStorage* fs, const char* struct_name, CvTermCriteria* termcrit ) { cvStartWriteStruct( fs, struct_name, CV_NODE_MAP, NULL, cvAttrList(0,0)); cvWriteComment( fs, "termination criteria", 1 ); // just a description if( termcrit->type & CV_TERMCRIT_ITER ) cvWriteInteger( fs, "max_iterations", termcrit->max_iter ); if( termcrit->type & CV_TERMCRIT_EPS ) cvWriteReal( fs, "accuracy", termcrit->epsilon ); cvEndWriteStruct( fs ); } cvWriteString (view/add comments) Writes a text string. 230 CHAPTER 1. CORE. THE CORE FUNCTIONALITY void cvWriteString( CvFileStorage* fs, const char* name, const char* str, int quote=0 ); fs File storage name Name of the written string . Should be NULL if and only if the parent structure is a sequence. str The written text string quote If non-zero, the written string is put in quotes, regardless of whether they are required. Otherwise, if the flag is zero, quotes are used only when they are required (e.g. when the string starts with a digit or contains spaces). The function writes a text string to file storage. 1.6 Clustering cvKMeans2 (view/add comments) Splits set of vectors by a given number of clusters. int cvKMeans2(const CvArr* samples, int nclusters, CvArr* labels, CvTermCriteria termcrit, int attempts=1, CvRNG* rng=0, int flags=0, CvArr* centers=0, double* compactness=0); samples Floating-point matrix of input samples, one row per sample nclusters Number of clusters to split the set by labels Output integer vector storing cluster indices for every sample 1.6. CLUSTERING 231 termcrit Specifies maximum number of iterations and/or accuracy (distance the centers can move by between subsequent iterations) attempts How many times the algorithm is executed using different initial labelings. The algo- rithm returns labels that yield the best compactness (see the last function parameter) rng Optional external random number generator; can be used to fully control the function be- haviour flags Can be 0 or CV KMEANS USE INITIAL LABELS. The latter value means that during the first (and possibly the only) attempt, the function uses the user-supplied labels as the initial approximation instead of generating random labels. For the second and further attempts, the function will use randomly generated labels in any case centers The optional output array of the cluster centers compactness The optional output parameter, which is computed as P i ||samplesi−centerslabelsi ||2 after every attempt; the best (minimum) value is chosen and the corresponding labels are re- turned by the function. Basically, the user can use only the core of the function, set the num- ber of attempts to 1, initialize labels each time using a custom algorithm (flags=CV KMEAN USE INITIAL LABELS) and, based on the output compactness or any other criteria, choose the best clustering. The function cvKMeans2 implements a k-means algorithm that finds the centers of nclusters clusters and groups the input samples around the clusters. On output, labelsi contains a cluster index for samples stored in the i-th row of the samples matrix. #include "cxcore.h" #include "highgui.h" void main( int argc, char** argv ) { #define MAX_CLUSTERS 5 CvScalar color_tab[MAX_CLUSTERS]; IplImage* img = cvCreateImage( cvSize( 500, 500 ), 8, 3 ); CvRNG rng = cvRNG(0xffffffff); color_tab[0] = CV_RGB(255,0,0); color_tab[1] = CV_RGB(0,255,0); color_tab[2] = CV_RGB(100,100,255); color_tab[3] = CV_RGB(255,0,255); color_tab[4] = CV_RGB(255,255,0); cvNamedWindow( "clusters", 1 ); 232 CHAPTER 1. CORE. THE CORE FUNCTIONALITY for(;;) { int k, cluster_count = cvRandInt(&rng)%MAX_CLUSTERS + 1; int i, sample_count = cvRandInt(&rng)%1000 + 1; CvMat* points = cvCreateMat( sample_count, 1, CV_32FC2 ); CvMat* clusters = cvCreateMat( sample_count, 1, CV_32SC1 ); /* generate random sample from multigaussian distribution */ for( k = 0; k < cluster_count; k++ ) { CvPoint center; CvMat point_chunk; center.x = cvRandInt(&rng)%img->width; center.y = cvRandInt(&rng)%img->height; cvGetRows( points, &point_chunk, k*sample_count/cluster_count, (k == (cluster_count - 1)) ? sample_count : (k+1)*sample_count/cluster_count ); cvRandArr( &rng, &point_chunk, CV_RAND_NORMAL, cvScalar(center.x,center.y,0,0), cvScalar(img->width/6, img->height/6,0,0) ); } /* shuffle samples */ for( i = 0; i < sample_count/2; i++ ) { CvPoint2D32f* pt1 = (CvPoint2D32f*)points->data.fl + cvRandInt(&rng)%sample_count; CvPoint2D32f* pt2 = (CvPoint2D32f*)points->data.fl + cvRandInt(&rng)%sample_count; CvPoint2D32f temp; CV_SWAP( *pt1, *pt2, temp ); } cvKMeans2( points, cluster_count, clusters, cvTermCriteria( CV_TERMCRIT_EPS+CV_TERMCRIT_ITER, 10, 1.0 )); cvZero( img ); for( i = 0; i < sample_count; i++ ) { CvPoint2D32f pt = ((CvPoint2D32f*)points->data.fl)[i]; int cluster_idx = clusters->data.i[i]; 1.6. CLUSTERING 233 cvCircle( img, cvPointFrom32f(pt), 2, color_tab[cluster_idx], CV_FILLED ); } cvReleaseMat( &points ); cvReleaseMat( &clusters ); cvShowImage( "clusters", img ); int key = cvWaitKey(0); if( key == 27 ) break; } } cvSeqPartition (view/add comments) Splits a sequence into equivalency classes. int cvSeqPartition( const CvSeq* seq, CvMemStorage* storage, CvSeq** labels, CvCmpFunc is equal, void* userdata ); seq The sequence to partition storage The storage block to store the sequence of equivalency classes. If it is NULL, the function uses seq->storage for output labels labels Ouput parameter. Double pointer to the sequence of 0-based labels of input sequence elements is equal The relation function that should return non-zero if the two particular sequence ele- ments are from the same class, and zero otherwise. The partitioning algorithm uses transi- tive closure of the relation function as an equivalency critria 234 CHAPTER 1. CORE. THE CORE FUNCTIONALITY userdata Pointer that is transparently passed to the is equal function typedef int (CV_CDECL* CvCmpFunc)(const void* a, const void* b, void* userdata); The function cvSeqPartition implements a quadratic algorithm for splitting a set into one or more equivalancy classes. The function returns the number of equivalency classes. #include "cxcore.h" #include "highgui.h" #include CvSeq* point_seq = 0; IplImage* canvas = 0; CvScalar* colors = 0; int pos = 10; int is_equal( const void*_a, const void*_b, void* userdata ) { CvPoint a = *(const CvPoint*)_a; CvPoint b = *(const CvPoint*)_b; double threshold = *(double*)userdata; return (double)((a.x - b.x)*(a.x - b.x) + (a.y - b.y)*(a.y - b.y)) <= threshold; } void on_track( int pos ) { CvSeq* labels = 0; double threshold = pos*pos; int i, class_count = cvSeqPartition( point_seq, 0, &labels, is_equal, &threshold ); printf("%4d classes\n", class_count ); cvZero( canvas ); for( i = 0; i < labels->total; i++ ) { CvPoint pt = *(CvPoint*)cvGetSeqElem( point_seq, i ); CvScalar color = colors[*(int*)cvGetSeqElem( labels, i )]; cvCircle( canvas, pt, 1, color, -1 ); } 1.7. UTILITY AND SYSTEM FUNCTIONS AND MACROS 235 cvShowImage( "points", canvas ); } int main( int argc, char** argv ) { CvMemStorage* storage = cvCreateMemStorage(0); point_seq = cvCreateSeq( CV_32SC2, sizeof(CvSeq), sizeof(CvPoint), storage ); CvRNG rng = cvRNG(0xffffffff); int width = 500, height = 500; int i, count = 1000; canvas = cvCreateImage( cvSize(width,height), 8, 3 ); colors = (CvScalar*)cvAlloc( count*sizeof(colors[0]) ); for( i = 0; i < count; i++ ) { CvPoint pt; int icolor; pt.x = cvRandInt( &rng ) % width; pt.y = cvRandInt( &rng ) % height; cvSeqPush( point_seq, &pt ); icolor = cvRandInt( &rng ) | 0x00404040; colors[i] = CV_RGB(icolor & 255, (icolor >> 8)&255, (icolor >> 16)&255); } cvNamedWindow( "points", 1 ); cvCreateTrackbar( "threshold", "points", &pos, 50, on_track ); on_track(pos); cvWaitKey(0); return 0; } 1.7 Utility and System Functions and Macros Error Handling Error handling in OpenCV is similar to IPL (Image Processing Library). In the case of an error, functions do not return the error code. Instead, they raise an error using CV ERROR macro that 236 CHAPTER 1. CORE. THE CORE FUNCTIONALITY calls cvError that, in its turn, sets the error status with cvSetErrStatus and calls a standard or user- defined error handler (that can display a message box, write to log, etc., see cvRedirectError). There is a global variable, one per each program thread, that contains current error status (an integer value). The status can be retrieved with the cvGetErrStatus function. There are three modes of error handling (see cvSetErrMode and cvGetErrMode): • Leaf. The program is terminated after the error handler is called. This is the default value. It is useful for debugging, as the error is signalled immediately after it occurs. However, for production systems, other two methods may be preferable as they provide more control. • Parent. The program is not terminated, but the error handler is called. The stack is unwound (it is done w/o using a C++ exception mechanism). The user may check error code after calling the CxCore function with cvGetErrStatus and react. • Silent. Similar to Parent mode, but no error handler is called. Actually, the semantics of the Leaf and Parent modes are implemented by error handlers and the above description is true for them. cvGuiBoxReport behaves slightly differently, and some custom error handlers may implement quite different semantics. Macros for raising an error, checking for errors, etc. /* special macros for enclosing processing statements within a function and separating them from prologue (resource initialization) and epilogue (guaranteed resource release) */ #define __BEGIN__ { #define __END__ goto exit; exit: ; } /* proceeds to "resource release" stage */ #define EXIT goto exit /* Declares locally the function name for CV_ERROR() use */ #define CV_FUNCNAME( Name ) \ static char cvFuncName[] = Name /* Raises an error within the current context */ #define CV_ERROR( Code, Msg ) \ {\ cvError( (Code), cvFuncName, Msg, __FILE__, __LINE__ ); \ EXIT; \ } /* Checks status after calling CXCORE function */ #define CV_CHECK() \ {\ if( cvGetErrStatus() < 0 ) \ 1.7. UTILITY AND SYSTEM FUNCTIONS AND MACROS 237 CV_ERROR( CV_StsBackTrace, "Inner function failed." ); \ } /* Provies shorthand for CXCORE function call and CV_CHECK() */ #define CV_CALL( Statement ) \ {\ Statement; \ CV_CHECK(); \ } /* Checks some condition in both debug and release configurations */ #define CV_ASSERT( Condition ) \ {\ if( !(Condition) ) \ CV_ERROR( CV_StsInternal, "Assertion: " #Condition " failed" ); \ } /* these macros are similar to their CV_... counterparts, but they do not need exit label nor cvFuncName to be defined */ #define OPENCV_ERROR(status,func_name,err_msg) ... #define OPENCV_ERRCHK(func_name,err_msg) ... #define OPENCV_ASSERT(condition,func_name,err_msg) ... #define OPENCV_CALL(statement) ... Instead of a discussion, below is a documented example of a typical CXCORE function and an example of the function use. Example: Use of Error Handling Macros #include "cxcore.h" #include void cvResizeDCT( CvMat* input_array, CvMat* output_array ) { CvMat* temp_array = 0; // declare pointer that should be released anyway. CV_FUNCNAME( "cvResizeDCT" ); // declare cvFuncName __BEGIN__; // start processing. There may be some declarations just after // this macro, but they could not be accessed from the epilogue. if( !CV_IS_MAT(input_array) || !CV_IS_MAT(output_array) ) // use CV_ERROR() to raise an error 238 CHAPTER 1. CORE. THE CORE FUNCTIONALITY CV_ERROR( CV_StsBadArg, "input_array or output_array are not valid matrices" ); // some restrictions that are going to be removed later, may be checked // with CV_ASSERT() CV_ASSERT( input_array->rows == 1 && output_array->rows == 1 ); // use CV_CALL for safe function call CV_CALL( temp_array = cvCreateMat( input_array->rows, MAX(input_array->cols, output_array->cols), input_array->type )); if( output_array->cols > input_array->cols ) CV_CALL( cvZero( temp_array )); temp_array->cols = input_array->cols; CV_CALL( cvDCT( input_array, temp_array, CV_DXT_FORWARD )); temp_array->cols = output_array->cols; CV_CALL( cvDCT( temp_array, output_array, CV_DXT_INVERSE )); CV_CALL( cvScale( output_array, output_array, 1./sqrt((double)input_array->cols*output_array->cols), 0 )); __END__; // finish processing. Epilogue follows after the macro. // release temp_array. If temp_array has not been allocated // before an error occured, cvReleaseMat // takes care of it and does nothing in this case. cvReleaseMat( &temp_array ); } int main( int argc, char** argv ) { CvMat* src = cvCreateMat( 1, 512, CV_32F ); #if 1 /* no errors */ CvMat* dst = cvCreateMat( 1, 256, CV_32F ); #else CvMat* dst = 0; /* test error processing mechanism */ #endif cvSet( src, cvRealScalar(1.), 0 ); #if 0 /* change 0 to 1 to suppress error handler invocation */ cvSetErrMode( CV_ErrModeSilent ); #endif cvResizeDCT( src, dst ); // if some error occurs, the message 1.7. UTILITY AND SYSTEM FUNCTIONS AND MACROS 239 // box will popup, or a message will be // written to log, or some user-defined // processing will be done if( cvGetErrStatus() < 0 ) printf("Some error occured" ); else printf("Everything is OK" ); return 0; } cvGetErrStatus (view/add comments) Returns the current error status. int cvGetErrStatus( void ); The function returns the current error status - the value set with the last cvSetErrStatus call. Note that in Leaf mode, the program terminates immediately after an error occurs, so to always gain control after the function call, one should call cvSetErrMode and set the Parent or Silent error mode. cvSetErrStatus (view/add comments) Sets the error status. void cvSetErrStatus( int status ); status The error status The function sets the error status to the specified value. Mostly, the function is used to reset the error status (set to it CV StsOk) to recover after an error. In other cases it is more natural to call cvError or CV ERROR. cvGetErrMode (view/add comments) Returns the current error mode. 240 CHAPTER 1. CORE. THE CORE FUNCTIONALITY int cvGetErrMode(void); The function returns the current error mode - the value set with the last cvSetErrMode call. cvSetErrMode (view/add comments) Sets the error mode. #define CV_ErrModeLeaf 0 #define CV_ErrModeParent 1 #define CV_ErrModeSilent 2 int cvSetErrMode( int mode ); mode The error mode The function sets the specified error mode. For descriptions of different error modes, see the beginning of the error section. cvError (view/add comments) Raises an error. int cvError( int status, const char* func name, const char* err msg, const char* filename, int line ); status The error status func name Name of the function where the error occured 1.7. UTILITY AND SYSTEM FUNCTIONS AND MACROS 241 err msg Additional information/diagnostics about the error filename Name of the file where the error occured line Line number, where the error occured The function sets the error status to the specified value (via cvSetErrStatus) and, if the error mode is not Silent, calls the error handler. cvErrorStr (view/add comments) Returns textual description of an error status code. const char* cvErrorStr( int status ); status The error status The function returns the textual description for the specified error status code. In the case of unknown status, the function returns a NULL pointer. cvRedirectError (view/add comments) Sets a new error handler. CvErrorCallback cvRedirectError( CvErrorCallback error handler, void* userdata=NULL, void** prevUserdata=NULL ); error handler The new error handler userdata Arbitrary pointer that is transparently passed to the error handler prevUserdata Pointer to the previously assigned user data pointer 242 CHAPTER 1. CORE. THE CORE FUNCTIONALITY typedef int (CV_CDECL *CvErrorCallback)( int status, const char* func_name, const char* err_msg, const char* file_name, int line ); The function sets a new error handler that can be one of the standard handlers or a custom handler that has a specific interface. The handler takes the same parameters as the cvError function. If the handler returns a non-zero value, the program is terminated; otherwise, it continues. The error handler may check the current error mode with cvGetErrMode to make a decision. cvNulDevReport cvStdErrReport cvGuiBoxReport (view/add comments) Provide standard error handling. int cvNulDevReport( int status, const char* func name, const char* err msg, const char* file name, int line, void* userdata ); int cvStdErrReport( int status, const char* func name, const char* err msg, const char* file name, int line, void* userdata ); int cvGuiBoxReport( int status, const char* func name, const char* err msg, const char* file name, int line, void* userdata ); status The error status func name Name of the function where the error occured err msg Additional information/diagnostics about the error filename Name of the file where the error occured line Line number, where the error occured userdata Pointer to the user data. Ignored by the standard handlers The functions cvNullDevReport, cvStdErrReport, and cvGuiBoxReport provide stan- dard error handling. cvGuiBoxReport is the default error handler on Win32 systems, cvStdErrReport is the default on other systems. cvGuiBoxReport pops up a message box with the error descrip- tion and suggest a few options. Below is an example message box that may be recieved with the sample code above, if one introduces an error as described in the sample. 1.7. UTILITY AND SYSTEM FUNCTIONS AND MACROS 243 Error Message Box If the error handler is set to cvStdErrReport, the above message will be printed to standard error output and the program will be terminated or continued, depending on the current error mode. Error Message printed to Standard Error Output (in Leaf mode) OpenCV ERROR: Bad argument (input_array or output_array are not valid matrices) in function cvResizeDCT, D:\User\VP\Projects\avl\_proba\a.cpp(75) Terminating the application... cvAlloc (view/add comments) Allocates a memory buffer. void* cvAlloc( size t size ); size Buffer size in bytes The function allocates size bytes and returns a pointer to the allocated buffer. In the case of an error the function reports an error and returns a NULL pointer. By default, cvAlloc calls icvAlloc which itself calls malloc. However it is possible to assign user-defined memory allo- cation/deallocation functions using the cvSetMemoryManager function. cvFree (view/add comments) Deallocates a memory buffer. void cvFree( void** ptr ); 244 CHAPTER 1. CORE. THE CORE FUNCTIONALITY ptr Double pointer to released buffer The function deallocates a memory buffer allocated by cvAlloc. It clears the pointer to buffer upon exit, which is why the double pointer is used. If the *buffer is already NULL, the function does nothing. cvGetTickCount (view/add comments) Returns the number of ticks. int64 cvGetTickCount( void ); The function returns number of the ticks starting from some platform-dependent event (number of CPU ticks from the startup, number of milliseconds from 1970th year, etc.). The function is useful for accurate measurement of a function/user-code execution time. To convert the number of ticks to time units, use cvGetTickFrequency. cvGetTickFrequency (view/add comments) Returns the number of ticks per microsecond. double cvGetTickFrequency( void ); The function returns the number of ticks per microsecond. Thus, the quotient of cvGetTick- Count and cvGetTickFrequency will give the number of microseconds starting from the platform- dependent event. cvRegisterModule (view/add comments) Registers another module. typedef struct CvPluginFuncInfo { void** func_addr; void* default_func_addr; const char* func_names; 1.7. UTILITY AND SYSTEM FUNCTIONS AND MACROS 245 int search_modules; int loaded_from; } CvPluginFuncInfo; typedef struct CvModuleInfo { struct CvModuleInfo* next; const char* name; const char* version; CvPluginFuncInfo* func_tab; } CvModuleInfo; int cvRegisterModule( const CvModuleInfo* moduleInfo ); moduleInfo Information about the module The function adds a module to the list of registered modules. After the module is registered, information about it can be retrieved using the cvGetModuleInfo function. Also, the registered module makes full use of optimized plugins (IPP, MKL, ...), supported by CXCORE. CXCORE it- self, CV (computer vision), CVAUX (auxilary computer vision), and HIGHGUI (visualization and image/video acquisition) are examples of modules. Registration is usually done when the shared library is loaded. See cxcore/src/cxswitcher.cpp and cv/src/cvswitcher.cpp for de- tails about how registration is done and look at cxcore/src/cxswitcher.cpp, cxcore/src/ cxipp.h on how IPP and MKL are connected to the modules. cvGetModuleInfo (view/add comments) Retrieves information about registered module(s) and plugins. void cvGetModuleInfo( const char* moduleName, const char** version, const char** loadedAddonPlugins); 246 CHAPTER 1. CORE. THE CORE FUNCTIONALITY moduleName Name of the module of interest, or NULL, which means all the modules version The output parameter. Information about the module(s), including version loadedAddonPlugins The list of names and versions of the optimized plugins that CXCORE was able to find and load The function returns information about one or all of the registered modules. The returned information is stored inside the libraries, so the user should not deallocate or modify the returned text strings. cvUseOptimized (view/add comments) Switches between optimized/non-optimized modes. int cvUseOptimized( int onoff ); onoff Use optimized (6= 0) or not (= 0) The function switches between the mode, where only pure C implementations from cxcore, OpenCV, etc. are used, and the mode, where IPP and MKL functions are used if available. When cvUseOptimized(0) is called, all the optimized libraries are unloaded. The function may be useful for debugging, IPP and MKL upgrading on the fly, online speed comparisons, etc. It returns the number of optimized functions loaded. Note that by default, the optimized plugins are loaded, so it is not necessary to call cvUseOptimized(1) in the beginning of the program (actually, it will only increase the startup time). cvSetMemoryManager (view/add comments) Accesses custom/default memory managing functions. typedef void*(CV_CDECL *CvAllocFunc)(size_t size, void* userdata); typedef int (CV_CDECL *CvFreeFunc)(void* pptr, void* userdata); void cvSetMemoryManager( CvAllocFunc allocFunc=NULL, CvFreeFunc freeFunc=NULL, void* userdata=NULL ); 1.7. UTILITY AND SYSTEM FUNCTIONS AND MACROS 247 allocFunc Allocation function; the interface is similar to malloc, except that userdata may be used to determine the context freeFunc Deallocation function; the interface is similar to free userdata User data that is transparently passed to the custom functions The function sets user-defined memory managment functions (substitutes for malloc and free) that will be called by cvAlloc, cvFree and higher-level functions (e.g., cvCreateImage). Note that the function should be called when there is data allocated using cvAlloc. Also, to avoid infinite recursive calls, it is not allowed to call cvAlloc and cvFree from the custom alloca- tion/deallocation functions. If the alloc func and free func pointers are NULL, the default memory managing functions are restored. cvSetIPLAllocators (view/add comments) Switches to IPL functions for image allocation/deallocation. typedef IplImage*(CV_STDCALL* Cv_iplCreateImageHeader) (int,int,int,char*,char*,int,int,int,int,int, IplROI*,IplImage*,void*,IplTileInfo*); typedef void (CV_STDCALL* Cv_iplAllocateImageData)(IplImage*,int,int); typedef void (CV_STDCALL* Cv_iplDeallocate)(IplImage*,int); typedef IplROI*(CV_STDCALL* Cv_iplCreateROI)(int,int,int,int,int); typedef IplImage*(CV_STDCALL* Cv_iplCloneImage)(const IplImage*); #define CV_TURN_ON_IPL_COMPATIBILITY() \ cvSetIPLAllocators( iplCreateImageHeader, iplAllocateImage, \ iplDeallocate, iplCreateROI, iplCloneImage ) void cvSetIPLAllocators( Cv iplCreateImageHeader create header, Cv iplAllocateImageData allocate data, Cv iplDeallocate deallocate, Cv iplCreateROI create roi, Cv iplCloneImage clone image ); create header Pointer to iplCreateImageHeader 248 CHAPTER 1. CORE. THE CORE FUNCTIONALITY allocate data Pointer to iplAllocateImage deallocate Pointer to iplDeallocate create roi Pointer to iplCreateROI clone image Pointer to iplCloneImage The function causes CXCORE to use IPL functions for image allocation/deallocation opera- tions. For convenience, there is the wrapping macro CV TURN ON IPL COMPATIBILITY. The function is useful for applications where IPL and CXCORE/OpenCV are used together and still there are calls to iplCreateImageHeader, etc. The function is not necessary if IPL is called only for data processing and all the allocation/deallocation is done by CXCORE, or if all the allo- cation/deallocation is done by IPL and some of OpenCV functions are used to process the data. Chapter 2 imgproc. Image Processing 2.1 Histograms CvHistogram (view/add comments) Multi-dimensional histogram. typedef struct CvHistogram { int type; CvArr* bins; float thresh[CV_MAX_DIM][2]; /* for uniform histograms */ float** thresh2; /* for non-uniform histograms */ CvMatND mat; /* embedded matrix header for array histograms */ } CvHistogram; cvCalcBackProject (view/add comments) Calculates the back projection. void cvCalcBackProject( IplImage** image, CvArr* back project, const CvHistogram* hist ); 249 250 CHAPTER 2. IMGPROC. IMAGE PROCESSING image Source images (though you may pass CvMat** as well) back project Destination back projection image of the same type as the source images hist Histogram The function calculates the back project of the histogram. For each tuple of pixels at the same position of all input single-channel images the function puts the value of the histogram bin, corresponding to the tuple in the destination image. In terms of statistics, the value of each output image pixel is the probability of the observed tuple given the distribution (histogram). For example, to find a red object in the picture, one may do the following: 1. Calculate a hue histogram for the red object assuming the image contains only this object. The histogram is likely to have a strong maximum, corresponding to red color. 2. Calculate back projection of a hue plane of input image where the object is searched, using the histogram. Threshold the image. 3. Find connected components in the resulting picture and choose the right component using some additional criteria, for example, the largest connected component. That is the approximate algorithm of Camshift color object tracker, except for the 3rd step, instead of which CAMSHIFT algorithm is used to locate the object on the back projection given the previous object position. cvCalcBackProjectPatch (view/add comments) Locates a template within an image by using a histogram comparison. void cvCalcBackProjectPatch( IplImage** images, CvArr* dst, CvSize patch size, CvHistogram* hist, int method, double factor ); images Source images (though, you may pass CvMat** as well) 2.1. HISTOGRAMS 251 dst Destination image patch size Size of the patch slid though the source image hist Histogram method Comparison method, passed to cvCompareHist (see description of that function) factor Normalization factor for histograms, will affect the normalization scale of the destination image, pass 1 if unsure The function calculates the back projection by comparing histograms of the source image patches with the given histogram. Taking measurement results from some image at each location over ROI creates an array image. These results might be one or more of hue, x derivative, y derivative, Laplacian filter, oriented Gabor filter, etc. Each measurement output is collected into its own separate image. The image image array is a collection of these measurement images. A multi-dimensional histogram hist is constructed by sampling from the image image array. The final histogram is normalized. The hist histogram has as many dimensions as the number of elements in image array. Each new image is measured and then converted into an image image array over a cho- sen ROI. Histograms are taken from this image image in an area covered by a ”patch” with an anchor at center as shown in the picture below. The histogram is normalized using the param- eter norm factor so that it may be compared with hist. The calculated histogram is com- pared to the model histogram; hist uses The function cvCompareHist with the comparison method=method). The resulting output is placed at the location corresponding to the patch an- chor in the probability image dst. This process is repeated as the patch is slid over the ROI. Iterative histogram update by subtracting trailing pixels covered by the patch and adding newly covered pixels to the histogram can save a lot of operations, though it is not implemented yet. Back Project Calculation by Patches 252 CHAPTER 2. IMGPROC. IMAGE PROCESSING cvCalcHist (view/add comments) Calculates the histogram of image(s). void cvCalcHist( IplImage** image, CvHistogram* hist, int accumulate=0, const CvArr* mask=NULL ); image Source images (though you may pass CvMat** as well) hist Pointer to the histogram accumulate Accumulation flag. If it is set, the histogram is not cleared in the beginning. This feature allows user to compute a single histogram from several images, or to update the histogram online mask The operation mask, determines what pixels of the source images are counted The function calculates the histogram of one or more single-channel images. The elements of a tuple that is used to increment a histogram bin are taken at the same location from the corresponding input images. #include #include int main( int argc, char** argv ) { IplImage* src; if( argc == 2 && (src=cvLoadImage(argv[1], 1))!= 0) { IplImage* h_plane = cvCreateImage( cvGetSize(src), 8, 1 ); IplImage* s_plane = cvCreateImage( cvGetSize(src), 8, 1 ); IplImage* v_plane = cvCreateImage( cvGetSize(src), 8, 1 ); IplImage* planes[] = { h_plane, s_plane }; IplImage* hsv = cvCreateImage( cvGetSize(src), 8, 3 ); int h_bins = 30, s_bins = 32; int hist_size[] = {h_bins, s_bins}; /* hue varies from 0 (˜0 deg red) to 180 (˜360 deg red again) */ float h_ranges[] = { 0, 180 }; 2.1. HISTOGRAMS 253 /* saturation varies from 0 (black-gray-white) to 255 (pure spectrum color) */ float s_ranges[] = { 0, 255 }; float* ranges[] = { h_ranges, s_ranges }; int scale = 10; IplImage* hist_img = cvCreateImage( cvSize(h_bins*scale,s_bins*scale), 8, 3 ); CvHistogram* hist; float max_value = 0; int h, s; cvCvtColor( src, hsv, CV_BGR2HSV ); cvCvtPixToPlane( hsv, h_plane, s_plane, v_plane, 0 ); hist = cvCreateHist( 2, hist_size, CV_HIST_ARRAY, ranges, 1 ); cvCalcHist( planes, hist, 0, 0 ); cvGetMinMaxHistValue( hist, 0, &max_value, 0, 0 ); cvZero( hist_img ); for( h = 0; h < h_bins; h++ ) { for( s = 0; s < s_bins; s++ ) { float bin_val = cvQueryHistValue\_2D( hist, h, s ); int intensity = cvRound(bin_val*255/max_value); cvRectangle( hist_img, cvPoint( h*scale, s*scale ), cvPoint( (h+1)*scale - 1, (s+1)*scale - 1), CV_RGB(intensity,intensity,intensity), CV_FILLED ); } } cvNamedWindow( "Source", 1 ); cvShowImage( "Source", src ); cvNamedWindow( "H-S Histogram", 1 ); cvShowImage( "H-S Histogram", hist_img ); cvWaitKey(0); } } cvCalcProbDensity (view/add comments) Divides one histogram by another. 254 CHAPTER 2. IMGPROC. IMAGE PROCESSING void cvCalcProbDensity( const CvHistogram* hist1, const CvHistogram* hist2, CvHistogram* dst hist, double scale=255 ); hist1 first histogram (the divisor) hist2 second histogram dst hist destination histogram scale scale factor for the destination histogram The function calculates the object probability density from the two histograms as: dist hist(I) =    0 if hist1(I) = 0 scale if hist1(I) 6= 0 and hist2(I) > hist1(I) hist2(I)·scale hist1(I) if hist1(I) 6= 0 and hist2(I) ≤ hist1(I) So the destination histogram bins are within less than scale. cvClearHist (view/add comments) Clears the histogram. void cvClearHist( CvHistogram* hist ); hist Histogram The function sets all of the histogram bins to 0 in the case of a dense histogram and removes all histogram bins in the case of a sparse array. 2.1. HISTOGRAMS 255 cvCompareHist (view/add comments) Compares two dense histograms. double cvCompareHist( const CvHistogram* hist1, const CvHistogram* hist2, int method ); hist1 The first dense histogram hist2 The second dense histogram method Comparison method, one of the following: CV COMP CORREL Correlation CV COMP CHISQR Chi-Square CV COMP INTERSECT Intersection CV COMP BHATTACHARYYA Bhattacharyya distance The function compares two dense histograms using the specified method (H1 denotes the first histogram, H2 the second): Correlation (method=CV COMP CORREL) d(H1,H2) = P I(H0 1(I)·H0 2(I)) pP I(H0 1(I)2)·P I(H0 2(I)2) where H0 k(I) = Hk(I) − 1 N·P JHk(J) where N is the number of histogram bins. Chi-Square (method=CV COMP CHISQR) d(H1,H2) = X I (H1(I) − H2(I))2 H1(I) + H2(I) 256 CHAPTER 2. IMGPROC. IMAGE PROCESSING Intersection (method=CV COMP INTERSECT) d(H1,H2) = X I min(H1(I),H2(I)) Bhattacharyya distance (method=CV COMP BHATTACHARYYA) d(H1,H2) = vuut1 − X I pH1(I)·H2(I) pP IH1(I)·P IH2(I) The function returns d(H1,H2). Note: the method CV COMP BHATTACHARYYA only works with normalized histograms. To compare a sparse histogram or more general sparse configurations of weighted points, consider using the cvCalcEMD2 function. cvCopyHist (view/add comments) Copies a histogram. void cvCopyHist( const CvHistogram* src, CvHistogram** dst ); src Source histogram dst Pointer to destination histogram The function makes a copy of the histogram. If the second histogram pointer *dst is NULL, a new histogram of the same size as src is created. Otherwise, both histograms must have equal types and sizes. Then the function copies the source histogram’s bin values to the destination histogram and sets the same bin value ranges as in src. cvCreateHist (view/add comments) Creates a histogram. 2.1. HISTOGRAMS 257 CvHistogram* cvCreateHist( int dims, int* sizes, int type, float** ranges=NULL, int uniform=1 ); dims Number of histogram dimensions sizes Array of the histogram dimension sizes type Histogram representation format: CV HIST ARRAY means that the histogram data is rep- resented as a multi-dimensional dense array CvMatND; CV HIST SPARSE means that his- togram data is represented as a multi-dimensional sparse array CvSparseMat ranges Array of ranges for the histogram bins. Its meaning depends on the uniform param- eter value. The ranges are used for when the histogram is calculated or backprojected to determine which histogram bin corresponds to which value/tuple of values from the input image(s) uniform Uniformity flag; if not 0, the histogram has evenly spaced bins and for every 0 <= i < cDims ranges[i] is an array of two numbers: lower and upper boundaries for the i-th his- togram dimension. The whole range [lower,upper] is then split into dims[i] equal parts to determine the i-th input tuple value ranges for every histogram bin. And if uniform=0, then i-th element of ranges array contains dims[i]+1 elements: lower0, upper0, lower1, upper1 = lower2, ...upperdims[i]−1 where lowerj and upperj are lower and upper boundaries of i-th input tuple value for j-th bin, respectively. In either case, the input values that are beyond the specified range for a histogram bin are not counted by cvCalcHist and filled with 0 by cvCalcBackProject The function creates a histogram of the specified size and returns a pointer to the created histogram. If the array ranges is 0, the histogram bin ranges must be specified later via the function cvSetHistBinRanges. Though cvCalcHist and cvCalcBackProject may process 8-bit images without setting bin ranges, they assume thy are equally spaced in 0 to 255 bins. cvGetHistValue*D (view/add comments) Returns a pointer to the histogram bin. 258 CHAPTER 2. IMGPROC. IMAGE PROCESSING float cvGetHistValue 1D(hist, idx0) float cvGetHistValue 2D(hist, idx0, idx1) float cvGetHistValue 3D(hist, idx0, idx1, idx2) float cvGetHistValue nD(hist, idx) hist Histogram idx0, idx1, idx2, idx3 Indices of the bin idx Array of indices #define cvGetHistValue_1D( hist, idx0 ) ((float*)(cvPtr1D( (hist)->bins, (idx0), 0 )) #define cvGetHistValue_2D( hist, idx0, idx1 ) ((float*)(cvPtr2D( (hist)->bins, (idx0), (idx1), 0 ))) #define cvGetHistValue_3D( hist, idx0, idx1, idx2 ) ((float*)(cvPtr3D( (hist)->bins, (idx0), (idx1), (idx2), 0 ))) #define cvGetHistValue_nD( hist, idx ) ((float*)(cvPtrND( (hist)->bins, (idx), 0 ))) The macros GetHistValue return a pointer to the specified bin of the 1D, 2D, 3D or N-D histogram. In the case of a sparse histogram the function creates a new bin and sets it to 0, unless it exists already. cvGetMinMaxHistValue (view/add comments) Finds the minimum and maximum histogram bins. void cvGetMinMaxHistValue( const CvHistogram* hist, float* min value, float* max value, int* min idx=NULL, int* max idx=NULL ); 2.1. HISTOGRAMS 259 hist Histogram min value Pointer to the minimum value of the histogram max value Pointer to the maximum value of the histogram min idx Pointer to the array of coordinates for the minimum max idx Pointer to the array of coordinates for the maximum The function finds the minimum and maximum histogram bins and their positions. All of output arguments are optional. Among several extremas with the same value the ones with the minimum index (in lexicographical order) are returned. In the case of several maximums or minimums, the earliest in lexicographical order (extrema locations) is returned. cvMakeHistHeaderForArray (view/add comments) Makes a histogram out of an array. CvHistogram* cvMakeHistHeaderForArray( int dims, int* sizes, CvHistogram* hist, float* data, float** ranges=NULL, int uniform=1 ); dims Number of histogram dimensions sizes Array of the histogram dimension sizes hist The histogram header initialized by the function data Array that will be used to store histogram bins ranges Histogram bin ranges, see cvCreateHist uniform Uniformity flag, see cvCreateHist The function initializes the histogram, whose header and bins are allocated by th user. cvRe- leaseHist does not need to be called afterwards. Only dense histograms can be initialized this way. The function returns hist. 260 CHAPTER 2. IMGPROC. IMAGE PROCESSING cvNormalizeHist (view/add comments) Normalizes the histogram. void cvNormalizeHist( CvHistogram* hist, double factor ); hist Pointer to the histogram factor Normalization factor The function normalizes the histogram bins by scaling them, such that the sum of the bins becomes equal to factor. cvQueryHistValue*D (view/add comments) Queries the value of the histogram bin. float QueryHistValue 1D(CvHistogram hist, int idx0) hist Histogram idx0, idx1, idx2, idx3 Indices of the bin idx Array of indices #define cvQueryHistValue\_1D( hist, idx0 ) \ cvGetReal1D( (hist)->bins, (idx0) ) #define cvQueryHistValue\_2D( hist, idx0, idx1 ) \ cvGetReal2D( (hist)->bins, (idx0), (idx1) ) #define cvQueryHistValue\_3D( hist, idx0, idx1, idx2 ) \ cvGetReal3D( (hist)->bins, (idx0), (idx1), (idx2) ) #define cvQueryHistValue\_nD( hist, idx ) \ cvGetRealND( (hist)->bins, (idx) ) The macros return the value of the specified bin of the 1D, 2D, 3D or N-D histogram. In the case of a sparse histogram the function returns 0, if the bin is not present in the histogram no new bin is created. 2.1. HISTOGRAMS 261 cvReleaseHist (view/add comments) Releases the histogram. void cvReleaseHist( CvHistogram** hist ); hist Double pointer to the released histogram The function releases the histogram (header and the data). The pointer to the histogram is cleared by the function. If *hist pointer is already NULL, the function does nothing. cvSetHistBinRanges (view/add comments) Sets the bounds of the histogram bins. void cvSetHistBinRanges( CvHistogram* hist, float** ranges, int uniform=1 ); hist Histogram ranges Array of bin ranges arrays, see cvCreateHist uniform Uniformity flag, see cvCreateHist The function is a stand-alone function for setting bin ranges in the histogram. For a more detailed description of the parameters ranges and uniform see the cvCalcHist function, that can initialize the ranges as well. Ranges for the histogram bins must be set before the histogram is calculated or the backproject of the histogram is calculated. cvThreshHist (view/add comments) Thresholds the histogram. 262 CHAPTER 2. IMGPROC. IMAGE PROCESSING void cvThreshHist( CvHistogram* hist, double threshold ); hist Pointer to the histogram threshold Threshold level The function clears histogram bins that are below the specified threshold. 2.2 Image Filtering Functions and classes described in this section are used to perform various linear or non-linear filtering operations on 2D images (represented as cv’s), that is, for each pixel location (x, y) in the source image some its (normally rectangular) neighborhood is considered and used to compute the response. In case of a linear filter it is a weighted sum of pixel values, in case of morphological operations it is the minimum or maximum etc. The computed response is stored to the destination image at the same location (x, y). It means, that the output image will be of the same size as the input image. Normally, the functions supports multi-channel arrays, in which case every channel is processed independently, therefore the output image will also have the same number of channels as the input one. Another common feature of the functions and classes described in this section is that, unlike simple arithmetic functions, they need to extrapolate values of some non-existing pixels. For ex- ample, if we want to smooth an image using a Gaussian 3 × 3 filter, then during the processing of the left-most pixels in each row we need pixels to the left of them, i.e. outside of the image. We can let those pixels be the same as the left-most image pixels (i.e. use ”replicated border” extrapo- lation method), or assume that all the non-existing pixels are zeros (”contant border” extrapolation method) etc. IplConvKernel (view/add comments) An IplConvKernel is a rectangular convolution kernel, created by function CreateStructuringEle- mentEx. cvCopyMakeBorder (view/add comments) Copies an image and makes a border around it. 2.2. IMAGE FILTERING 263 void cvCopyMakeBorder( const CvArr* src, CvArr* dst, CvPoint offset, int bordertype, CvScalar value=cvScalarAll(0) ); src The source image dst The destination image offset Coordinates of the top-left corner (or bottom-left in the case of images with bottom-left origin) of the destination image rectangle where the source image (or its ROI) is copied. Size of the rectanlge matches the source image size/ROI size bordertype Type of the border to create around the copied source image rectangle; types in- clude: IPL BORDER CONSTANT border is filled with the fixed value, passed as last parameter of the function. IPL BORDER REPLICATE the pixels from the top and bottom rows, the left-most and right- most columns are replicated to fill the border. (The other two border types from IPL, IPL BORDER REFLECT and IPL BORDER WRAP, are currently unsupported) value Value of the border pixels if bordertype is IPL BORDER CONSTANT The function copies the source 2D array into the interior of the destination array and makes a border of the specified type around the copied area. The function is useful when one needs to emulate border type that is different from the one embedded into a specific algorithm implementa- tion. For example, morphological functions, as well as most of other filtering functions in OpenCV, internally use replication border type, while the user may need a zero border or a border, filled with 1’s or 255’s. cvCreateStructuringElementEx (view/add comments) Creates a structuring element. 264 CHAPTER 2. IMGPROC. IMAGE PROCESSING IplConvKernel* cvCreateStructuringElementEx( int cols, int rows, int anchorX, int anchorY, int shape, int* values=NULL ); cols Number of columns in the structuring element rows Number of rows in the structuring element anchorX Relative horizontal offset of the anchor point anchorY Relative vertical offset of the anchor point shape Shape of the structuring element; may have the following values: CV SHAPE RECT a rectangular element CV SHAPE CROSS a cross-shaped element CV SHAPE ELLIPSE an elliptic element CV SHAPE CUSTOM a user-defined element. In this case the parameter values specifies the mask, that is, which neighbors of the pixel must be considered values Pointer to the structuring element data, a plane array, representing row-by-row scanning of the element matrix. Non-zero values indicate points that belong to the element. If the pointer is NULL, then all values are considered non-zero, that is, the element is of a rectan- gular shape. This parameter is considered only if the shape is CV SHAPE CUSTOM The function CreateStructuringElementEx allocates and fills the structure IplConvKernel, which can be used as a structuring element in the morphological operations. cvDilate (view/add comments) Dilates an image by using a specific structuring element. 2.2. IMAGE FILTERING 265 void cvDilate( const CvArr* src, CvArr* dst, IplConvKernel* element=NULL, int iterations=1 ); src Source image dst Destination image element Structuring element used for dilation. If it is NULL, a 3 × 3 rectangular structuring element is used iterations Number of times dilation is applied The function dilates the source image using the specified structuring element that determines the shape of a pixel neighborhood over which the maximum is taken: max (x0,y0) in element src(x + x0, y + y0) The function supports the in-place mode. Dilation can be applied several (iterations) times. For color images, each channel is processed independently. cvErode (view/add comments) Erodes an image by using a specific structuring element. void cvErode( const CvArr* src, CvArr* dst, IplConvKernel* element=NULL, int iterations=1); src Source image dst Destination image 266 CHAPTER 2. IMGPROC. IMAGE PROCESSING element Structuring element used for erosion. If it is NULL, a 3 × 3 rectangular structuring element is used iterations Number of times erosion is applied The function erodes the source image using the specified structuring element that determines the shape of a pixel neighborhood over which the minimum is taken: min (x0,y0) in element src(x + x0, y + y0) The function supports the in-place mode. Erosion can be applied several (iterations) times. For color images, each channel is processed independently. cvFilter2D (view/add comments) Convolves an image with the kernel. void cvFilter2D( const CvArr* src, CvArr* dst, const CvMat* kernel, CvPoint anchor=cvPoint(-1,-1)); src The source image dst The destination image kernel Convolution kernel, a single-channel floating point matrix. If you want to apply different kernels to different channels, split the image into separate color planes using cvSplit and process them individually anchor The anchor of the kernel that indicates the relative position of a filtered point within the kernel. The anchor shoud lie within the kernel. The special default value (-1,-1) means that it is at the kernel center The function applies an arbitrary linear filter to the image. In-place operation is supported. When the aperture is partially outside the image, the function interpolates outlier pixel values from the nearest pixels that are inside the image. 2.2. IMAGE FILTERING 267 cvLaplace (view/add comments) Calculates the Laplacian of an image. void cvLaplace( const CvArr* src, CvArr* dst, int apertureSize=3); src Source image dst Destination image apertureSize Aperture size (it has the same meaning as cvSobel) The function calculates the Laplacian of the source image by adding up the second x and y derivatives calculated using the Sobel operator: dst(x, y) = d2src dx2 + d2src dy2 Setting apertureSize = 1 gives the fastest variant that is equal to convolving the image with the following kernel:   0 1 0 1 −4 1 0 1 0   Similar to the cvSobel function, no scaling is done and the same combinations of input and output formats are supported. cvMorphologyEx (view/add comments) Performs advanced morphological transformations. 268 CHAPTER 2. IMGPROC. IMAGE PROCESSING void cvMorphologyEx( const CvArr* src, CvArr* dst, CvArr* temp, IplConvKernel* element, int operation, int iterations=1 ); src Source image dst Destination image temp Temporary image, required in some cases element Structuring element operation Type of morphological operation, one of the following: CV MOP OPEN opening CV MOP CLOSE closing CV MOP GRADIENT morphological gradient CV MOP TOPHAT ”top hat” CV MOP BLACKHAT ”black hat” iterations Number of times erosion and dilation are applied The function can perform advanced morphological transformations using erosion and dilation as basic operations. Opening: dst = open(src, element) = dilate(erode(src, element), element) Closing: dst = close(src, element) = erode(dilate(src, element), element) Morphological gradient: dst = morph grad(src, element) = dilate(src, element) − erode(src, element) 2.2. IMAGE FILTERING 269 ”Top hat”: dst = tophat(src, element) = src − open(src, element) ”Black hat”: dst = blackhat(src, element) = close(src, element) − src The temporary image temp is required for a morphological gradient and, in the case of in-place operation, for ”top hat” and ”black hat”. cvPyrDown (view/add comments) Downsamples an image. void cvPyrDown( const CvArr* src, CvArr* dst, int filter=CV GAUSSIAN 5x5 ); src The source image dst The destination image, should have a half as large width and height than the source filter Type of the filter used for convolution; only CV GAUSSIAN 5x5 is currently supported The function performs the downsampling step of the Gaussian pyramid decomposition. First it convolves the source image with the specified filter and then downsamples the image by rejecting even rows and columns. cvReleaseStructuringElement (view/add comments) Deletes a structuring element. void cvReleaseStructuringElement( IplConvKernel** element ); 270 CHAPTER 2. IMGPROC. IMAGE PROCESSING element Pointer to the deleted structuring element The function releases the structure IplConvKernel that is no longer needed. If *element is NULL, the function has no effect. cvSmooth (view/add comments) Smooths the image in one of several ways. void cvSmooth( const CvArr* src, CvArr* dst, int smoothtype=CV GAUSSIAN, int param1=3, int param2=0, double param3=0, double param4=0); src The source image dst The destination image smoothtype Type of the smoothing: CV BLUR NO SCALE linear convolution with param1 × param2 box kernel (all 1’s). If you want to smooth different pixels with different-size box kernels, you can use the integral image that is computed using cvIntegral CV BLUR linear convolution with param1 × param2 box kernel (all 1’s) with subsequent scaling by 1/(param1 · param2) CV GAUSSIAN linear convolution with a param1 × param2 Gaussian kernel CV MEDIAN median filter with a param1 × param1 square aperture CV BILATERAL bilateral filter with a param1×param1 square aperture, color sigma=param3 and spatial sigma=param4. If param1=0, the aperture square side is set to cvRound(param4*1.5)*2+1. Information about bilateral filtering can be found at http://www.dai.ed.ac.uk/ CVonline/LOCAL_COPIES/MANDUCHI1/Bilateral_Filtering.html param1 The first parameter of the smoothing operation, the aperture width. Must be a positive odd number (1, 3, 5, ...) 2.2. IMAGE FILTERING 271 param2 The second parameter of the smoothing operation, the aperture height. Ignored by CV MEDIAN and CV BILATERAL methods. In the case of simple scaled/non-scaled and Gaussian blur if param2 is zero, it is set to param1. Otherwise it must be a positive odd number. param3 In the case of a Gaussian parameter this parameter may specify Gaussian σ (standard deviation). If it is zero, it is calculated from the kernel size: σ = 0.3(n/2 − 1) + 0.8 where n = param1 for horizontal kernel param2 for vertical kernel Using standard sigma for small kernels (3 × 3 to 7 × 7) gives better speed. If param3 is not zero, while param1 and param2 are zeros, the kernel size is calculated from the sigma (to provide accurate enough operation). The function smooths an image using one of several methods. Every of the methods has some features and restrictions listed below Blur with no scaling works with single-channel images only and supports accumulation of 8-bit to 16-bit format (similar to cvSobel and cvLaplace) and 32-bit floating point to 32-bit floating-point format. Simple blur and Gaussian blur support 1- or 3-channel, 8-bit and 32-bit floating point images. These two methods can process images in-place. Median and bilateral filters work with 1- or 3-channel 8-bit images and can not process images in-place. cvSobel (view/add comments) Calculates the first, second, third or mixed image derivatives using an extended Sobel operator. void cvSobel( const CvArr* src, CvArr* dst, int xorder, int yorder, int apertureSize=3 ); src Source image of type CvArr* 272 CHAPTER 2. IMGPROC. IMAGE PROCESSING dst Destination image xorder Order of the derivative x yorder Order of the derivative y apertureSize Size of the extended Sobel kernel, must be 1, 3, 5 or 7 In all cases except 1, an apertureSize × apertureSize separable kernel will be used to calculate the derivative. For apertureSize = 1 a 3 × 1 or 1 × 3 a kernel is used (Gaussian smoothing is not done). There is also the special value CV SCHARR (-1) that corresponds to a 3×3 Scharr filter that may give more accurate results than a 3 × 3 Sobel. Scharr aperture is   −3 0 3 −10 0 10 −3 0 3   for the x-derivative or transposed for the y-derivative. The function calculates the image derivative by convolving the image with the appropriate kernel: dst(x, y) = dxorder+yordersrc dxxorder · dyyorder The Sobel operators combine Gaussian smoothing and differentiation so the result is more or less resistant to the noise. Most often, the function is called with (xorder = 1, yorder = 0, apertureSize = 3) or (xorder = 0, yorder = 1, apertureSize = 3) to calculate the first x- or y- image derivative. The first case corresponds to a kernel of:   −1 0 1 −2 0 2 −1 0 1   and the second one corresponds to a kernel of:   −1 −2 −1 0 0 0 1 2 1   or a kernel of:   1 2 1 0 0 0 −1 2 −1   2.3. GEOMETRIC IMAGE TRANSFORMATIONS 273 depending on the image origin (origin field of IplImage structure). No scaling is done, so the destination image usually has larger numbers (in absolute values) than the source image does. To avoid overflow, the function requires a 16-bit destination image if the source image is 8-bit. The result can be converted back to 8-bit using the cvConvertScale or the cvConvertScaleAbs function. Besides 8-bit images the function can process 32-bit floating-point images. Both the source and the destination must be single-channel images of equal size or equal ROI size. 2.3 Geometric Image Transformations The functions in this section perform various geometrical transformations of 2D images. That is, they do not change the image content, but deform the pixel grid, and map this deformed grid to the destination image. In fact, to avoid sampling artifacts, the mapping is done in the reverse order, from destination to the source. That is, for each pixel (x, y) of the destination image, the functions compute coordinates of the corresponding ”donor” pixel in the source image and copy the pixel value, that is: dst(x, y) = src(fx(x, y), fy(x, y)) In the case when the user specifies the forward mapping: hgx, gyi : src → dst, the OpenCV functions first compute the corresponding inverse mapping: hfx, fyi : dst → src and then use the above formula. The actual implementations of the geometrical transformations, from the most generic cvRemap and to the simplest and the fastest cvResize, need to solve the 2 main problems with the above formula: 1. extrapolation of non-existing pixels. Similarly to the filtering functions, described in the pre- vious section, for some (x, y) one of fx(x, y) or fy(x, y), or they both, may fall outside of the image, in which case some extrapolation method needs to be used. OpenCV provides the same selection of the extrapolation methods as in the filtering functions, but also an ad- ditional method BORDER TRANSPARENT, which means that the corresponding pixels in the destination image will not be modified at all. 2. interpolation of pixel values. Usually fx(x, y) and fy(x, y) are floating-point numbers (i.e. hfx, fyi can be an affine or perspective transformation, or radial lens distortion correction etc.), so a pixel values at fractional coordinates needs to be retrieved. In the simplest case the coordinates can be just rounded to the nearest integer coordinates and the correspond- ing pixel used, which is called nearest-neighbor interpolation. However, a better result can be achieved by using more sophisticated interpolation methods, where a polynomial function is fit into some neighborhood of the computed pixel (fx(x, y), fy(x, y)) and then the value of the polynomial at (fx(x, y), fy(x, y)) is taken as the interpolated pixel value. In OpenCV you can choose between several interpolation methods, see cvResize. 274 CHAPTER 2. IMGPROC. IMAGE PROCESSING cvGetRotationMatrix2D (view/add comments) Calculates the affine matrix of 2d rotation. CvMat* cv2DRotationMatrix( CvPoint2D32f center, double angle, double scale, CvMat* mapMatrix ); center Center of the rotation in the source image angle The rotation angle in degrees. Positive values mean counter-clockwise rotation (the coor- dinate origin is assumed to be the top-left corner) scale Isotropic scale factor mapMatrix Pointer to the destination 2 × 3 matrix The function cv2DRotationMatrix calculates the following matrix:  α β (1 − α)· center.x − β · center.y −β α β · center.x − (1 − α)· center.y  where α = scale · cos(angle), β = scale · sin(angle) The transformation maps the rotation center to itself. If this is not the purpose, the shift should be adjusted. cvGetAffineTransform (view/add comments) Calculates the affine transform from 3 corresponding points. CvMat* cvGetAffineTransform( const CvPoint2D32f* src, const CvPoint2D32f* dst, CvMat* mapMatrix ); 2.3. GEOMETRIC IMAGE TRANSFORMATIONS 275 src Coordinates of 3 triangle vertices in the source image dst Coordinates of the 3 corresponding triangle vertices in the destination image mapMatrix Pointer to the destination 2 × 3 matrix The function cvGetAffineTransform calculates the matrix of an affine transform such that: x0 i y0 i  = mapMatrix ·   xi yi 1   where dst(i) = (x0 i, y0 i), src(i) = (xi, yi), i = 0, 1, 2 cvGetPerspectiveTransform (view/add comments) Calculates the perspective transform from 4 corresponding points. CvMat* cvGetPerspectiveTransform( const CvPoint2D32f* src, const CvPoint2D32f* dst, CvMat* mapMatrix ); src Coordinates of 4 quadrangle vertices in the source image dst Coordinates of the 4 corresponding quadrangle vertices in the destination image mapMatrix Pointer to the destination 3 × 3 matrix The function cvGetPerspectiveTransform calculates a matrix of perspective transforms such that: x0 i y0 i  = mapMatrix ·   xi yi 1   where dst(i) = (x0 i, y0 i), src(i) = (xi, yi), i = 0, 1, 2, 3 276 CHAPTER 2. IMGPROC. IMAGE PROCESSING cvGetQuadrangleSubPix (view/add comments) Retrieves the pixel quadrangle from an image with sub-pixel accuracy. void cvGetQuadrangleSubPix( const CvArr* src, CvArr* dst, const CvMat* mapMatrix ); src Source image dst Extracted quadrangle mapMatrix The transformation 2 × 3 matrix [A|b](see the discussion) The function cvGetQuadrangleSubPix extracts pixels from src at sub-pixel accuracy and stores them to dst as follows: dst(x, y) = src(A11x0 + A12y0 + b1,A21x0 + A22y0 + b2) where x0 = x − (width(dst) − 1) 2 , y0 = y − (height(dst) − 1) 2 and mapMatrix = A11 A12 b1 A21 A22 b2  The values of pixels at non-integer coordinates are retrieved using bilinear interpolation. When the function needs pixels outside of the image, it uses replication border mode to reconstruct the values. Every channel of multiple-channel images is processed independently. cvGetRectSubPix (view/add comments) Retrieves the pixel rectangle from an image with sub-pixel accuracy. 2.3. GEOMETRIC IMAGE TRANSFORMATIONS 277 void cvGetRectSubPix( const CvArr* src, CvArr* dst, CvPoint2D32f center ); src Source image dst Extracted rectangle center Floating point coordinates of the extracted rectangle center within the source image. The center must be inside the image The function cvGetRectSubPix extracts pixels from src: dst(x, y) = src(x + center.x − (width(dst) − 1) ∗ 0.5, y + center.y − (height(dst) − 1) ∗ 0.5) where the values of the pixels at non-integer coordinates are retrieved using bilinear interpo- lation. Every channel of multiple-channel images is processed independently. While the rectangle center must be inside the image, parts of the rectangle may be outside. In this case, the replication border mode is used to get pixel values beyond the image boundaries. cvLogPolar (view/add comments) Remaps an image to log-polar space. void cvLogPolar( const CvArr* src, CvArr* dst, CvPoint2D32f center, double M, int flags=CV INTER LINEAR+CV WARP FILL OUTLIERS ); src Source image dst Destination image 278 CHAPTER 2. IMGPROC. IMAGE PROCESSING center The transformation center; where the output precision is maximal M Magnitude scale parameter. See below flags A combination of interpolation methods and the following optional flags: CV WARP FILL OUTLIERS fills all of the destination image pixels. If some of them corre- spond to outliers in the source image, they are set to zero CV WARP INVERSE MAP See below The function cvLogPolar transforms the source image using the following transformation: Forward transformation (CV WARP INVERSE MAP is not set): dst(φ, ρ) = src(x, y) Inverse transformation (CV WARP INVERSE MAP is set): dst(x, y) = src(φ, ρ) where ρ = M· log px2 + y2, φ = atan(y/x) The function emulates the human ”foveal” vision and can be used for fast scale and rotation- invariant template matching, for object tracking and so forth. The function can not operate in-place. #include #include int main(int argc, char** argv) { IplImage* src; if( argc == 2 && (src=cvLoadImage(argv[1],1) != 0 ) { IplImage* dst = cvCreateImage( cvSize(256,256), 8, 3 ); IplImage* src2 = cvCreateImage( cvGetSize(src), 8, 3 ); cvLogPolar( src, dst, cvPoint2D32f(src->width/2,src->height/2), 40, CV_INTER_LINEAR+CV_WARP_FILL_OUTLIERS ); cvLogPolar( dst, src2, cvPoint2D32f(src->width/2,src->height/2), 40, CV_INTER_LINEAR+CV_WARP_FILL_OUTLIERS+CV_WARP_INVERSE_MAP ); cvNamedWindow( "log-polar", 1 ); cvShowImage( "log-polar", dst ); cvNamedWindow( "inverse log-polar", 1 ); cvShowImage( "inverse log-polar", src2 ); 2.3. GEOMETRIC IMAGE TRANSFORMATIONS 279 cvWaitKey(); } return 0; } And this is what the program displays when opencv/samples/c/fruits.jpg is passed to it cvRemap (view/add comments) Applies a generic geometrical transformation to the image. void cvRemap( const CvArr* src, CvArr* dst, const CvArr* mapx, const CvArr* mapy, int flags=CV INTER LINEAR+CV WARP FILL OUTLIERS, CvScalar fillval=cvScalarAll(0) ); src Source image dst Destination image mapx The map of x-coordinates (CV 32FC1 image) 280 CHAPTER 2. IMGPROC. IMAGE PROCESSING mapy The map of y-coordinates (CV 32FC1 image) flags A combination of interpolation method and the following optional flag(s): CV WARP FILL OUTLIERS fills all of the destination image pixels. If some of them corre- spond to outliers in the source image, they are set to fillval fillval A value used to fill outliers The function cvRemap transforms the source image using the specified map: dst(x, y) = src(mapx(x, y), mapy(x, y)) Similar to other geometrical transformations, some interpolation method (specified by user) is used to extract pixels with non-integer coordinates. Note that the function can not operate in-place. cvResize (view/add comments) Resizes an image. void cvResize( const CvArr* src, CvArr* dst, int interpolation=CV INTER LINEAR ); src Source image dst Destination image interpolation Interpolation method: CV INTER NN nearest-neigbor interpolation CV INTER LINEAR bilinear interpolation (used by default) CV INTER AREA resampling using pixel area relation. It is the preferred method for im- age decimation that gives moire-free results. In terms of zooming it is similar to the CV INTER NN method CV INTER CUBIC bicubic interpolation The function cvResize resizes an image src so that it fits exactly into dst. If ROI is set, the function considers the ROI as supported. 2.3. GEOMETRIC IMAGE TRANSFORMATIONS 281 cvWarpAffine (view/add comments) Applies an affine transformation to an image. void cvWarpAffine( const CvArr* src, CvArr* dst, const CvMat* mapMatrix, int flags=CV INTER LINEAR+CV WARP FILL OUTLIERS, CvScalar fillval=cvScalarAll(0) ); src Source image dst Destination image mapMatrix 2 × 3 transformation matrix flags A combination of interpolation methods and the following optional flags: CV WARP FILL OUTLIERS fills all of the destination image pixels; if some of them corre- spond to outliers in the source image, they are set to fillval CV WARP INVERSE MAP indicates that matrix is inversely transformed from the destination image to the source and, thus, can be used directly for pixel interpolation. Otherwise, the function finds the inverse transform from mapMatrix fillval A value used to fill outliers The function cvWarpAffine transforms the source image using the specified matrix: dst(x0, y0) = src(x, y) where x0 y0  = mapMatrix ·   x y 1   if CV WARP INVERSE MAP is not set x y  = mapMatrix ·   x0 y0 1   otherwise 282 CHAPTER 2. IMGPROC. IMAGE PROCESSING The function is similar to cvGetQuadrangleSubPix but they are not exactly the same. cvWarpAffine requires input and output image have the same data type, has larger overhead (so it is not quite suitable for small images) and can leave part of destination image unchanged. While cvGetQuad- rangleSubPix may extract quadrangles from 8-bit images into floating-point buffer, has smaller overhead and always changes the whole destination image content. Note that the function can not operate in-place. To transform a sparse set of points, use the cvTransform function from cxcore. cvWarpPerspective (view/add comments) Applies a perspective transformation to an image. void cvWarpPerspective( const CvArr* src, CvArr* dst, const CvMat* mapMatrix, int flags=CV INTER LINEAR+CV WARP FILL OUTLIERS, CvScalar fillval=cvScalarAll(0) ); src Source image dst Destination image mapMatrix 3 × 3 transformation matrix flags A combination of interpolation methods and the following optional flags: CV WARP FILL OUTLIERS fills all of the destination image pixels; if some of them corre- spond to outliers in the source image, they are set to fillval CV WARP INVERSE MAP indicates that matrix is inversely transformed from the destination image to the source and, thus, can be used directly for pixel interpolation. Otherwise, the function finds the inverse transform from mapMatrix fillval A value used to fill outliers The function cvWarpPerspective transforms the source image using the specified matrix: 2.4. MISCELLANEOUS IMAGE TRANSFORMATIONS 283 x0 y0  = mapMatrix ·   x y 1   if CV WARP INVERSE MAP is not set x y  = mapMatrix ·   x0 y0 1   otherwise Note that the function can not operate in-place. For a sparse set of points use the cvPerspec- tiveTransform function from CxCore. 2.4 Miscellaneous Image Transformations cvAdaptiveThreshold (view/add comments) Applies an adaptive threshold to an array. void cvAdaptiveThreshold( const CvArr* src, CvArr* dst, double maxValue, int adaptive method=CV ADAPTIVE THRESH MEAN C, int thresholdType=CV THRESH BINARY, int blockSize=3, double param1=5 ); src Source image dst Destination image maxValue Maximum value that is used with CV THRESH BINARY and CV THRESH BINARY INV adaptive method Adaptive thresholding algorithm to use: CV ADAPTIVE THRESH MEAN C or CV ADAPTIVE THRESH GAUSSIAN C(see the discussion) thresholdType Thresholding type; must be one of CV THRESH BINARY xxx CV THRESH BINARY INV xxx 284 CHAPTER 2. IMGPROC. IMAGE PROCESSING blockSize The size of a pixel neighborhood that is used to calculate a threshold value for the pixel: 3, 5, 7, and so on param1 The method-dependent parameter. For the methods CV ADAPTIVE THRESH MEAN C and CV ADAPTIVE THRESH GAUSSIAN C it is a constant subtracted from the mean or weighted mean (see the discussion), though it may be negative The function transforms a grayscale image to a binary image according to the formulas: CV THRESH BINARY dst(x, y) =  maxValue if src(x, y) > T(x, y) 0 otherwise CV THRESH BINARY INV dst(x, y) =  0 if src(x, y) > T(x, y) maxValue otherwise where T(x, y) is a threshold calculated individually for each pixel. For the method CV ADAPTIVE THRESH MEAN C it is the mean of a blockSize × blockSize pixel neighborhood, minus param1. For the method CV ADAPTIVE THRESH GAUSSIAN C it is the weighted sum (gaussian) of a blockSize × blockSize pixel neighborhood, minus param1. cvCvtColor (view/add comments) Converts an image from one color space to another. void cvCvtColor( const CvArr* src, CvArr* dst, int code ); src The source 8-bit (8u), 16-bit (16u) or single-precision floating-point (32f) image dst The destination image of the same data type as the source. The number of channels may be different code Color conversion operation that can be specifed using CV src color space 2 dst color space constants (see below) 2.4. MISCELLANEOUS IMAGE TRANSFORMATIONS 285 The function converts the input image from one color space to another. The function ignores the colorModel and channelSeq fields of the IplImage header, so the source image color space should be specified correctly (including order of the channels in the case of RGB space. For example, BGR means 24-bit format with B0,G0,R0,B1,G1,R1, ... layout whereas RGB means 24-format with R0,G0,B0,R1,G1,B1, ... layout). The conventional range for R,G,B channel values is: • 0 to 255 for 8-bit images • 0 to 65535 for 16-bit images and • 0 to 1 for floating-point images. Of course, in the case of linear transformations the range can be specific, but in order to get correct results in the case of non-linear transformations, the input image should be scaled. The function can do the following transformations: • Transformations within RGB space like adding/removing the alpha channel, reversing the channel order, conversion to/from 16-bit RGB color (R5:G6:B5 or R5:G5:B5), as well as conversion to/from grayscale using: RGB[A] to Gray:Y ← 0.299 ·R + 0.587 ·G + 0.114 ·B and Gray to RGB[A]:R ← Y,G ← Y,B ← Y,A ← 0 The conversion from a RGB image to gray is done with: cvCvtColor(src ,bwsrc, CV_RGB2GRAY) • RGB ↔ CIE XYZ.Rec 709 with D65 white point (CV BGR2XYZ, CV RGB2XYZ, CV XYZ2BGR, CV XYZ2RGB):   X Y Z   ←   0.412453 0.357580 0.180423 0.212671 0.715160 0.072169 0.019334 0.119193 0.950227   ·   R G B     R G B   ←   3.240479 −1.53715 −0.498535 −0.969256 1.875991 0.041556 0.055648 −0.204043 1.057311   ·   X Y Z   X,Y and Z cover the whole value range (in the case of floating-point images Z may exceed 1). 286 CHAPTER 2. IMGPROC. IMAGE PROCESSING • RGB ↔ YCrCb JPEG (a.k.a. YCC) (CV BGR2YCrCb, CV RGB2YCrCb, CV YCrCb2BGR, CV YCrCb2RGB) Y ← 0.299 ·R + 0.587 ·G + 0.114 ·B Cr ← (R − Y)· 0.713 + delta Cb ← (B − Y)· 0.564 + delta R ← Y + 1.403 ·(Cr − delta) G ← Y − 0.344 ·(Cr − delta) − 0.714 ·(Cb − delta) B ← Y + 1.773 ·(Cb − delta) where delta =    128 for 8-bit images 32768 for 16-bit images 0.5 for floating-point images Y, Cr and Cb cover the whole value range. • RGB ↔ HSV (CV BGR2HSV, CV RGB2HSV, CV HSV2BGR, CV HSV2RGB) in the case of 8-bit and 16-bit images R, G and B are converted to floating-point format and scaled to fit the 0 to 1 range V ← max(R, G, B) S ←  V −min(R,G,B) V if V 6= 0 0 otherwise H ←    60(G − B)/S if V = R 120 + 60(B − R)/S if V = G 240 + 60(R − G)/S if V = B if H < 0 then H ← H + 360 On output 0 ≤ V ≤ 1, 0 ≤ S ≤ 1, 0 ≤ H ≤ 360. The values are then converted to the destination data type: 8-bit images V ← 255V,S ← 255S, H ← H/2(to fit to 0 to 255) 16-bit images (currently not supported) V < −65535V, S < −65535S, H < −H 32-bit images H, S, V are left as is 2.4. MISCELLANEOUS IMAGE TRANSFORMATIONS 287 • RGB ↔ HLS (CV BGR2HLS, CV RGB2HLS, CV HLS2BGR, CV HLS2RGB). in the case of 8-bit and 16-bit images R, G and B are converted to floating-point format and scaled to fit the 0 to 1 range. Vmax ← max(R, G, B) Vmin ← min(R, G, B) L ← Vmax + Vmin 2 S ← (Vmax−Vmin Vmax+Vmin if L < 0.5 Vmax−Vmin 2−(Vmax+Vmin) if L ≥ 0.5 H ←    60(G − B)/S if Vmax = R 120 + 60(B − R)/S if Vmax = G 240 + 60(R − G)/S if Vmax = B if H < 0 then H ← H + 360 On output 0 ≤ L ≤ 1, 0 ≤ S ≤ 1, 0 ≤ H ≤ 360. The values are then converted to the destination data type: 8-bit images V ← 255V,S ← 255S, H ← H/2(to fit to 0 to 255) 16-bit images (currently not supported) V < −65535V, S < −65535S, H < −H 32-bit images H, S, V are left as is • RGB ↔ CIE L*a*b* (CV BGR2Lab, CV RGB2Lab, CV Lab2BGR, CV Lab2RGB) in the case of 8-bit and 16-bit images R, G and B are converted to floating-point format and scaled to fit the 0 to 1 range   X Y Z   ←   0.412453 0.357580 0.180423 0.212671 0.715160 0.072169 0.019334 0.119193 0.950227   ·   R G B   X ← X/Xn, whereXn = 0.950456 Z ← Z/Zn, whereZn = 1.088754 L ←  116 ∗ Y 1/3 − 16 for Y > 0.008856 903.3 ∗ Y for Y ≤ 0.008856 a ← 500(f(X) − f(Y)) + delta b ← 200(f(Y) − f(Z)) + delta 288 CHAPTER 2. IMGPROC. IMAGE PROCESSING where f(t) =  t1/3 for t > 0.008856 7.787t + 16/116 for t <= 0.008856 and delta =  128 for 8-bit images 0 for floating-point images On output 0 ≤ L ≤ 100, −127 ≤ a ≤ 127, −127 ≤ b ≤ 127 The values are then converted to the destination data type: 8-bit images L ← L ∗ 255/100, a ← a + 128, b ← b + 128 16-bit images currently not supported 32-bit images L, a, b are left as is • RGB ↔ CIE L*u*v* (CV BGR2Luv, CV RGB2Luv, CV Luv2BGR, CV Luv2RGB) in the case of 8-bit and 16-bit images R, G and B are converted to floating-point format and scaled to fit 0 to 1 range   X Y Z   ←   0.412453 0.357580 0.180423 0.212671 0.715160 0.072169 0.019334 0.119193 0.950227   ·   R G B   L ←  116Y 1/3 for Y > 0.008856 903.3Y for Y <= 0.008856 u0 ← 4 ∗ X/(X + 15 ∗ Y + 3Z) v0 ← 9 ∗ Y/(X + 15 ∗ Y + 3Z) u ← 13 ∗ L ∗ (u0 − un) where un = 0.19793943 v ← 13 ∗ L ∗ (v0 − vn) where vn = 0.46831096 On output 0 ≤ L ≤ 100, −134 ≤ u ≤ 220, −140 ≤ v ≤ 122. The values are then converted to the destination data type: 8-bit images L ← 255/100L, u ← 255/354(u + 134), v ← 255/256(v + 140) 16-bit images currently not supported 32-bit images L, u, v are left as is 2.4. MISCELLANEOUS IMAGE TRANSFORMATIONS 289 The above formulas for converting RGB to/from various color spaces have been taken from multiple sources on Web, primarily from the Ford98 at the Charles Poynton site. • Bayer → RGB (CV BayerBG2BGR, CV BayerGB2BGR, CV BayerRG2BGR, CV BayerGR2BGR, CV BayerBG2RGB, CV BayerGB2RGB, CV BayerRG2RGB, CV BayerGR2RGB) The Bayer pattern is widely used in CCD and CMOS cameras. It allows one to get color pictures from a single plane where R,G and B pixels (sensors of a particular component) are interleaved like this: RGRGR GBGBG RGRGR GBGBG RGRGR The output RGB components of a pixel are interpolated from 1, 2 or 4 neighbors of the pixel having the same color. There are several modifications of the above pattern that can be achieved by shifting the pattern one pixel left and/or one pixel up. The two letters C1 and C2 in the conversion constants CV Bayer C1C2 2BGR and CV Bayer C1C2 2RGB indicate the particular pattern type - these are components from the second row, second and third columns, respectively. For example, the above pattern has very popular ”BG” type. cvDistTransform (view/add comments) Calculates the distance to the closest zero pixel for all non-zero pixels of the source image. void cvDistTransform( const CvArr* src, CvArr* dst, int distance type=CV DIST L2, int mask size=3, const float* mask=NULL, CvArr* labels=NULL ); src 8-bit, single-channel (binary) source image dst Output image with calculated distances (32-bit floating-point, single-channel) 290 CHAPTER 2. IMGPROC. IMAGE PROCESSING distance type Type of distance; can be CV DIST L1, CV DIST L2, CV DIST C or CV DIST USER mask size Size of the distance transform mask; can be 3 or 5. in the case of CV DIST L1 or CV DIST C the parameter is forced to 3, because a 3 × 3 mask gives the same result as a 5 × 5 yet it is faster mask User-defined mask in the case of a user-defined distance, it consists of 2 numbers (hor- izontal/vertical shift cost, diagonal shift cost) in the case ofa 3 × 3 mask and 3 numbers (horizontal/vertical shift cost, diagonal shift cost, knight’s move cost) in the case of a 5 × 5 mask labels The optional output 2d array of integer type labels, the same size as src and dst The function calculates the approximated distance from every binary image pixel to the nearest zero pixel. For zero pixels the function sets the zero distance, for others it finds the shortest path consisting of basic shifts: horizontal, vertical, diagonal or knight’s move (the latest is available for a 5 × 5 mask). The overall distance is calculated as a sum of these basic distances. Because the distance function should be symmetric, all of the horizontal and vertical shifts must have the same cost (that is denoted as a), all the diagonal shifts must have the same cost (denoted b), and all knight’s moves must have the same cost (denoted c). For CV DIST C and CV DIST L1 types the distance is calculated precisely, whereas for CV DIST L2 (Euclidian distance) the distance can be calculated only with some relative error (a 5 × 5 mask gives more accurate results), OpenCV uses the values suggested in [4]: CV DIST C(3 × 3) a = 1, b = 1 CV DIST L1 (3 × 3) a = 1, b = 2 CV DIST L2 (3 × 3) a=0.955, b=1.3693 CV DIST L2 (5 × 5) a=1, b=1.4, c=2.1969 And below are samples of the distance field (black (0) pixel is in the middle of white square) in the case of a user-defined distance: User-defined 3 × 3 mask (a=1, b=1.5) 4.5 4 3.5 3 3.5 4 4.5 4 3 2.5 2 2.5 3 4 3.5 2.5 1.5 1 1.5 2.5 3.5 3 2 1 1 2 3 3.5 2.5 1.5 1 1.5 2.5 3.5 4 3 2.5 2 2.5 3 4 4.5 4 3.5 3 3.5 4 4.5 User-defined 5 × 5 mask (a=1, b=1.5, c=2) 2.4. MISCELLANEOUS IMAGE TRANSFORMATIONS 291 4.5 3.5 3 3 3 3.5 4.5 3.5 3 2 2 2 3 3.5 3 2 1.5 1 1.5 2 3 3 2 1 1 2 3 3 2 1.5 1 1.5 2 3 3.5 3 2 2 2 3 3.5 4 3.5 3 3 3 3.5 4 Typically, for a fast, coarse distance estimation CV DIST L2, a 3 × 3 mask is used, and for a more accurate distance estimation CV DIST L2, a 5 × 5 mask is used. When the output parameter labels is not NULL, for every non-zero pixel the function also finds the nearest connected component consisting of zero pixels. The connected components themselves are found as contours in the beginning of the function. In this mode the processing time is still O(N), where N is the number of pixels. Thus, the function provides a very fast way to compute approximate Voronoi diagram for the binary image. CvConnectedComp (view/add comments) typedef struct CvConnectedComp { double area; /* area of the segmented component */ CvScalar value; /* average color of the connected component */ CvRect rect; /* ROI of the segmented component */ CvSeq* contour; /* optional component boundary (the contour might have child contours corresponding to the holes) */ } CvConnectedComp; cvFloodFill (view/add comments) Fills a connected component with the given color. void cvFloodFill( CvArr* image, CvPoint seed point, CvScalar new val, CvScalar lo diff=cvScalarAll(0), CvScalar up diff=cvScalarAll(0), CvConnectedComp* comp=NULL, int flags=4, CvArr* mask=NULL ); 292 CHAPTER 2. IMGPROC. IMAGE PROCESSING image Input 1- or 3-channel, 8-bit or floating-point image. It is modified by the function unless the CV FLOODFILL MASK ONLY flag is set (see below) seed point The starting point new val New value of the repainted domain pixels lo diff Maximal lower brightness/color difference between the currently observed pixel and one of its neighbors belonging to the component, or a seed pixel being added to the component. In the case of 8-bit color images it is a packed value up diff Maximal upper brightness/color difference between the currently observed pixel and one of its neighbors belonging to the component, or a seed pixel being added to the component. In the case of 8-bit color images it is a packed value comp Pointer to the structure that the function fills with the information about the repainted do- main. Note that the function does not fill comp->contour field. The boundary of the filled component can be retrieved from the output mask image using cvFindContours flags The operation flags. Lower bits contain connectivity value, 4 (by default) or 8, used within the function. Connectivity determines which neighbors of a pixel are considered. Upper bits can be 0 or a combination of the following flags: CV FLOODFILL FIXED RANGE if set, the difference between the current pixel and seed pixel is considered, otherwise the difference between neighbor pixels is considered (the range is floating) CV FLOODFILL MASK ONLY if set, the function does not fill the image (new val is ignored), but fills the mask (that must be non-NULL in this case) mask Operation mask, should be a single-channel 8-bit image, 2 pixels wider and 2 pixels taller than image. If not NULL, the function uses and updates the mask, so the user takes re- sponsibility of initializing the mask content. Floodfilling can’t go across non-zero pixels in the mask, for example, an edge detector output can be used as a mask to stop filling at edges. It is possible to use the same mask in multiple calls to the function to make sure the filled area do not overlap. Note: because the mask is larger than the filled image, a pixel in mask that corresponds to (x, y) pixel in image will have coordinates (x + 1, y + 1) The function fills a connected component starting from the seed point with the specified color. The connectivity is determined by the closeness of pixel values. The pixel at (x, y) is considered to belong to the repainted domain if: grayscale image, floating range src(x0, y0) − lo diff <= src(x, y) <= src(x0, y0) + up diff 2.4. MISCELLANEOUS IMAGE TRANSFORMATIONS 293 grayscale image, fixed range src(seed.x, seed.y) − lo diff <= src(x, y) <= src(seed.x, seed.y) + up diff color image, floating range src(x0, y0)r − lo diffr <= src(x, y)r <= src(x0, y0)r + up diffr src(x0, y0)g − lo diffg <= src(x, y)g <= src(x0, y0)g + up diffg src(x0, y0)b − lo diffb <= src(x, y)b <= src(x0, y0)b + up diffb color image, fixed range src(seed.x, seed.y)r − lo diffr <= src(x, y)r <= src(seed.x, seed.y)r + up diffr src(seed.x, seed.y)g − lo diffg <= src(x, y)g <= src(seed.x, seed.y)g + up diffg src(seed.x, seed.y)b − lo diffb <= src(x, y)b <= src(seed.x, seed.y)b + up diffb where src(x0, y0) is the value of one of pixel neighbors. That is, to be added to the connected component, a pixel’s color/brightness should be close enough to the: • color/brightness of one of its neighbors that are already referred to the connected component in the case of floating range • color/brightness of the seed point in the case of fixed range. cvInpaint (view/add comments) Inpaints the selected region in the image. void cvInpaint( const CvArr* src, const CvArr* mask, CvArr* dst, double inpaintRadius, int flags); src The input 8-bit 1-channel or 3-channel image. 294 CHAPTER 2. IMGPROC. IMAGE PROCESSING mask The inpainting mask, 8-bit 1-channel image. Non-zero pixels indicate the area that needs to be inpainted. dst The output image of the same format and the same size as input. inpaintRadius The radius of circlular neighborhood of each point inpainted that is considered by the algorithm. flags The inpainting method, one of the following: CV INPAINT NS Navier-Stokes based method. CV INPAINT TELEA The method by Alexandru Telea [21] The function reconstructs the selected image area from the pixel near the area boundary. The function may be used to remove dust and scratches from a scanned photo, or to remove undesirable objects from still images or video. cvIntegral (view/add comments) Calculates the integral of an image. void cvIntegral( const CvArr* image, CvArr* sum, CvArr* sqsum=NULL, CvArr* tiltedSum=NULL ); image The source image, W × H, 8-bit or floating-point (32f or 64f) sum The integral image, (W + 1) × (H + 1), 32-bit integer or double precision floating-point (64f) sqsum The integral image for squared pixel values, (W + 1) × (H + 1), double precision floating- point (64f) tiltedSum The integral for the image rotated by 45 degrees, (W + 1) × (H + 1), the same data type as sum The function calculates one or more integral images for the source image as following: 2.4. MISCELLANEOUS IMAGE TRANSFORMATIONS 295 sum(X,Y) = X x 0 , the gaussian pyramid of max level + 1 levels is built, and the above procedure is run on the smallest layer. After that, the results are propagated to the larger layer and the iterations are run again only on those pixels where the layer colors differ much ( > sr ) from the lower-resolution layer, that is, the boundaries of the color regions are clarified. Note, that the results will be actually different from the ones obtained by running the meanshift procedure on the whole original image (i.e. when max level == 0 ). cvPyrSegmentation (view/add comments) Implements image segmentation by pyramids. void cvPyrSegmentation( IplImage* src, IplImage* dst, CvMemStorage* storage, CvSeq** comp, int level, double threshold1, double threshold2 ); 2.4. MISCELLANEOUS IMAGE TRANSFORMATIONS 297 src The source image dst The destination image storage Storage; stores the resulting sequence of connected components comp Pointer to the output sequence of the segmented components level Maximum level of the pyramid for the segmentation threshold1 Error threshold for establishing the links threshold2 Error threshold for the segments clustering The function implements image segmentation by pyramids. The pyramid builds up to the level level. The links between any pixel a on level i and its candidate father pixel b on the adjacent level are established if p(c(a), c(b)) < threshold1. After the connected components are defined, they are joined into several clusters. Any two segments A and B belong to the same cluster, if p(c(A), c(B)) < threshold2. If the input image has only one channel, then p(c1, c2) = |c1 − c2|. If the input image has three channels (red, green and blue), then p(c1, c2) = 0.30(c1 r − c2 r) + 0.59(c1 g − c2 g) + 0.11(c1 b − c2 b). There may be more than one connected component per a cluster. The images src and dst should be 8-bit single-channel or 3-channel images or equal size. cvThreshold (view/add comments) Applies a fixed-level threshold to array elements. double cvThreshold( const CvArr* src, CvArr* dst, double threshold, double maxValue, int thresholdType ); 298 CHAPTER 2. IMGPROC. IMAGE PROCESSING src Source array (single-channel, 8-bit or 32-bit floating point) dst Destination array; must be either the same type as src or 8-bit threshold Threshold value maxValue Maximum value to use with CV THRESH BINARY and CV THRESH BINARY INV thresh- olding types thresholdType Thresholding type (see the discussion) The function applies fixed-level thresholding to a single-channel array. The function is typi- cally used to get a bi-level (binary) image out of a grayscale image ( cvCmpS could be also used for this purpose) or for removing a noise, i.e. filtering out pixels with too small or too large val- ues. There are several types of thresholding that the function supports that are determined by thresholdType: CV THRESH BINARY dst(x, y) =  maxValue if src(x, y) > threshold 0 otherwise CV THRESH BINARY INV dst(x, y) =  0 if src(x, y) > threshold maxValue otherwise CV THRESH TRUNC dst(x, y) =  threshold if src(x, y) > threshold src(x, y) otherwise CV THRESH TOZERO dst(x, y) =  src(x, y) if src(x, y) > threshold 0 otherwise CV THRESH TOZERO INV dst(x, y) =  0 if src(x, y) > threshold src(x, y) otherwise 2.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 299 Also, the special value CV THRESH OTSU may be combined with one of the above values. In this case the function determines the optimal threshold value using Otsu’s algorithm and uses it instead of the specified thresh. The function returns the computed threshold value. Currently, Otsu’s method is implemented only for 8-bit images. 2.5 Structural Analysis and Shape Descriptors cvApproxChains (view/add comments) Approximates Freeman chain(s) with a polygonal curve. CvSeq* cvApproxChains( CvSeq* src seq, CvMemStorage* storage, int method=CV CHAIN APPROX SIMPLE, 300 CHAPTER 2. IMGPROC. IMAGE PROCESSING double parameter=0, int minimal perimeter=0, int recursive=0 ); src seq Pointer to the chain that can refer to other chains storage Storage location for the resulting polylines method Approximation method (see the description of the function cvFindContours) parameter Method parameter (not used now) minimal perimeter Approximates only those contours whose perimeters are not less than minimal perimeter. Other chains are removed from the resulting structure recursive If not 0, the function approximates all chains that access can be obtained to from src seq by using the h next or v next links. If 0, the single chain is approximated This is a stand-alone approximation routine. The function cvApproxChains works exactly in the same way as cvFindContours with the corresponding approximation flag. The function returns pointer to the first resultant contour. Other approximated contours, if any, can be accessed via the v next or h next fields of the returned structure. cvApproxPoly (view/add comments) Approximates polygonal curve(s) with the specified precision. CvSeq* cvApproxPoly( const void* src seq, int header size, CvMemStorage* storage, int method, double parameter, int parameter2=0 ); src seq Sequence of an array of points 2.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 301 header size Header size of the approximated curve[s] storage Container for the approximated contours. If it is NULL, the input sequences’ storage is used method Approximation method; only CV POLY APPROX DP is supported, that corresponds to the Douglas-Peucker algorithm parameter Method-specific parameter; in the case of CV POLY APPROX DP it is a desired ap- proximation accuracy parameter2 If case if src seq is a sequence, the parameter determines whether the single se- quence should be approximated or all sequences on the same level or below src seq (see cvFindContours for description of hierarchical contour structures). If src seq is an array CvMat* of points, the parameter specifies whether the curve is closed (parameter2!=0) or not (parameter2 =0) The function approximates one or more curves and returns the approximation result[s]. In the case of multiple curves, the resultant tree will have the same structure as the input one (1:1 correspondence). cvArcLength (view/add comments) Calculates the contour perimeter or the curve length. double cvArcLength( const void* curve, CvSlice slice=CV WHOLE SEQ, int isClosed=-1 ); curve Sequence or array of the curve points slice Starting and ending points of the curve, by default, the whole curve length is calculated isClosed Indicates whether the curve is closed or not. There are 3 cases: • isClosed = 0 the curve is assumed to be unclosed. • isClosed > 0 the curve is assumed to be closed. 302 CHAPTER 2. IMGPROC. IMAGE PROCESSING • isClosed < 0 if curve is sequence, the flag CV SEQ FLAG CLOSED of ((CvSeq*)curve)->flags is checked to determine if the curve is closed or not, otherwise (curve is represented by array (CvMat*) of points) it is assumed to be unclosed. The function calculates the length or curve as the sum of lengths of segments between subse- quent points cvBoundingRect (view/add comments) Calculates the up-right bounding rectangle of a point set. CvRect cvBoundingRect( CvArr* points, int update=0 ); points 2D point set, either a sequence or vector (CvMat) of points update The update flag. See below. The function returns the up-right bounding rectangle for a 2d point set. Here is the list of possible combination of the flag values and type of points: update points action 0 CvContour the bounding rectangle is not calculated, but it is taken from rect field of the contour header. 1 CvContour the bounding rectangle is calculated and writ- ten to rect field of the contour header. 0 CvSeq or CvMat the bounding rectangle is calculated and re- turned. 1 CvSeq or CvMat runtime error is raised. cvBoxPoints (view/add comments) Finds the box vertices. void cvBoxPoints( CvBox2D box, CvPoint2D32f pt[4] ); 2.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 303 box Box points Array of vertices The function calculates the vertices of the input 2d box. Here is the function code: void cvBoxPoints( CvBox2D box, CvPoint2D32f pt[4] ) { float a = (float)cos(box.angle)*0.5f; float b = (float)sin(box.angle)*0.5f; pt[0].x = box.center.x - a*box.size.height - b*box.size.width; pt[0].y = box.center.y + b*box.size.height - a*box.size.width; pt[1].x = box.center.x + a*box.size.height - b*box.size.width; pt[1].y = box.center.y - b*box.size.height - a*box.size.width; pt[2].x = 2*box.center.x - pt[0].x; pt[2].y = 2*box.center.y - pt[0].y; pt[3].x = 2*box.center.x - pt[1].x; pt[3].y = 2*box.center.y - pt[1].y; } cvCalcPGH (view/add comments) Calculates a pair-wise geometrical histogram for a contour. void cvCalcPGH( const CvSeq* contour, CvHistogram* hist ); contour Input contour. Currently, only integer point coordinates are allowed hist Calculated histogram; must be two-dimensional The function calculates a 2D pair-wise geometrical histogram (PGH), described in cvIivari- nen97 for the contour. The algorithm considers every pair of contour edges. The angle between the edges and the minimum/maximum distances are determined for every pair. To do this each of the edges in turn is taken as the base, while the function loops through all the other edges. When the base edge and any other edge are considered, the minimum and maximum distances from the points on the non-base edge and line of the base edge are selected. The angle between the edges defines the row of the histogram in which all the bins that correspond to the distance between the calculated minimum and maximum distances are incremented (that is, the histogram 304 CHAPTER 2. IMGPROC. IMAGE PROCESSING is transposed relatively to the cvIivarninen97 definition). The histogram can be used for contour matching. cvCalcEMD2 (view/add comments) Computes the ”minimal work” distance between two weighted point configurations. float cvCalcEMD2( const CvArr* signature1, const CvArr* signature2, int distance type, CvDistanceFunction distance func=NULL, const CvArr* cost matrix=NULL, CvArr* flow=NULL, float* lower bound=NULL, void* userdata=NULL ); signature1 First signature, a size1×dims+ 1 floating-point matrix. Each row stores the point weight followed by the point coordinates. The matrix is allowed to have a single column (weights only) if the user-defined cost matrix is used signature2 Second signature of the same format as signature1, though the number of rows may be different. The total weights may be different, in this case an extra ”dummy” point is added to either signature1 or signature2 distance type Metrics used; CV DIST L1, CV DIST L2, and CV DIST C stand for one of the standard metrics; CV DIST USER means that a user-defined function distance func or pre-calculated cost matrix is used distance func The user-supplied distance function. It takes coordinates of two points and re- turns the distance between the points typedef float (*CvDistanceFunction)(const float* f1, const float* f2, void* userdata); cost matrix The user-defined size1 × size2 cost matrix. At least one of cost matrix and distance func must be NULL. Also, if a cost matrix is used, lower boundary (see below) can not be calculated, because it needs a metric function flow The resultant size1 × size2 flow matrix: flowi,j is a flow from i th point of signature1 to j th point of signature2 2.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 305 lower bound Optional input/output parameter: lower boundary of distance between the two sig- natures that is a distance between mass centers. The lower boundary may not be calculated if the user-defined cost matrix is used, the total weights of point configurations are not equal, or if the signatures consist of weights only (i.e. the signature matrices have a single column). The user must initialize *lower bound. If the calculated distance between mass centers is greater or equal to *lower bound (it means that the signatures are far enough) the function does not calculate EMD. In any case *lower bound is set to the calculated distance be- tween mass centers on return. Thus, if user wants to calculate both distance between mass centers and EMD, *lower bound should be set to 0 userdata Pointer to optional data that is passed into the user-defined distance function The function computes the earth mover distance and/or a lower boundary of the distance between the two weighted point configurations. One of the applications described in cvRubn- erSept98 is multi-dimensional histogram comparison for image retrieval. EMD is a a transporta- tion problem that is solved using some modification of a simplex algorithm, thus the complexity is exponential in the worst case, though, on average it is much faster. In the case of a real metric the lower boundary can be calculated even faster (using linear-time algorithm) and it can be used to determine roughly whether the two signatures are far enough so that they cannot relate to the same object. cvCheckContourConvexity (view/add comments) Tests contour convexity. int cvCheckContourConvexity( const CvArr* contour ); contour Tested contour (sequence or array of points) The function tests whether the input contour is convex or not. The contour must be simple, without self-intersections. CvConvexityDefect (view/add comments) Structure describing a single contour convexity defect. typedef struct CvConvexityDefect { 306 CHAPTER 2. IMGPROC. IMAGE PROCESSING CvPoint* start; /* point of the contour where the defect begins */ CvPoint* end; /* point of the contour where the defect ends */ CvPoint* depth_point; /* the farthest from the convex hull point within the defect */ float depth; /* distance between the farthest point and the convex hull */ } CvConvexityDefect; cvContourArea (view/add comments) Calculates the area of a whole contour or a contour section. double cvContourArea( const CvArr* contour, CvSlice slice=CV WHOLE SEQ ); contour Contour (sequence or array of vertices) slice Starting and ending points of the contour section of interest, by default, the area of the whole contour is calculated 2.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 307 The function calculates the area of a whole contour or a contour section. In the latter case the total area bounded by the contour arc and the chord connecting the 2 selected points is calculated as shown on the picture below: Orientation of the contour affects the area sign, thus the function may return a negative result. Use the fabs() function from C runtime to get the absolute value of the area. cvContourFromContourTree (view/add comments) Restores a contour from the tree. CvSeq* cvContourFromContourTree( const CvContourTree* tree, CvMemStorage* storage, CvTermCriteria criteria ); tree Contour tree storage Container for the reconstructed contour criteria Criteria, where to stop reconstruction The function restores the contour from its binary tree representation. The parameter criteria determines the accuracy and/or the number of tree levels used for reconstruction, so it is possible to build an approximated contour. The function returns the reconstructed contour. 308 CHAPTER 2. IMGPROC. IMAGE PROCESSING cvConvexHull2 (view/add comments) Finds the convex hull of a point set. CvSeq* cvConvexHull2( const CvArr* input, void* storage=NULL, int orientation=CV CLOCKWISE, int return points=0 ); points Sequence or array of 2D points with 32-bit integer or floating-point coordinates storage The destination array (CvMat*) or memory storage (CvMemStorage*) that will store the convex hull. If it is an array, it should be 1d and have the same number of elements as the input array/sequence. On output the header is modified as to truncate the array down to the hull size. If storage is NULL then the convex hull will be stored in the same storage as the input sequence orientation Desired orientation of convex hull: CV CLOCKWISE or CV COUNTER CLOCKWISE return points If non-zero, the points themselves will be stored in the hull instead of indices if storage is an array, or pointers if storage is memory storage The function finds the convex hull of a 2D point set using Sklansky’s algorithm. If storage is memory storage, the function creates a sequence containing the hull points or pointers to them, depending on return points value and returns the sequence on output. If storage is a CvMat, the function returns NULL. Example. Building convex hull for a sequence or array of points #include "cv.h" #include "highgui.h" #include #define ARRAY 0 /* switch between array/sequence method by replacing 0<=>1 */ void main( int argc, char** argv ) { IplImage* img = cvCreateImage( cvSize( 500, 500 ), 8, 3 ); cvNamedWindow( "hull", 1 ); 2.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 309 #if !ARRAY CvMemStorage* storage = cvCreateMemStorage(); #endif for(;;) { int i, count = rand()%100 + 1, hullcount; CvPoint pt0; #if !ARRAY CvSeq* ptseq = cvCreateSeq( CV_SEQ_KIND_GENERIC|CV_32SC2, sizeof(CvContour), sizeof(CvPoint), storage ); CvSeq* hull; for( i = 0; i < count; i++ ) { pt0.x = rand() % (img->width/2) + img->width/4; pt0.y = rand() % (img->height/2) + img->height/4; cvSeqPush( ptseq, &pt0 ); } hull = cvConvexHull2( ptseq, 0, CV_CLOCKWISE, 0 ); hullcount = hull->total; #else CvPoint* points = (CvPoint*)malloc( count * sizeof(points[0])); int* hull = (int*)malloc( count * sizeof(hull[0])); CvMat point_mat = cvMat( 1, count, CV_32SC2, points ); CvMat hull_mat = cvMat( 1, count, CV_32SC1, hull ); for( i = 0; i < count; i++ ) { pt0.x = rand() % (img->width/2) + img->width/4; pt0.y = rand() % (img->height/2) + img->height/4; points[i] = pt0; } cvConvexHull2( &point_mat, &hull_mat, CV_CLOCKWISE, 0 ); hullcount = hull_mat.cols; #endif cvZero( img ); for( i = 0; i < count; i++ ) { #if !ARRAY pt0 = *CV_GET_SEQ_ELEM( CvPoint, ptseq, i ); #else pt0 = points[i]; 310 CHAPTER 2. IMGPROC. IMAGE PROCESSING #endif cvCircle( img, pt0, 2, CV_RGB( 255, 0, 0 ), CV_FILLED ); } #if !ARRAY pt0 = **CV_GET_SEQ_ELEM( CvPoint*, hull, hullcount - 1 ); #else pt0 = points[hull[hullcount-1]]; #endif for( i = 0; i < hullcount; i++ ) { #if !ARRAY CvPoint pt = **CV_GET_SEQ_ELEM( CvPoint*, hull, i ); #else CvPoint pt = points[hull[i]]; #endif cvLine( img, pt0, pt, CV_RGB( 0, 255, 0 )); pt0 = pt; } cvShowImage( "hull", img ); int key = cvWaitKey(0); if( key == 27 ) // ’ESC’ break; #if !ARRAY cvClearMemStorage( storage ); #else free( points ); free( hull ); #endif } } cvConvexityDefects (view/add comments) Finds the convexity defects of a contour. CvSeq* cvConvexityDefects( 2.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 311 const CvArr* contour, const CvArr* convexhull, CvMemStorage* storage=NULL ); contour Input contour convexhull Convex hull obtained using cvConvexHull2 that should contain pointers or indices to the contour points, not the hull points themselves (the return points parameter in cvConvexHull2 should be 0) storage Container for the output sequence of convexity defects. If it is NULL, the contour or hull (in that order) storage is used The function finds all convexity defects of the input contour and returns a sequence of the CvConvexityDefect structures. cvCreateContourTree (view/add comments) Creates a hierarchical representation of a contour. CvContourTree* cvCreateContourTree( const CvSeq* contour, CvMemStorage* storage, double threshold ); contour Input contour storage Container for output tree threshold Approximation accuracy The function creates a binary tree representation for the input contour and returns the pointer to its root. If the parameter threshold is less than or equal to 0, the function creates a full binary tree representation. If the threshold is greater than 0, the function creates a representation with the precision threshold: if the vertices with the interceptive area of its base line are less than threshold, the tree should not be built any further. The function returns the created tree. 312 CHAPTER 2. IMGPROC. IMAGE PROCESSING cvEndFindContours (view/add comments) Finishes the scanning process. CvSeq* cvEndFindContours( CvContourScanner* scanner ); scanner Pointer to the contour scanner The function finishes the scanning process and returns a pointer to the first contour on the highest level. cvFindContours (view/add comments) Finds the contours in a binary image. int cvFindContours( CvArr* image, CvMemStorage* storage, CvSeq** first contour, int header size=sizeof(CvContour), int mode=CV RETR LIST, int method=CV CHAIN APPROX SIMPLE, CvPoint offset=cvPoint(0,0) ); image The source, an 8-bit single channel image. Non-zero pixels are treated as 1’s, zero pixels remain 0’s - the image is treated as binary. To get such a binary image from grayscale, one may use cvThreshold, cvAdaptiveThreshold or cvCanny. The function modifies the source image’s content storage Container of the retrieved contours first contour Output parameter, will contain the pointer to the first outer contour header size Size of the sequence header, ≥ sizeof(CvChain) if method = CV CHAIN CODE, and ≥ sizeof(CvContour) otherwise 2.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 313 mode Retrieval mode CV RETR EXTERNAL retrives only the extreme outer contours CV RETR LIST retrieves all of the contours and puts them in the list CV RETR CCOMP retrieves all of the contours and organizes them into a two-level hierarchy: on the top level are the external boundaries of the components, on the second level are the boundaries of the holes CV RETR TREE retrieves all of the contours and reconstructs the full hierarchy of nested contours method Approximation method (for all the modes, except CV LINK RUNS, which uses built-in approximation) CV CHAIN CODE outputs contours in the Freeman chain code. All other methods output polygons (sequences of vertices) CV CHAIN APPROX NONE translates all of the points from the chain code into points CV CHAIN APPROX SIMPLE compresses horizontal, vertical, and diagonal segments and leaves only their end points CV CHAIN APPROX TC89 L1,CV CHAIN APPROX TC89 KCOS applies one of the flavors of the Teh-Chin chain approximation algorithm. CV LINK RUNS uses a completely different contour retrieval algorithm by linking horizontal segments of 1’s. Only the CV RETR LIST retrieval mode can be used with this method. offset Offset, by which every contour point is shifted. This is useful if the contours are extracted from the image ROI and then they should be analyzed in the whole image context The function retrieves contours from the binary image using the algorithm [19]. The contours are a useful tool for shape analysis and object detection and recognition. The function retrieves contours from the binary image and returns the number of retrieved contours. The pointer first contour is filled by the function. It will contain a pointer to the first outermost contour or NULL if no contours are detected (if the image is completely black). Other contours may be reached from first contour using the h next and v next links. The sample in the cvDrawContours discussion shows how to use contours for connected component detection. Contours can be also used for shape analysis and object recognition - see squares.c in the OpenCV sample directory. Note: the source image is modified by this function. 314 CHAPTER 2. IMGPROC. IMAGE PROCESSING cvFindNextContour (view/add comments) Finds the next contour in the image. CvSeq* cvFindNextContour( CvContourScanner scanner ); scanner Contour scanner initialized by cvStartFindContours The function locates and retrieves the next contour in the image and returns a pointer to it. The function returns NULL if there are no more contours. cvFitEllipse2 (view/add comments) Fits an ellipse around a set of 2D points. CvBox2D cvFitEllipse2( const CvArr* points ); points Sequence or array of points The function calculates the ellipse that fits best (in least-squares sense) around a set of 2D points. The meaning of the returned structure fields is similar to those in cvEllipse except that size stores the full lengths of the ellipse axises, not half-lengths. cvFitLine (view/add comments) Fits a line to a 2D or 3D point set. void cvFitLine( const CvArr* points, int dist type, double param, 2.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 315 double reps, double aeps, float* line ); points Sequence or array of 2D or 3D points with 32-bit integer or floating-point coordinates dist type The distance used for fitting (see the discussion) param Numerical parameter (C) for some types of distances, if 0 then some optimal value is chosen reps Sufficient accuracy for the radius (distance between the coordinate origin and the line). 0.01 is a good default value. aeps Sufficient accuracy for the angle. 0.01 is a good default value. line The output line parameters. In the case of a 2d fitting, it is an array of 4 floats (vx, vy, x0, y0) where (vx, vy) is a normalized vector collinear to the line and (x0, y0) is some point on the line. in the case of a 3D fitting it is an array of 6 floats (vx, vy, vz, x0, y0, z0) where (vx, vy, vz) is a normalized vector collinear to the line and (x0, y0, z0) is some point on the line The function fits a line to a 2D or 3D point set by minimizing P i ρ(ri) where ri is the distance between the i th point and the line and ρ(r) is a distance function, one of: dist type=CV DIST L2 ρ(r) = r2/2 (the simplest and the fastest least-squares method) dist type=CV DIST L1 ρ(r) = r dist type=CV DIST L12 ρ(r) = 2 ·( r 1 + r2 2 − 1) dist type=CV DIST FAIR ρ (r) = C2 ·  r C − log 1 + r C  where C = 1.3998 316 CHAPTER 2. IMGPROC. IMAGE PROCESSING dist type=CV DIST WELSCH ρ (r) = C2 2 ·  1 − exp  −  r C 2 where C = 2.9846 dist type=CV DIST HUBER ρ(r) =  r2/2 if r < C C·(r − C/2) otherwise where C = 1.345 cvGetCentralMoment (view/add comments) Retrieves the central moment from the moment state structure. double cvGetCentralMoment( CvMoments* moments, int x order, int y order ); moments Pointer to the moment state structure x order x order of the retrieved moment, x order >= 0 y order y order of the retrieved moment, y order >= 0 and x order + y order <= 3 The function retrieves the central moment, which in the case of image moments is defined as: µx order, y order = X x,y (I(x, y)·(x − xc)x order ·(y − yc)y order) where xc, yc are the coordinates of the gravity center: xc = M10 M00 , yc = M01 M00 cvGetHuMoments (view/add comments) Calculates the seven Hu invariants. 2.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 317 void cvGetHuMoments( const CvMoments* moments,CvHuMoments* hu ); moments The input moments, computed with cvMoments hu The output Hu invariants The function calculates the seven Hu invariants, see http://en.wikipedia.org/wiki/ Image_moment, that are defined as: hu1 = η20 + η02 hu2 = (η20 − η02)2 + 4η2 11 hu3 = (η30 − 3η12)2 + (3η21 − η03)2 hu4 = (η30 + η12)2 + (η21 + η03)2 hu5 = (η30 − 3η12)(η30 + η12)[(η30 + η12)2 − 3(η21 + η03)2] + (3η21 − η03)(η21 + η03)[3(η30 + η12)2 − (η21 + η03)2] hu6 = (η20 − η02)[(η30 + η12)2 − (η21 + η03)2] + 4η11(η30 + η12)(η21 + η03) hu7 = (3η21 − η03)(η21 + η03)[3(η30 + η12)2 − (η21 + η03)2] − (η30 − 3η12)(η21 + η03)[3(η30 + η12)2 − (η21 + η03)2] where ηji denote the normalized central moments. These values are proved to be invariant to the image scale, rotation, and reflection except the seventh one, whose sign is changed by reflection. Of course, this invariance was proved with the assumption of infinite image resolution. In case of a raster images the computed Hu invariants for the original and transformed images will be a bit different. cvGetNormalizedCentralMoment (view/add comments) Retrieves the normalized central moment from the moment state structure. double cvGetNormalizedCentralMoment( CvMoments* moments, int x order, int y order ); moments Pointer to the moment state structure x order x order of the retrieved moment, x order >= 0 318 CHAPTER 2. IMGPROC. IMAGE PROCESSING y order y order of the retrieved moment, y order >= 0 and x order + y order <= 3 The function retrieves the normalized central moment: ηx order, y order = µx order, y order M(y order+x order)/2+1 00 cvGetSpatialMoment (view/add comments) Retrieves the spatial moment from the moment state structure. double cvGetSpatialMoment( CvMoments* moments, int x order, int y order ); moments The moment state, calculated by cvMoments x order x order of the retrieved moment, x order >= 0 y order y order of the retrieved moment, y order >= 0 and x order + y order <= 3 The function retrieves the spatial moment, which in the case of image moments is defined as: Mx order, y order = X x,y (I(x, y)· xx order · yy order) where I(x, y) is the intensity of the pixel (x, y). cvMatchContourTrees (view/add comments) Compares two contours using their tree representations. double cvMatchContourTrees( const CvContourTree* tree1, const CvContourTree* tree2, int method, double threshold ); 2.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 319 tree1 First contour tree tree2 Second contour tree method Similarity measure, only CV CONTOUR TREES MATCH I1 is supported threshold Similarity threshold The function calculates the value of the matching measure for two contour trees. The similarity measure is calculated level by level from the binary tree roots. If at a certain level the difference between contours becomes less than threshold, the reconstruction process is interrupted and the current difference is returned. cvMatchShapes (view/add comments) Compares two shapes. double cvMatchShapes( const void* object1, const void* object2, int method, double parameter=0 ); object1 First contour or grayscale image object2 Second contour or grayscale image method Comparison method; CV CONTOUR MATCH I1, CV CONTOURS MATCH I2 or CV CONTOURS MATCH I3 parameter Method-specific parameter (is not used now) The function compares two shapes. The 3 implemented methods all use Hu moments (see cvGetHuMoments)(A is object1,B is object2): method=CV CONTOUR MATCH I1 I1(A, B) = X i=1...7 1 mA i − 1 mB i 320 CHAPTER 2. IMGPROC. IMAGE PROCESSING method=CV CONTOUR MATCH I2 I2(A, B) = X i=1...7 mA i − mB i method=CV CONTOUR MATCH I3 I3(A, B) = X i=1...7 mA i − mB i mA i where mA i = sign(hA i )· log hA i mB i = sign(hB i )· log hB i and hA i , hB i are the Hu moments of A and B respectively. cvMinAreaRect2 (view/add comments) Finds the circumscribed rectangle of minimal area for a given 2D point set. CvBox2D cvMinAreaRect2( const CvArr* points, CvMemStorage* storage=NULL ); points Sequence or array of points storage Optional temporary memory storage The function finds a circumscribed rectangle of the minimal area for a 2D point set by building a convex hull for the set and applying the rotating calipers technique to the hull. Picture. Minimal-area bounding rectangle for contour 2.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 321 cvMinEnclosingCircle (view/add comments) Finds the circumscribed circle of minimal area for a given 2D point set. int cvMinEnclosingCircle( const CvArr* points, CvPoint2D32f* center, float* radius ); points Sequence or array of 2D points center Output parameter; the center of the enclosing circle radius Output parameter; the radius of the enclosing circle The function finds the minimal circumscribed circle for a 2D point set using an iterative algo- rithm. It returns nonzero if the resultant circle contains all the input points and zero otherwise (i.e. the algorithm failed). 322 CHAPTER 2. IMGPROC. IMAGE PROCESSING cvMoments (view/add comments) Calculates all of the moments up to the third order of a polygon or rasterized shape. void cvMoments( const CvArr* arr, CvMoments* moments, int binary=0 ); arr Image (1-channel or 3-channel with COI set) or polygon (CvSeq of points or a vector of points) moments Pointer to returned moment’s state structure binary (For images only) If the flag is non-zero, all of the zero pixel values are treated as zeroes, and all of the others are treated as 1’s The function calculates spatial and central moments up to the third order and writes them to moments. The moments may then be used then to calculate the gravity center of the shape, its area, main axises and various shape characeteristics including 7 Hu invariants. cvPointPolygonTest (view/add comments) Point in contour test. double cvPointPolygonTest( const CvArr* contour, CvPoint2D32f pt, int measure dist ); contour Input contour pt The point tested against the contour measure dist If it is non-zero, the function estimates the distance from the point to the nearest contour edge 2.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 323 The function determines whether the point is inside a contour, outside, or lies on an edge (or coinsides with a vertex). It returns positive, negative or zero value, correspondingly. When measure dist = 0, the return value is +1, -1 and 0, respectively. When measure dist 6= 0, it is a signed distance between the point and the nearest contour edge. Here is the sample output of the function, where each image pixel is tested against the contour. cvPointSeqFromMat (view/add comments) Initializes a point sequence header from a point vector. CvSeq* cvPointSeqFromMat( int seq kind, const CvArr* mat, CvContour* contour header, CvSeqBlock* block ); seq kind Type of the point sequence: point set (0), a curve (CV SEQ KIND CURVE), closed curve (CV SEQ KIND CURVE+CV SEQ FLAG CLOSED) etc. mat Input matrix. It should be a continuous, 1-dimensional vector of points, that is, it should have type CV 32SC2 or CV 32FC2 324 CHAPTER 2. IMGPROC. IMAGE PROCESSING contour header Contour header, initialized by the function block Sequence block header, initialized by the function The function initializes a sequence header to create a ”virtual” sequence in which elements reside in the specified matrix. No data is copied. The initialized sequence header may be passed to any function that takes a point sequence on input. No extra elements can be added to the sequence, but some may be removed. The function is a specialized variant of cvMakeSeqHead- erForArray and uses the latter internally. It returns a pointer to the initialized contour header. Note that the bounding rectangle (field rect of CvContour strucuture) is not initialized by the function. If you need one, use cvBoundingRect. Here is a simple usage example. CvContour header; CvSeqBlock block; CvMat* vector = cvCreateMat( 1, 3, CV_32SC2 ); CV_MAT_ELEM( *vector, CvPoint, 0, 0 ) = cvPoint(100,100); CV_MAT_ELEM( *vector, CvPoint, 0, 1 ) = cvPoint(100,200); CV_MAT_ELEM( *vector, CvPoint, 0, 2 ) = cvPoint(200,100); IplImage* img = cvCreateImage( cvSize(300,300), 8, 3 ); cvZero(img); cvDrawContours( img, cvPointSeqFromMat(CV_SEQ_KIND_CURVE+CV_SEQ_FLAG_CLOSED, vector, &header, &block), CV_RGB(255,0,0), CV_RGB(255,0,0), 0, 3, 8, cvPoint(0,0)); cvReadChainPoint (view/add comments) Gets the next chain point. CvPoint cvReadChainPoint( CvChainPtReader* reader ); reader Chain reader state The function returns the current chain point and updates the reader position. 2.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 325 cvStartFindContours (view/add comments) Initializes the contour scanning process. CvContourScanner cvStartFindContours( CvArr* image, CvMemStorage* storage, int header size=sizeof(CvContour), int mode=CV RETR LIST, int method=CV CHAIN APPROX SIMPLE, CvPoint offset=cvPoint(0, 0) ); image The 8-bit, single channel, binary source image storage Container of the retrieved contours header size Size of the sequence header, >= sizeof(CvChain) if method =CV CHAIN CODE, and >= sizeof(CvContour) otherwise mode Retrieval mode; see cvFindContours method Approximation method. It has the same meaning in cvFindContours, but CV LINK RUNS can not be used here offset ROI offset; see cvFindContours The function initializes and returns a pointer to the contour scanner. The scanner is used in cvFindNextContour to retrieve the rest of the contours. cvStartReadChainPoints (view/add comments) Initializes the chain reader. void cvStartReadChainPoints( CvChain* chain, CvChainPtReader* reader ); The function initializes a special reader. 326 CHAPTER 2. IMGPROC. IMAGE PROCESSING cvSubstituteContour (view/add comments) Replaces a retrieved contour. void cvSubstituteContour( CvContourScanner scanner, CvSeq* new contour ); scanner Contour scanner initialized by cvStartFindContours new contour Substituting contour The function replaces the retrieved contour, that was returned from the preceding call of cvFindNextContour and stored inside the contour scanner state, with the user-specified contour. The contour is inserted into the resulting structure, list, two-level hierarchy, or tree, depending on the retrieval mode. If the parameter new contour is NULL, the retrieved contour is not included in the resulting structure, nor are any of its children that might be added to this structure later. 2.6 Planar Subdivisions CvSubdiv2D (view/add comments) Planar subdivision. #define CV_SUBDIV2D_FIELDS() \ CV_GRAPH_FIELDS() \ int quad_edges; \ int is_geometry_valid; \ CvSubdiv2DEdge recent_edge; \ CvPoint2D32f topleft; \ CvPoint2D32f bottomright; typedef struct CvSubdiv2D { CV_SUBDIV2D_FIELDS() } CvSubdiv2D; Planar subdivision is the subdivision of a plane into a set of non-overlapped regions (facets) that cover the whole plane. The above structure describes a subdivision built on a 2d point set, 2.6. PLANAR SUBDIVISIONS 327 where the points are linked together and form a planar graph, which, together with a few edges connecting the exterior subdivision points (namely, convex hull points) with infinity, subdivides a plane into facets by its edges. For every subdivision there exists a dual subdivision in which facets and points (subdivision vertices) swap their roles, that is, a facet is treated as a vertex (called a virtual point below) of the dual subdivision and the original subdivision vertices become facets. On the picture below original subdivision is marked with solid lines and dual subdivision with dotted lines. OpenCV subdivides a plane into triangles using Delaunay’s algorithm. Subdivision is built iteratively starting from a dummy triangle that includes all the subdivision points for sure. In this case the dual subdivision is a Voronoi diagram of the input 2d point set. The subdivisions can be used for the 3d piece-wise transformation of a plane, morphing, fast location of points on the plane, building special graphs (such as NNG,RNG) and so forth. CvQuadEdge2D (view/add comments) Quad-edge of planar subdivision. /* one of edges within quad-edge, lower 2 bits is index (0..3) and upper bits are quad-edge pointer */ typedef long CvSubdiv2DEdge; /* quad-edge structure fields */ #define CV_QUADEDGE2D_FIELDS() \ int flags; \ struct CvSubdiv2DPoint* pt[4]; \ CvSubdiv2DEdge next[4]; typedef struct CvQuadEdge2D { CV_QUADEDGE2D_FIELDS() } 328 CHAPTER 2. IMGPROC. IMAGE PROCESSING CvQuadEdge2D; Quad-edge is a basic element of subdivision containing four edges (e, eRot, reversed e and reversed eRot): CvSubdiv2DPoint (view/add comments) Point of original or dual subdivision. #define CV_SUBDIV2D_POINT_FIELDS()\ int flags; \ CvSubdiv2DEdge first; \ CvPoint2D32f pt; \ int id; #define CV_SUBDIV2D_VIRTUAL_POINT_FLAG (1 << 30) typedef struct CvSubdiv2DPoint { CV_SUBDIV2D_POINT_FIELDS() } CvSubdiv2DPoint; id This integer can be used to index auxillary data associated with each vertex of the planar subdivision 2.6. PLANAR SUBDIVISIONS 329 cvCalcSubdivVoronoi2D (view/add comments) Calculates the coordinates of Voronoi diagram cells. void cvCalcSubdivVoronoi2D( CvSubdiv2D* subdiv ); subdiv Delaunay subdivision, in which all the points are already added The function calculates the coordinates of virtual points. All virtual points corresponding to some vertex of the original subdivision form (when connected together) a boundary of the Voronoi cell at that point. cvClearSubdivVoronoi2D (view/add comments) Removes all virtual points. void cvClearSubdivVoronoi2D( CvSubdiv2D* subdiv ); subdiv Delaunay subdivision The function removes all of the virtual points. It is called internally in cvCalcSubdivVoronoi2D if the subdivision was modified after previous call to the function. cvCreateSubdivDelaunay2D (view/add comments) Creates an empty Delaunay triangulation. CvSubdiv2D* cvCreateSubdivDelaunay2D( CvRect rect, CvMemStorage* storage ); 330 CHAPTER 2. IMGPROC. IMAGE PROCESSING rect Rectangle that includes all of the 2d points that are to be added to the subdivision storage Container for subdivision The function creates an empty Delaunay subdivision, where 2d points can be added using the function cvSubdivDelaunay2DInsert. All of the points to be added must be within the specified rectangle, otherwise a runtime error will be raised. Note that the triangulation is a single large triangle that covers the given rectangle. Hence the three vertices of this triangle are outside the rectangle rect. cvFindNearestPoint2D (view/add comments) Finds the closest subdivision vertex to the given point. CvSubdiv2DPoint* cvFindNearestPoint2D( CvSubdiv2D* subdiv, CvPoint2D32f pt ); subdiv Delaunay or another subdivision pt Input point The function is another function that locates the input point within the subdivision. It finds the subdivision vertex that is the closest to the input point. It is not necessarily one of vertices of the facet containing the input point, though the facet (located using cvSubdiv2DLocate) is used as a starting point. The function returns a pointer to the found subdivision vertex. cvSubdiv2DEdgeDst (view/add comments) Returns the edge destination. CvSubdiv2DPoint* cvSubdiv2DEdgeDst( CvSubdiv2DEdge edge ); edge Subdivision edge (not a quad-edge) 2.6. PLANAR SUBDIVISIONS 331 The function returns the edge destination. The returned pointer may be NULL if the edge is from dual subdivision and the virtual point coordinates are not calculated yet. The virtual points can be calculated using the function cvCalcSubdivVoronoi2D. cvSubdiv2DGetEdge (view/add comments) Returns one of the edges related to the given edge. CvSubdiv2DEdge cvSubdiv2DGetEdge( CvSubdiv2DEdge edge, CvNextEdgeType type ); edge Subdivision edge (not a quad-edge) type Specifies which of the related edges to return, one of the following: CV NEXT AROUND ORG next around the edge origin (eOnext on the picture below if e is the input edge) CV NEXT AROUND DST next around the edge vertex (eDnext) CV PREV AROUND ORG previous around the edge origin (reversed eRnext) CV PREV AROUND DST previous around the edge destination (reversed eLnext) CV NEXT AROUND LEFT next around the left facet (eLnext) CV NEXT AROUND RIGHT next around the right facet (eRnext) CV PREV AROUND LEFT previous around the left facet (reversed eOnext) CV PREV AROUND RIGHT previous around the right facet (reversed eDnext) 332 CHAPTER 2. IMGPROC. IMAGE PROCESSING The function returns one of the edges related to the input edge. cvSubdiv2DNextEdge (view/add comments) Returns next edge around the edge origin CvSubdiv2DEdge cvSubdiv2DNextEdge( CvSubdiv2DEdge edge ); edge Subdivision edge (not a quad-edge) 2.6. PLANAR SUBDIVISIONS 333 The function returns the next edge around the edge origin: eOnext on the picture above if e is the input edge) cvSubdiv2DLocate (view/add comments) Returns the location of a point within a Delaunay triangulation. CvSubdiv2DPointLocation cvSubdiv2DLocate( CvSubdiv2D* subdiv, CvPoint2D32f pt, CvSubdiv2DEdge* edge, CvSubdiv2DPoint** vertex=NULL ); subdiv Delaunay or another subdivision pt The point to locate edge The output edge the point falls onto or right to vertex Optional output vertex double pointer the input point coinsides with The function locates the input point within the subdivision. There are 5 cases: 334 CHAPTER 2. IMGPROC. IMAGE PROCESSING • The point falls into some facet. The function returns CV PTLOC INSIDE and *edge will contain one of edges of the facet. • The point falls onto the edge. The function returns CV PTLOC ON EDGE and *edge will contain this edge. • The point coincides with one of the subdivision vertices. The function returns CV PTLOC VERTEX and *vertex will contain a pointer to the vertex. • The point is outside the subdivsion reference rectangle. The function returns CV PTLOC OUTSIDE RECT and no pointers are filled. • One of input arguments is invalid. A runtime error is raised or, if silent or ”parent” error processing mode is selected, CV PTLOC ERROR is returnd. cvSubdiv2DRotateEdge (view/add comments) Returns another edge of the same quad-edge. CvSubdiv2DEdge cvSubdiv2DRotateEdge( CvSubdiv2DEdge edge, int rotate ); edge Subdivision edge (not a quad-edge) rotate Specifies which of the edges of the same quad-edge as the input one to return, one of the following: 0 the input edge (e on the picture below if e is the input edge) 1 the rotated edge (eRot) 2 the reversed edge (reversed e (in green)) 3 the reversed rotated edge (reversed eRot (in green)) 2.6. PLANAR SUBDIVISIONS 335 The function returns one of the edges of the same quad-edge as the input edge. cvSubdivDelaunay2DInsert (view/add comments) Inserts a single point into a Delaunay triangulation. CvSubdiv2DPoint* cvSubdivDelaunay2DInsert( CvSubdiv2D* subdiv, CvPoint2D32f pt); subdiv Delaunay subdivision created by the function cvCreateSubdivDelaunay2D pt Inserted point The function inserts a single point into a subdivision and modifies the subdivision topology appropriately. If a point with the same coordinates exists already, no new point is added. The function returns a pointer to the allocated point. No virtual point coordinates are calculated at this stage. 336 CHAPTER 2. IMGPROC. IMAGE PROCESSING 2.7 Motion Analysis and Object Tracking cvAcc (view/add comments) Adds a frame to an accumulator. void cvAcc( const CvArr* image, CvArr* sum, const CvArr* mask=NULL ); image Input image, 1- or 3-channel, 8-bit or 32-bit floating point. (each channel of multi-channel image is processed independently) sum Accumulator with the same number of channels as input image, 32-bit or 64-bit floating-point mask Optional operation mask The function adds the whole image image or its selected region to the accumulator sum: sum(x, y) ← sum(x, y) + image(x, y) if mask(x, y) 6= 0 cvMultiplyAcc (view/add comments) Adds the product of two input images to the accumulator. void cvMultiplyAcc( const CvArr* image1, const CvArr* image2, CvArr* acc, const CvArr* mask=NULL ); image1 First input image, 1- or 3-channel, 8-bit or 32-bit floating point (each channel of multi- channel image is processed independently) 2.7. MOTION ANALYSIS AND OBJECT TRACKING 337 image2 Second input image, the same format as the first one acc Accumulator with the same number of channels as input images, 32-bit or 64-bit floating-point mask Optional operation mask The function adds the product of 2 images or their selected regions to the accumulator acc: acc(x, y) ← acc(x, y) + image1(x, y)· image2(x, y) if mask(x, y) 6= 0 cvRunningAvg (view/add comments) Updates the running average. void cvRunningAvg( const CvArr* image, CvArr* acc, double alpha, const CvArr* mask=NULL ); image Input image, 1- or 3-channel, 8-bit or 32-bit floating point (each channel of multi-channel image is processed independently) acc Accumulator with the same number of channels as input image, 32-bit or 64-bit floating-point alpha Weight of input image mask Optional operation mask The function calculates the weighted sum of the input image image and the accumulator acc so that acc becomes a running average of frame sequence: acc(x, y) ← (1 − α)· acc(x, y) + α · image(x, y) if mask(x, y) 6= 0 where α regulates the update speed (how fast the accumulator forgets about previous frames). 338 CHAPTER 2. IMGPROC. IMAGE PROCESSING cvSquareAcc (view/add comments) Adds the square of the source image to the accumulator. void cvSquareAcc( const CvArr* image, CvArr* sqsum, const CvArr* mask=NULL ); image Input image, 1- or 3-channel, 8-bit or 32-bit floating point (each channel of multi-channel image is processed independently) sqsum Accumulator with the same number of channels as input image, 32-bit or 64-bit floating- point mask Optional operation mask The function adds the input image image or its selected region, raised to power 2, to the accumulator sqsum: sqsum(x, y) ← sqsum(x, y) + image(x, y)2 if mask(x, y) 6= 0 2.8 Feature Detection cvCanny (view/add comments) Implements the Canny algorithm for edge detection. void cvCanny( const CvArr* image, CvArr* edges, double threshold1, double threshold2, int aperture size=3 ); 2.8. FEATURE DETECTION 339 image Single-channel input image edges Single-channel image to store the edges found by the function threshold1 The first threshold threshold2 The second threshold aperture size Aperture parameter for the Sobel operator (see cvSobel) The function finds the edges on the input image image and marks them in the output image edges using the Canny algorithm. The smallest value between threshold1 and threshold2 is used for edge linking, the largest value is used to find the initial segments of strong edges. cvCornerEigenValsAndVecs (view/add comments) Calculates eigenvalues and eigenvectors of image blocks for corner detection. void cvCornerEigenValsAndVecs( const CvArr* image, CvArr* eigenvv, int blockSize, int aperture size=3 ); image Input image eigenvv Image to store the results. It must be 6 times wider than the input image blockSize Neighborhood size (see discussion) aperture size Aperture parameter for the Sobel operator (see cvSobel) For every pixel, the function cvCornerEigenValsAndVecs considers a blockSize×blockSize neigborhood S(p). It calcualtes the covariation matrix of derivatives over the neigborhood as: M = "P S(p)(dI/dx)2 P S(p)(dI/dx · dI/dy)2 P S(p)(dI/dx · dI/dy)2 P S(p)(dI/dy)2 # After that it finds eigenvectors and eigenvalues of the matrix and stores them into destination image in form (λ1, λ2, x1, y1, x2, y2) where 340 CHAPTER 2. IMGPROC. IMAGE PROCESSING λ1, λ2 are the eigenvalues of M; not sorted x1, y1 are the eigenvectors corresponding to λ1 x2, y2 are the eigenvectors corresponding to λ2 cvCornerHarris (view/add comments) Harris edge detector. void cvCornerHarris( const CvArr* image, CvArr* harris dst, int blockSize, int aperture size=3, double k=0.04 ); image Input image harris dst Image to store the Harris detector responses. Should have the same size as image blockSize Neighborhood size (see the discussion of cvCornerEigenValsAndVecs) aperture size Aperture parameter for the Sobel operator (see cvSobel). k Harris detector free parameter. See the formula below The function runs the Harris edge detector on the image. Similarly to cvCornerMinEigenVal and cvCornerEigenValsAndVecs, for each pixel it calculates a 2 × 2 gradient covariation matrix M over a blockSize × blockSize neighborhood. Then, it stores det(M) − k trace(M)2 to the destination image. Corners in the image can be found as the local maxima of the destination image. 2.8. FEATURE DETECTION 341 cvCornerMinEigenVal (view/add comments) Calculates the minimal eigenvalue of gradient matrices for corner detection. void cvCornerMinEigenVal( const CvArr* image, CvArr* eigenval, int blockSize, int aperture size=3 ); image Input image eigenval Image to store the minimal eigenvalues. Should have the same size as image blockSize Neighborhood size (see the discussion of cvCornerEigenValsAndVecs) aperture size Aperture parameter for the Sobel operator (see cvSobel). The function is similar to cvCornerEigenValsAndVecs but it calculates and stores only the minimal eigen value of derivative covariation matrix for every pixel, i.e. min(λ1, λ2) in terms of the previous function. cvFindCornerSubPix (view/add comments) Refines the corner locations. void cvFindCornerSubPix( const CvArr* image, CvPoint2D32f* corners, int count, CvSize win, CvSize zero zone, CvTermCriteria criteria ); image Input image 342 CHAPTER 2. IMGPROC. IMAGE PROCESSING corners Initial coordinates of the input corners; refined coordinates on output count Number of corners win Half of the side length of the search window. For example, if win=(5,5), then a 5 ∗ 2 + 1 × 5 ∗ 2 + 1 = 11 × 11 search window would be used zero zone Half of the size of the dead region in the middle of the search zone over which the summation in the formula below is not done. It is used sometimes to avoid possible sin- gularities of the autocorrelation matrix. The value of (-1,-1) indicates that there is no such size criteria Criteria for termination of the iterative process of corner refinement. That is, the pro- cess of corner position refinement stops either after a certain number of iterations or when a required accuracy is achieved. The criteria may specify either of or both the maximum number of iteration and the required accuracy The function iterates to find the sub-pixel accurate location of corners, or radial saddle points, as shown in on the picture below. Sub-pixel accurate corner locator is based on the observation that every vector from the center q to a point p located within a neighborhood of q is orthogonal to the image gradient at p subject to image and measurement noise. Consider the expression: i = DIpi T·(q − pi) where DIpi is the image gradient at the one of the points pi in a neighborhood of q. The value of q is to be found such that i is minimized. A system of equations may be set up with i set to zero: 2.8. FEATURE DETECTION 343 X i (DIpi ·DIpi T)q = X i (DIpi ·DIpi T· pi) where the gradients are summed within a neighborhood (”search window”) of q. Calling the first gradient term G and the second gradient term b gives: q = G−1 · b The algorithm sets the center of the neighborhood window at this new center q and then iterates until the center keeps within a set threshold. cvGoodFeaturesToTrack (view/add comments) Determines strong corners on an image. void cvGoodFeaturesToTrack( const CvArr* image CvArr* eigImage, CvArr* tempImage CvPoint2D32f* corners int* cornerCount double qualityLevel double minDistance const CvArr* mask=NULL int blockSize=3 int useHarris=0 double k=0.04 ); image The source 8-bit or floating-point 32-bit, single-channel image eigImage Temporary floating-point 32-bit image, the same size as image tempImage Another temporary image, the same size and format as eigImage corners Output parameter; detected corners cornerCount Output parameter; number of detected corners qualityLevel Multiplier for the max/min eigenvalue; specifies the minimal accepted quality of image corners 344 CHAPTER 2. IMGPROC. IMAGE PROCESSING minDistance Limit, specifying the minimum possible distance between the returned corners; Euclidian distance is used mask Region of interest. The function selects points either in the specified region or in the whole image if the mask is NULL blockSize Size of the averaging block, passed to the underlying cvCornerMinEigenVal or cv- CornerHarris used by the function useHarris If nonzero, Harris operator ( cvCornerHarris) is used instead of default cvCorner- MinEigenVal k Free parameter of Harris detector; used only if (useHarris! = 0) The function finds the corners with big eigenvalues in the image. The function first calculates the minimal eigenvalue for every source image pixel using the cvCornerMinEigenVal function and stores them in eigImage. Then it performs non-maxima suppression (only the local maxima in 3 × 3 neighborhood are retained). The next step rejects the corners with the minimal eigenvalue less than qualityLevel · max(eigImage(x, y)). Finally, the function ensures that the distance between any two corners is not smaller than minDistance. The weaker corners (with a smaller min eigenvalue) that are too close to the stronger corners are rejected. Note that the if the function is called with different values A and B of the parameter qualityLevel, and A¿ B, the array of returned corners with qualityLevel=A will be the prefix of the output corners array with qualityLevel=B. cvHoughLines2 (view/add comments) Finds lines in a binary image using a Hough transform. CvSeq* cvHoughLines2( CvArr* image, void* storage, int method, double rho, double theta, int threshold, double param1=0, double param2=0 ); 2.8. FEATURE DETECTION 345 image The 8-bit, single-channel, binary source image. In the case of a probabilistic method, the image is modified by the function storage The storage for the lines that are detected. It can be a memory storage (in this case a sequence of lines is created in the storage and returned by the function) or single row/single column matrix (CvMat*) of a particular type (see below) to which the lines’ parameters are written. The matrix header is modified by the function so its cols or rows will contain the number of lines detected. If storage is a matrix and the actual number of lines exceeds the matrix size, the maximum possible number of lines is returned (in the case of standard hough transform the lines are sorted by the accumulator value) method The Hough transform variant, one of the following: CV HOUGH STANDARD classical or standard Hough transform. Every line is represented by two floating-point numbers (ρ, θ), where ρ is a distance between (0,0) point and the line, and θ is the angle between x-axis and the normal to the line. Thus, the matrix must be (the created sequence will be) of CV 32FC2 type CV HOUGH PROBABILISTIC probabilistic Hough transform (more efficient in case if picture contains a few long linear segments). It returns line segments rather than the whole line. Each segment is represented by starting and ending points, and the matrix must be (the created sequence will be) of CV 32SC4 type CV HOUGH MULTI SCALE multi-scale variant of the classical Hough transform. The lines are encoded the same way as CV HOUGH STANDARD rho Distance resolution in pixel-related units theta Angle resolution measured in radians threshold Threshold parameter. A line is returned by the function if the corresponding accumu- lator value is greater than threshold param1 The first method-dependent parameter: • For the classical Hough transform it is not used (0). • For the probabilistic Hough transform it is the minimum line length. • For the multi-scale Hough transform it is the divisor for the distance resolution ρ. (The coarse distance resolution will be ρ and the accurate resolution will be (ρ/param1)). param2 The second method-dependent parameter: • For the classical Hough transform it is not used (0). 346 CHAPTER 2. IMGPROC. IMAGE PROCESSING • For the probabilistic Hough transform it is the maximum gap between line segments lying on the same line to treat them as a single line segment (i.e. to join them). • For the multi-scale Hough transform it is the divisor for the angle resolution θ. (The coarse angle resolution will be θ and the accurate resolution will be (θ/param2)). The function implements a few variants of the Hough transform for line detection. Example. Detecting lines with Hough transform. /* This is a standalone program. Pass an image name as a first parameter of the program. Switch between standard and probabilistic Hough transform by changing "#if 1" to "#if 0" and back */ #include #include #include int main(int argc, char** argv) { IplImage* src; if( argc == 2 && (src=cvLoadImage(argv[1], 0))!= 0) { IplImage* dst = cvCreateImage( cvGetSize(src), 8, 1 ); IplImage* color_dst = cvCreateImage( cvGetSize(src), 8, 3 ); CvMemStorage* storage = cvCreateMemStorage(0); CvSeq* lines = 0; int i; cvCanny( src, dst, 50, 200, 3 ); cvCvtColor( dst, color_dst, CV_GRAY2BGR ); #if 1 lines = cvHoughLines2( dst, storage, CV_HOUGH_STANDARD, 1, CV_PI/180, 100, 0, 0 ); for( i = 0; i < MIN(lines->total,100); i++ ) { float* line = (float*)cvGetSeqElem(lines,i); float rho = line[0]; float theta = line[1]; CvPoint pt1, pt2; double a = cos(theta), b = sin(theta); double x0 = a*rho, y0 = b*rho; 2.8. FEATURE DETECTION 347 pt1.x = cvRound(x0 + 1000*(-b)); pt1.y = cvRound(y0 + 1000*(a)); pt2.x = cvRound(x0 - 1000*(-b)); pt2.y = cvRound(y0 - 1000*(a)); cvLine( color_dst, pt1, pt2, CV_RGB(255,0,0), 3, 8 ); } #else lines = cvHoughLines2( dst, storage, CV_HOUGH_PROBABILISTIC, 1, CV_PI/180, 80, 30, 10 ); for( i = 0; i < lines->total; i++ ) { CvPoint* line = (CvPoint*)cvGetSeqElem(lines,i); cvLine( color_dst, line[0], line[1], CV_RGB(255,0,0), 3, 8 ); } #endif cvNamedWindow( "Source", 1 ); cvShowImage( "Source", src ); cvNamedWindow( "Hough", 1 ); cvShowImage( "Hough", color_dst ); cvWaitKey(0); } } This is the sample picture the function parameters have been tuned for: 348 CHAPTER 2. IMGPROC. IMAGE PROCESSING And this is the output of the above program in the case of probabilistic Hough transform (#if 0 case): cvPreCornerDetect (view/add comments) Calculates the feature map for corner detection. void cvPreCornerDetect( const CvArr* image, CvArr* corners, int apertureSize=3 ); image Input image 2.8. FEATURE DETECTION 349 corners Image to store the corner candidates apertureSize Aperture parameter for the Sobel operator (see cvSobel) The function calculates the function D2 xDyy + D2 yDxx − 2DxDyDxy where D? denotes one of the first image derivatives and D?? denotes a second image deriva- tive. The corners can be found as local maximums of the function below: // assume that the image is floating-point IplImage* corners = cvCloneImage(image); IplImage* dilated_corners = cvCloneImage(image); IplImage* corner_mask = cvCreateImage( cvGetSize(image), 8, 1 ); cvPreCornerDetect( image, corners, 3 ); cvDilate( corners, dilated_corners, 0, 1 ); cvSubS( corners, dilated_corners, corners ); cvCmpS( corners, 0, corner_mask, CV_CMP_GE ); cvReleaseImage( &corners ); cvReleaseImage( &dilated_corners ); cvSampleLine (view/add comments) Reads the raster line to the buffer. int cvSampleLine( const CvArr* image CvPoint pt1 CvPoint pt2 void* buffer int connectivity=8 ); image Image to sample the line from pt1 Starting line point pt2 Ending line point 350 CHAPTER 2. IMGPROC. IMAGE PROCESSING buffer Buffer to store the line points; must have enough size to store max(|pt2.x − pt1.x| + 1, |pt2.y − pt1.y| + 1) points in the case of an 8-connected line and (|pt2.x − pt1.x| + |pt2.y − pt1.y| + 1) in the case of a 4-connected line connectivity The line connectivity, 4 or 8 The function implements a particular application of line iterators. The function reads all of the image points lying on the line between pt1 and pt2, including the end points, and stores them into the buffer. 2.9 Object Detection cvMatchTemplate (view/add comments) Compares a template against overlapped image regions. void cvMatchTemplate( const CvArr* image, const CvArr* templ, CvArr* result, int method ); image Image where the search is running; should be 8-bit or 32-bit floating-point templ Searched template; must be not greater than the source image and the same data type as the image result A map of comparison results; single-channel 32-bit floating-point. If image is W ×H and templ is w × h then result must be (W − w + 1) × (H − h + 1) method Specifies the way the template must be compared with the image regions (see below) The function is similar to cvCalcBackProjectPatch. It slides through image, compares the overlapped patches of size w × h against templ using the specified method and stores the com- parison results to result. Here are the formulas for the different comparison methods one may use (I denotes image,T template,R result). The summation is done over template and/or the image patch: x0 = 0...w − 1, y0 = 0...h − 1 2.9. OBJECT DETECTION 351 method=CV TM SQDIFF R(x, y) = X x0,y0 (T(x0, y0) − I(x + x0, y + y0))2 method=CV TM SQDIFF NORMED R(x, y) = P x0,y0 (T(x0, y0) − I(x + x0, y + y0))2 qP x0,y0 T(x0, y0)2 ·P x0,y0 I(x + x0, y + y0)2 method=CV TM CCORR R(x, y) = X x0,y0 (T(x0, y0)·I(x + x0, y + y0)) method=CV TM CCORR NORMED R(x, y) = P x0,y0 (T(x0, y0)·I0(x + x0, y + y0)) qP x0,y0 T(x0, y0)2 ·P x0,y0 I(x + x0, y + y0)2 method=CV TM CCOEFF R(x, y) = X x0,y0 (T 0(x0, y0)·I(x + x0, y + y0)) where T 0(x0, y0) = T(x0, y0) − 1/(w · h)·P x00,y00 T(x00, y00) I0(x + x0, y + y0) = I(x + x0, y + y0) − 1/(w · h)·P x00,y00 I(x + x00, y + y00) method=CV TM CCOEFF NORMED R(x, y) = P x0,y0 (T 0(x0, y0)·I0(x + x0, y + y0)) qP x0,y0 T 0(x0, y0)2 ·P x0,y0 I0(x + x0, y + y0)2 After the function finishes the comparison, the best matches can be found as global minimums (CV TM SQDIFF) or maximums (CV TM CCORR and CV TM CCOEFF) using the cvMinMaxLoc func- tion. In the case of a color image, template summation in the numerator and each sum in the denominator is done over all of the channels (and separate mean values are used for each chan- nel). 352 CHAPTER 2. IMGPROC. IMAGE PROCESSING Chapter 3 features2d. Feature Detection and Descriptor Extraction 3.1 Feature detection and description image The image. Keypoints (corners) will be detected on this. keypoints Keypoints detected on the image. threshold Threshold on difference between intensity of center pixel and pixels on circle around this pixel. See description of the algorithm. nonmaxSupression If it is true then non-maximum supression will be applied to detected cor- ners (keypoints). cvExtractSURF (view/add comments) Extracts Speeded Up Robust Features from an image. void cvExtractSURF( const CvArr* image, const CvArr* mask, CvSeq** keypoints, CvSeq** descriptors, CvMemStorage* storage, CvSURFParams params ); 353 354 CHAPTER 3. FEATURES2D. FEATURE DETECTION AND DESCRIPTOR EXTRACTION image The input 8-bit grayscale image mask The optional input 8-bit mask. The features are only found in the areas that contain more than 50% of non-zero mask pixels keypoints The output parameter; double pointer to the sequence of keypoints. The sequence of CvSURFPoint structures is as follows: typedef struct CvSURFPoint { CvPoint2D32f pt; // position of the feature within the image int laplacian; // -1, 0 or +1. sign of the laplacian at the point. // can be used to speedup feature comparison // (normally features with laplacians of different // signs can not match) int size; // size of the feature float dir; // orientation of the feature: 0..360 degrees float hessian; // value of the hessian (can be used to // approximately estimate the feature strengths; // see also params.hessianThreshold) } CvSURFPoint; descriptors The optional output parameter; double pointer to the sequence of descriptors. Depending on the params.extended value, each element of the sequence will be either a 64-element or a 128-element floating-point (CV 32F) vector. If the parameter is NULL, the descriptors are not computed storage Memory storage where keypoints and descriptors will be stored params Various algorithm parameters put to the structure CvSURFParams: typedef struct CvSURFParams { int extended; // 0 means basic descriptors (64 elements each), // 1 means extended descriptors (128 elements each) double hessianThreshold; // only features with keypoint.hessian // larger than that are extracted. // good default value is ˜300-500 (can depend on the // average local contrast and sharpness of the image). // user can further filter out some features based on // their hessian values and other characteristics. int nOctaves; // the number of octaves to be used for extraction. // With each next octave the feature size is doubled // (3 by default) int nOctaveLayers; // The number of layers within each octave 3.1. FEATURE DETECTION AND DESCRIPTION 355 // (4 by default) } CvSURFParams; CvSURFParams cvSURFParams(double hessianThreshold, int extended=0); // returns default parameters The function cvExtractSURF finds robust features in the image, as described in [3]. For each feature it returns its location, size, orientation and optionally the descriptor, basic or extended. The function can be used for object tracking and localization, image stitching etc. See the find obj.cpp demo in OpenCV samples directory. cvGetStarKeypoints (view/add comments) Retrieves keypoints using the StarDetector algorithm. CvSeq* cvGetStarKeypoints( const CvArr* image, CvMemStorage* storage, CvStarDetectorParams params=cvStarDetectorParams() ); image The input 8-bit grayscale image storage Memory storage where the keypoints will be stored params Various algorithm parameters given to the structure CvStarDetectorParams: typedef struct CvStarDetectorParams { int maxSize; // maximal size of the features detected. The following // values of the parameter are supported: // 4, 6, 8, 11, 12, 16, 22, 23, 32, 45, 46, 64, 90, 128 int responseThreshold; // threshold for the approximatd laplacian, // used to eliminate weak features int lineThresholdProjected; // another threshold for laplacian to // eliminate edges int lineThresholdBinarized; // another threshold for the feature // scale to eliminate edges int suppressNonmaxSize; // linear size of a pixel neighborhood // for non-maxima suppression 356 CHAPTER 3. FEATURES2D. FEATURE DETECTION AND DESCRIPTOR EXTRACTION } CvStarDetectorParams; The function GetStarKeypoints extracts keypoints that are local scale-space extremas. The scale-space is constructed by computing approximate values of laplacians with different sigma’s at each pixel. Instead of using pyramids, a popular approach to save computing time, all of the laplacians are computed at each pixel of the original high-resolution image. But each approximate laplacian value is computed in O(1) time regardless of the sigma, thanks to the use of integral images. The algorithm is based on the paper Agrawal08 , but instead of a square, hexagon or octagon it uses an 8-end star shape, hence the name, consisting of overlapping upright and tilted squares. Each computed feature is represented by the following structure: typedef struct CvStarKeypoint { CvPoint pt; // coordinates of the feature int size; // feature size, see CvStarDetectorParams::maxSize float response; // the approximated laplacian value at that point. } CvStarKeypoint; inline CvStarKeypoint cvStarKeypoint(CvPoint pt, int size, float response); Below is the small usage sample: #include "cv.h" #include "highgui.h" int main(int argc, char** argv) { const char* filename = argc > 1 ? argv[1] : "lena.jpg"; IplImage* img = cvLoadImage( filename, 0 ), *cimg; CvMemStorage* storage = cvCreateMemStorage(0); CvSeq* keypoints = 0; int i; if( !img ) return 0; cvNamedWindow( "image", 1 ); cvShowImage( "image", img ); cvNamedWindow( "features", 1 ); cimg = cvCreateImage( cvGetSize(img), 8, 3 ); cvCvtColor( img, cimg, CV_GRAY2BGR ); keypoints = cvGetStarKeypoints( img, storage, cvStarDetectorParams(45) ); 3.1. FEATURE DETECTION AND DESCRIPTION 357 for( i = 0; i < (keypoints ? keypoints->total : 0); i++ ) { CvStarKeypoint kpt = *(CvStarKeypoint*)cvGetSeqElem(keypoints, i); int r = kpt.size/2; cvCircle( cimg, kpt.pt, r, CV_RGB(0,255,0)); cvLine( cimg, cvPoint(kpt.pt.x + r, kpt.pt.y + r), cvPoint(kpt.pt.x - r, kpt.pt.y - r), CV_RGB(0,255,0)); cvLine( cimg, cvPoint(kpt.pt.x - r, kpt.pt.y + r), cvPoint(kpt.pt.x + r, kpt.pt.y - r), CV_RGB(0,255,0)); } cvShowImage( "features", cimg ); cvWaitKey(); } 358 CHAPTER 3. FEATURES2D. FEATURE DETECTION AND DESCRIPTOR EXTRACTION Chapter 4 flann. Clustering and Search in Multi-Dimensional Spaces 4.1 Fast Approximate Nearest Neighbor Search 359 360 CHAPTER 4. FLANN. CLUSTERING AND SEARCH IN MULTI-DIMENSIONAL SPACES Chapter 5 objdetect. Object Detection 5.1 Cascade Classification Haar Feature-based Cascade Classifier for Object Detection The object detector described below has been initially proposed by Paul Viola cvViola01 and improved by Rainer Lienhart cvLienhart02 . First, a classifier (namely a cascade of boosted clas- sifiers working with haar-like features) is trained with a few hundred sample views of a particular object (i.e., a face or a car), called positive examples, that are scaled to the same size (say, 20x20), and negative examples - arbitrary images of the same size. After a classifier is trained, it can be applied to a region of interest (of the same size as used during the training) in an input image. The classifier outputs a ”1” if the region is likely to show the object (i.e., face/car), and ”0” otherwise. To search for the object in the whole image one can move the search window across the image and check every location using the classifier. The classifier is designed so that it can be easily ”resized” in order to be able to find the objects of interest at different sizes, which is more efficient than resizing the image itself. So, to find an object of an unknown size in the image the scan procedure should be done several times at different scales. The word ”cascade” in the classifier name means that the resultant classifier consists of several simpler classifiers (stages) that are applied subsequently to a region of interest until at some stage the candidate is rejected or all the stages are passed. The word ”boosted” means that the classifiers at every stage of the cascade are complex themselves and they are built out of basic classifiers using one of four different boosting techniques (weighted voting). Currently Discrete Adaboost, Real Adaboost, Gentle Adaboost and Logitboost are supported. The basic classifiers are decision-tree classifiers with at least 2 leaves. Haar-like features are the input to the basic classifers, and are calculated as described below. The current algorithm uses the following Haar- like features: 361 362 CHAPTER 5. OBJDETECT. OBJECT DETECTION The feature used in a particular classifier is specified by its shape (1a, 2b etc.), position within the region of interest and the scale (this scale is not the same as the scale used at the detection stage, though these two scales are multiplied). For example, in the case of the third line feature (2c) the response is calculated as the difference between the sum of image pixels under the rectangle covering the whole feature (including the two white stripes and the black stripe in the middle) and the sum of the image pixels under the black stripe multiplied by 3 in order to compensate for the differences in the size of areas. The sums of pixel values over a rectangular regions are calculated rapidly using integral images (see below and the cvIntegral description). To see the object detector at work, have a look at the HaarFaceDetect demo. The following reference is for the detection part only. There is a separate application called haartraining that can train a cascade of boosted classifiers from a set of samples. See opencv/apps/haartraining for details. CvHaarFeature, CvHaarClassifier, CvHaarStageClassifier, CvHaarClas- sifierCascade (view/add comments) Boosted Haar classifier structures. #define CV_HAAR_FEATURE_MAX 3 /* a haar feature consists of 2-3 rectangles with appropriate weights */ typedef struct CvHaarFeature { int tilted; /* 0 means up-right feature, 1 means 45--rotated feature */ /* 2-3 rectangles with weights of opposite signs and with absolute values inversely proportional to the areas of the rectangles. If rect[2].weight !=0, then the feature consists of 3 rectangles, otherwise it consists of 2 */ struct { 5.1. CASCADE CLASSIFICATION 363 CvRect r; float weight; } rect[CV_HAAR_FEATURE_MAX]; } CvHaarFeature; /* a single tree classifier (stump in the simplest case) that returns the response for the feature at the particular image location (i.e. pixel sum over subrectangles of the window) and gives out a value depending on the response */ typedef struct CvHaarClassifier { int count; /* number of nodes in the decision tree */ /* these are "parallel" arrays. Every index \texttt{i} corresponds to a node of the decision tree (root has 0-th index). left[i] - index of the left child (or negated index if the left child is a leaf) right[i] - index of the right child (or negated index if the right child is a leaf) threshold[i] - branch threshold. if feature responce is <= threshold, left branch is chosen, otherwise right branch is chosen. alpha[i] - output value correponding to the leaf. */ CvHaarFeature* haar_feature; float* threshold; int* left; int* right; float* alpha; } CvHaarClassifier; /* a boosted battery of classifiers(=stage classifier): the stage classifier returns 1 if the sum of the classifiers responses is greater than \texttt{threshold} and 0 otherwise */ typedef struct CvHaarStageClassifier { int count; /* number of classifiers in the battery */ float threshold; /* threshold for the boosted classifier */ CvHaarClassifier* classifier; /* array of classifiers */ /* these fields are used for organizing trees of stage classifiers, rather than just stright cascades */ int next; 364 CHAPTER 5. OBJDETECT. OBJECT DETECTION int child; int parent; } CvHaarStageClassifier; typedef struct CvHidHaarClassifierCascade CvHidHaarClassifierCascade; /* cascade or tree of stage classifiers */ typedef struct CvHaarClassifierCascade { int flags; /* signature */ int count; /* number of stages */ CvSize orig_window_size; /* original object size (the cascade is trained for)*/ /* these two parameters are set by cvSetImagesForHaarClassifierCascade */ CvSize real_window_size; /* current object size */ double scale; /* current scale */ CvHaarStageClassifier* stage_classifier; /* array of stage classifiers */ CvHidHaarClassifierCascade* hid_cascade; /* hidden optimized representation of the cascade, created by cvSetImagesForHaarClassifierCascade */ } CvHaarClassifierCascade; All the structures are used for representing a cascaded of boosted Haar classifiers. The cas- cade has the following hierarchical structure: Cascade: Stage,,1,,: Classifier,,11,,: Feature,,11,, Classifier,,12,,: Feature,,12,, ... Stage,,2,,: Classifier,,21,,: Feature,,21,, ... ... The whole hierarchy can be constructed manually or loaded from a file or an embedded base using the function cvLoadHaarClassifierCascade. 5.1. CASCADE CLASSIFICATION 365 cvLoadHaarClassifierCascade (view/add comments) Loads a trained cascade classifier from a file or the classifier database embedded in OpenCV. CvHaarClassifierCascade* cvLoadHaarClassifierCascade( const char* directory, CvSize orig window size ); directory Name of the directory containing the description of a trained cascade classifier orig window size Original size of the objects the cascade has been trained on. Note that it is not stored in the cascade and therefore must be specified separately The function loads a trained cascade of haar classifiers from a file or the classifier database embedded in OpenCV. The base can be trained using the haartraining application (see opencv/app- s/haartraining for details). The function is obsolete. Nowadays object detection classifiers are stored in XML or YAML files, rather than in directories. To load a cascade from a file, use the cvLoad function. cvHaarDetectObjects (view/add comments) Detects objects in the image. typedef struct CvAvgComp { CvRect rect; /* bounding rectangle for the object (average rectangle of a group) */ int neighbors; /* number of neighbor rectangles in the group */ } CvAvgComp; CvSeq* cvHaarDetectObjects( const CvArr* image, CvHaarClassifierCascade* cascade, CvMemStorage* storage, double scaleFactor=1.1, int minNeighbors=3, 366 CHAPTER 5. OBJDETECT. OBJECT DETECTION int flags=0, CvSize minSize=cvSize(0, 0), CvSize maxSize=cvSize(0,0) ); image Image to detect objects in cascade Haar classifier cascade in internal representation storage Memory storage to store the resultant sequence of the object candidate rectangles scaleFactor The factor by which the search window is scaled between the subsequent scans, 1.1 means increasing window by 10% minNeighbors Minimum number (minus 1) of neighbor rectangles that makes up an object. All the groups of a smaller number of rectangles than min neighbors-1 are rejected. If minNeighbors is 0, the function does not any grouping at all and returns all the detected candidate rectangles, which may be useful if the user wants to apply a customized grouping procedure flags Mode of operation. Currently the only flag that may be specified is CV HAAR DO CANNY PRUNING. If it is set, the function uses Canny edge detector to reject some image regions that contain too few or too much edges and thus can not contain the searched object. The particular threshold values are tuned for face detection and in this case the pruning speeds up the processing minSize Minimum window size. By default, it is set to the size of samples the classifier has been trained on (∼ 20 × 20 for face detection) maxSize Maximum window size to use. By default, it is set to the size of the image. The function finds rectangular regions in the given image that are likely to contain objects the cascade has been trained for and returns those regions as a sequence of rectangles. The function scans the image several times at different scales (see cvSetImagesForHaarClassifierCascade). Each time it considers overlapping regions in the image and applies the classifiers to the regions using cvRunHaarClassifierCascade. It may also apply some heuristics to reduce number of an- alyzed regions, such as Canny prunning. After it has proceeded and collected the candidate rectangles (regions that passed the classifier cascade), it groups them and returns a sequence of average rectangles for each large enough group. The default parameters (scale factor =1.1, min neighbors =3, flags =0) are tuned for accurate yet slow object detection. For a faster op- eration on real video images the settings are: scale factor =1.2, min neighbors =2, flags 5.1. CASCADE CLASSIFICATION 367 =CV HAAR DO CANNY PRUNING, min size =minimum possible face size (for example, ∼ 1/4 to 1/16 of the image area in the case of video conferencing). #include "cv.h" #include "highgui.h" CvHaarClassifierCascade* load_object_detector( const char* cascade_path ) { return (CvHaarClassifierCascade*)cvLoad( cascade_path ); } void detect_and_draw_objects( IplImage* image, CvHaarClassifierCascade* cascade, int do_pyramids ) { IplImage* small_image = image; CvMemStorage* storage = cvCreateMemStorage(0); CvSeq* faces; int i, scale = 1; /* if the flag is specified, down-scale the input image to get a performance boost w/o loosing quality (perhaps) */ if( do_pyramids ) { small_image = cvCreateImage( cvSize(image->width/2,image->height/2), IPL_DEPTH_8U, 3 ); cvPyrDown( image, small_image, CV_GAUSSIAN_5x5 ); scale = 2; } /* use the fastest variant */ faces = cvHaarDetectObjects( small_image, cascade, storage, 1.2, 2, CV_HAAR_DO_CANNY_PRUNING ); /* draw all the rectangles */ for( i = 0; i < faces->total; i++ ) { /* extract the rectanlges only */ CvRect face_rect = *(CvRect*)cvGetSeqElem( faces, i ); cvRectangle( image, cvPoint(face_rect.x*scale,face_rect.y*scale), cvPoint((face_rect.x+face_rect.width)*scale, (face_rect.y+face_rect.height)*scale), CV_RGB(255,0,0), 3 ); } if( small_image != image ) cvReleaseImage( &small_image ); 368 CHAPTER 5. OBJDETECT. OBJECT DETECTION cvReleaseMemStorage( &storage ); } /* takes image filename and cascade path from the command line */ int main( int argc, char** argv ) { IplImage* image; if( argc==3 && (image = cvLoadImage( argv[1], 1 )) != 0 ) { CvHaarClassifierCascade* cascade = load_object_detector(argv[2]); detect_and_draw_objects( image, cascade, 1 ); cvNamedWindow( "test", 0 ); cvShowImage( "test", image ); cvWaitKey(0); cvReleaseHaarClassifierCascade( &cascade ); cvReleaseImage( &image ); } return 0; } cvSetImagesForHaarClassifierCascade (view/add comments) Assigns images to the hidden cascade. void cvSetImagesForHaarClassifierCascade( CvHaarClassifierCascade* cascade, const CvArr* sum, const CvArr* sqsum, const CvArr* tilted sum, double scale ); cascade Hidden Haar classifier cascade, created by cvCreateHidHaarClassifierCascade sum Integral (sum) single-channel image of 32-bit integer format. This image as well as the two subsequent images are used for fast feature evaluation and brightness/contrast normaliza- tion. They all can be retrieved from input 8-bit or floating point single-channel image using the function cvIntegral sqsum Square sum single-channel image of 64-bit floating-point format 5.1. CASCADE CLASSIFICATION 369 tilted sum Tilted sum single-channel image of 32-bit integer format scale Window scale for the cascade. If scale =1, the original window size is used (objects of that size are searched) - the same size as specified in cvLoadHaarClassifierCascade (24x24 in the case of default face cascade), if scale =2, a two times larger window is used (48x48 in the case of default face cascade). While this will speed-up search about four times, faces smaller than 48x48 cannot be detected The function assigns images and/or window scale to the hidden classifier cascade. If image pointers are NULL, the previously set images are used further (i.e. NULLs mean ”do not change images”). Scale parameter has no such a ”protection” value, but the previous value can be re- trieved by the cvGetHaarClassifierCascadeScale function and reused again. The function is used to prepare cascade for detecting object of the particular size in the particular image. The function is called internally by cvHaarDetectObjects, but it can be called by the user if they are using the lower-level function cvRunHaarClassifierCascade. cvReleaseHaarClassifierCascade (view/add comments) Releases the haar classifier cascade. void cvReleaseHaarClassifierCascade( CvHaarClassifierCascade** cascade ); cascade Double pointer to the released cascade. The pointer is cleared by the function The function deallocates the cascade that has been created manually or loaded using cvLoad- HaarClassifierCascade or cvLoad. cvRunHaarClassifierCascade (view/add comments) Runs a cascade of boosted classifiers at the given image location. int cvRunHaarClassifierCascade( CvHaarClassifierCascade* cascade, CvPoint pt, int start stage=0 ); 370 CHAPTER 5. OBJDETECT. OBJECT DETECTION cascade Haar classifier cascade pt Top-left corner of the analyzed region. Size of the region is a original window size scaled by the currenly set scale. The current window size may be retrieved using the cvGetHaarClas- sifierCascadeWindowSize function start stage Initial zero-based index of the cascade stage to start from. The function assumes that all the previous stages are passed. This feature is used internally by cvHaarDetectOb- jects for better processor cache utilization The function runs the Haar classifier cascade at a single image location. Before using this function the integral images and the appropriate scale (window size) should be set using cvSe- tImagesForHaarClassifierCascade. The function returns a positive value if the analyzed rectangle passed all the classifier stages (it is a candidate) and a zero or negative value otherwise. Chapter 6 video. Video Analysis 6.1 Motion Analysis and Object Tracking cvCalcGlobalOrientation (view/add comments) Calculates the global motion orientation of some selected region. double cvCalcGlobalOrientation( const CvArr* orientation, const CvArr* mask, const CvArr* mhi, double timestamp, double duration ); orientation Motion gradient orientation image; calculated by the function cvCalcMotionGradi- ent mask Mask image. It may be a conjunction of a valid gradient mask, obtained with cvCalcMotion- Gradient and the mask of the region, whose direction needs to be calculated mhi Motion history image timestamp Current time in milliseconds or other units, it is better to store time passed to cvUp- dateMotionHistory before and reuse it here, because running cvUpdateMotionHistory and cvCalcMotionGradient on large images may take some time 371 372 CHAPTER 6. VIDEO. VIDEO ANALYSIS duration Maximal duration of motion track in milliseconds, the same as cvUpdateMotionHistory The function calculates the general motion direction in the selected region and returns the angle between 0 degrees and 360 degrees . At first the function builds the orientation histogram and finds the basic orientation as a coordinate of the histogram maximum. After that the function calculates the shift relative to the basic orientation as a weighted sum of all of the orientation vectors: the more recent the motion, the greater the weight. The resultant angle is a circular sum of the basic orientation and the shift. cvCalcMotionGradient (view/add comments) Calculates the gradient orientation of a motion history image. void cvCalcMotionGradient( const CvArr* mhi, CvArr* mask, CvArr* orientation, double delta1, double delta2, int apertureSize=3 ); mhi Motion history image mask Mask image; marks pixels where the motion gradient data is correct; output parameter orientation Motion gradient orientation image; contains angles from 0 to 360 degrees delta1 See below delta2 See below apertureSize Aperture size of derivative operators used by the function: CV SCHARR, 1, 3, 5 or 7 (see cvSobel) The function calculates the derivatives Dx and Dy of mhi and then calculates gradient orien- tation as: orientation(x, y) = arctan Dy(x, y) Dx(x, y) 6.1. MOTION ANALYSIS AND OBJECT TRACKING 373 where both Dx(x, y) and Dy(x, y) signs are taken into account (as in the cvCartToPolar func- tion). After that mask is filled to indicate where the orientation is valid (see the delta1 and delta2 description). The function finds the minimum (m(x, y)) and maximum (M(x, y)) mhi values over each pixel (x, y) neighborhood and assumes the gradient is valid only if min(delta1, delta2) ≤ M(x, y) − m(x, y) ≤ max(delta1, delta2). cvCalcOpticalFlowBM (view/add comments) Calculates the optical flow for two images by using the block matching method. void cvCalcOpticalFlowBM( const CvArr* prev, const CvArr* curr, CvSize blockSize, CvSize shiftSize, CvSize max range, int usePrevious, CvArr* velx, CvArr* vely ); prev First image, 8-bit, single-channel curr Second image, 8-bit, single-channel blockSize Size of basic blocks that are compared shiftSize Block coordinate increments max range Size of the scanned neighborhood in pixels around the block usePrevious Uses the previous (input) velocity field velx Horizontal component of the optical flow of prev->width − blockSize.width shiftSize.width  × prev->height − blockSize.height shiftSize.height  size, 32-bit floating-point, single-channel 374 CHAPTER 6. VIDEO. VIDEO ANALYSIS vely Vertical component of the optical flow of the same size velx, 32-bit floating-point, single- channel The function calculates the optical flow for overlapped blocks blockSize.width×blockSize.height pixels each, thus the velocity fields are smaller than the original images. For every block in prev the functions tries to find a similar block in curr in some neighborhood of the original block or shifted by (velx(x0,y0),vely(x0,y0)) block as has been calculated by previous function call (if usePrevious=1) cvCalcOpticalFlowHS (view/add comments) Calculates the optical flow for two images. void cvCalcOpticalFlowHS( const CvArr* prev, const CvArr* curr, int usePrevious, CvArr* velx, CvArr* vely, double lambda, CvTermCriteria criteria ); prev First image, 8-bit, single-channel curr Second image, 8-bit, single-channel usePrevious Uses the previous (input) velocity field velx Horizontal component of the optical flow of the same size as input images, 32-bit floating- point, single-channel vely Vertical component of the optical flow of the same size as input images, 32-bit floating-point, single-channel lambda Lagrangian multiplier criteria Criteria of termination of velocity computing The function computes the flow for every pixel of the first input image using the Horn and Schunck algorithm [12]. 6.1. MOTION ANALYSIS AND OBJECT TRACKING 375 cvCalcOpticalFlowLK (view/add comments) Calculates the optical flow for two images. void cvCalcOpticalFlowLK( const CvArr* prev, const CvArr* curr, CvSize winSize, CvArr* velx, CvArr* vely ); prev First image, 8-bit, single-channel curr Second image, 8-bit, single-channel winSize Size of the averaging window used for grouping pixels velx Horizontal component of the optical flow of the same size as input images, 32-bit floating- point, single-channel vely Vertical component of the optical flow of the same size as input images, 32-bit floating-point, single-channel The function computes the flow for every pixel of the first input image using the Lucas and Kanade algorithm [14]. cvCalcOpticalFlowPyrLK (view/add comments) Calculates the optical flow for a sparse feature set using the iterative Lucas-Kanade method with pyramids. void cvCalcOpticalFlowPyrLK( const CvArr* prev, const CvArr* curr, CvArr* prevPyr, CvArr* currPyr, 376 CHAPTER 6. VIDEO. VIDEO ANALYSIS const CvPoint2D32f* prevFeatures, CvPoint2D32f* currFeatures, int count, CvSize winSize, int level, char* status, float* track error, CvTermCriteria criteria, int flags ); prev First frame, at time t curr Second frame, at time t + dt prevPyr Buffer for the pyramid for the first frame. If the pointer is not NULL , the buffer must have a sufficient size to store the pyramid from level 1 to level level ; the total size of (image width+8)*image height/3 bytes is sufficient currPyr Similar to prevPyr, used for the second frame prevFeatures Array of points for which the flow needs to be found currFeatures Array of 2D points containing the calculated new positions of the input features in the second image count Number of feature points winSize Size of the search window of each pyramid level level Maximal pyramid level number. If 0 , pyramids are not used (single level), if 1 , two levels are used, etc status Array. Every element of the array is set to 1 if the flow for the corresponding feature has been found, 0 otherwise track error Array of double numbers containing the difference between patches around the original and moved points. Optional parameter; can be NULL criteria Specifies when the iteration process of finding the flow for each point on each pyramid level should be stopped flags Miscellaneous flags: 6.1. MOTION ANALYSIS AND OBJECT TRACKING 377 CV LKFLOWPyr A READY pyramid for the first frame is precalculated before the call CV LKFLOWPyr B READY pyramid for the second frame is precalculated before the call CV LKFLOW INITIAL GUESSES array B contains initial coordinates of features before the function call The function implements the sparse iterative version of the Lucas-Kanade optical flow in pyra- mids [5] . It calculates the coordinates of the feature points on the current video frame given their coordinates on the previous frame. The function finds the coordinates with sub-pixel accuracy. Both parameters prevPyr and currPyr comply with the following rules: if the image pointer is 0, the function allocates the buffer internally, calculates the pyramid, and releases the buffer after processing. Otherwise, the function calculates the pyramid and stores it in the buffer unless the flag CV LKFLOWPyr A[B] READY is set. The image should be large enough to fit the Gaussian pyramid data. After the function call both pyramids are calculated and the readiness flag for the corresponding image can be set in the next call (i.e., typically, for all the image pairs except the very first one CV LKFLOWPyr A READY is set). cvCamShift (view/add comments) Finds the object center, size, and orientation. int cvCamShift( const CvArr* prob image, CvRect window, CvTermCriteria criteria, CvConnectedComp* comp, CvBox2D* box=NULL ); prob image Back projection of object histogram (see cvCalcBackProject) window Initial search window criteria Criteria applied to determine when the window search should be finished comp Resultant structure that contains the converged search window coordinates (comp->rect field) and the sum of all of the pixels inside the window (comp->area field) box Circumscribed box for the object. If not NULL, it contains object size and orientation 378 CHAPTER 6. VIDEO. VIDEO ANALYSIS The function implements the CAMSHIFT object tracking algrorithm [6]. First, it finds an object center using cvMeanShift and, after that, calculates the object size and orientation. The function returns number of iterations made within cvMeanShift. The CamShiftTracker class declared in cv.hpp implements the color object tracker that uses the function. CvConDensation ConDenstation state. typedef struct CvConDensation { int MP; //Dimension of measurement vector int DP; // Dimension of state vector float* DynamMatr; // Matrix of the linear Dynamics system float* State; // Vector of State int SamplesNum; // Number of the Samples float** flSamples; // array of the Sample Vectors float** flNewSamples; // temporary array of the Sample Vectors float* flConfidence; // Confidence for each Sample float* flCumulative; // Cumulative confidence float* Temp; // Temporary vector float* RandomSample; // RandomVector to update sample set CvRandState* RandS; // Array of structures to generate random vectors } CvConDensation; The structure CvConDensation stores the CONditional DENSity propagATION tracker state. The information about the algorithm can be found at http://www.dai.ed.ac.uk/CVonline/ LOCAL_COPIES/ISARD1/condensation.html. cvCreateConDensation (view/add comments) Allocates the ConDensation filter structure. CvConDensation* cvCreateConDensation( int dynam params, int measure params, int sample count ); dynam params Dimension of the state vector 6.1. MOTION ANALYSIS AND OBJECT TRACKING 379 measure params Dimension of the measurement vector sample count Number of samples The function creates a CvConDensation structure and returns a pointer to the structure. cvConDensInitSampleSet (view/add comments) Initializes the sample set for the ConDensation algorithm. void cvConDensInitSampleSet( CvConDensation* condens, CvMat* lower bound, CvMat* upper bound ); condens Pointer to a structure to be initialized lower bound Vector of the lower boundary for each dimension upper bound Vector of the upper boundary for each dimension The function fills the samples arrays in the structure condens with values within the specified ranges. CvKalman (view/add comments) Kalman filter state. typedef struct CvKalman { int MP; /* number of measurement vector dimensions */ int DP; /* number of state vector dimensions */ int CP; /* number of control vector dimensions */ /* backward compatibility fields */ #if 1 float* PosterState; /* =state_pre->data.fl */ float* PriorState; /* =state_post->data.fl */ float* DynamMatr; /* =transition_matrix->data.fl */ float* MeasurementMatr; /* =measurement_matrix->data.fl */ float* MNCovariance; /* =measurement_noise_cov->data.fl */ 380 CHAPTER 6. VIDEO. VIDEO ANALYSIS float* PNCovariance; /* =process_noise_cov->data.fl */ float* KalmGainMatr; /* =gain->data.fl */ float* PriorErrorCovariance;/* =error_cov_pre->data.fl */ float* PosterErrorCovariance;/* =error_cov_post->data.fl */ float* Temp1; /* temp1->data.fl */ float* Temp2; /* temp2->data.fl */ #endif CvMat* state_pre; /* predicted state (x’(k)): x(k)=A*x(k-1)+B*u(k) */ CvMat* state_post; /* corrected state (x(k)): x(k)=x’(k)+K(k)*(z(k)-H*x’(k)) */ CvMat* transition_matrix; /* state transition matrix (A) */ CvMat* control_matrix; /* control matrix (B) (it is not used if there is no control)*/ CvMat* measurement_matrix; /* measurement matrix (H) */ CvMat* process_noise_cov; /* process noise covariance matrix (Q) */ CvMat* measurement_noise_cov; /* measurement noise covariance matrix (R) */ CvMat* error_cov_pre; /* priori error estimate covariance matrix (P’(k)): P’(k)=A*P(k-1)*At + Q*/ CvMat* gain; /* Kalman gain matrix (K(k)): K(k)=P’(k)*Ht*inv(H*P’(k)*Ht+R)*/ CvMat* error_cov_post; /* posteriori error estimate covariance matrix (P(k)): P(k)=(I-K(k)*H)*P’(k) */ CvMat* temp1; /* temporary matrices */ CvMat* temp2; CvMat* temp3; CvMat* temp4; CvMat* temp5; } CvKalman; The structure CvKalman is used to keep the Kalman filter state. It is created by the cvCre- ateKalman function, updated by the cvKalmanPredict and cvKalmanCorrect functions and re- leased by the cvReleaseKalman function . Normally, the structure is used for the standard Kalman filter (notation and the formulas below are borrowed from the excellent Kalman tutorial [24]) xk = A· xk−1 + B· uk + wk zk = H· xk + vk where: xk (xk−1) state of the system at the moment k (k-1) zk measurement of the system state at the moment k uk external control applied at the moment k 6.1. MOTION ANALYSIS AND OBJECT TRACKING 381 wk and vk are normally-distributed process and measurement noise, respectively: p(w) ∼ N(0,Q) p(v) ∼ N(0,R) that is, Q process noise covariance matrix, constant or variable, R measurement noise covariance matrix, constant or variable In the case of the standard Kalman filter, all of the matrices: A, B, H, Q and R are initialized once after the cvCvKalman structure is allocated via cvCreateKalman. However, the same struc- ture and the same functions may be used to simulate the extended Kalman filter by linearizing the extended Kalman filter equation in the current system state neighborhood, in this case A, B, H (and, probably, Q and R) should be updated on every step. cvCreateKalman (view/add comments) Allocates the Kalman filter structure. CvKalman* cvCreateKalman( int dynam params, int measure params, int control params=0 ); dynam params dimensionality of the state vector measure params dimensionality of the measurement vector control params dimensionality of the control vector The function allocates cvCvKalman and all its matrices and initializes them somehow. cvKalmanCorrect (view/add comments) Adjusts the model state. const CvMat* cvKalmanCorrect( CvKalman* kalman, const CvMat* measurement ); 382 CHAPTER 6. VIDEO. VIDEO ANALYSIS kalman Pointer to the structure to be updated measurement CvMat containing the measurement vector The function adjusts the stochastic model state on the basis of the given measurement of the model state: Kk = P 0 k ·HT·(H·P 0 k ·HT + R)−1 xk = x0 k + Kk ·(zk − H· x0 k) Pk = (I − Kk ·H)·P 0 k where zk given measurement (mesurement parameter) Kk Kalman ”gain” matrix. The function stores the adjusted state at kalman->state post and returns it on output. Example. Using Kalman filter to track a rotating point #include "cv.h" #include "highgui.h" #include int main(int argc, char** argv) { /* A matrix data */ const float A[] = { 1, 1, 0, 1 }; IplImage* img = cvCreateImage( cvSize(500,500), 8, 3 ); CvKalman* kalman = cvCreateKalman( 2, 1, 0 ); /* state is (phi, delta_phi) - angle and angle increment */ CvMat* state = cvCreateMat( 2, 1, CV_32FC1 ); CvMat* process_noise = cvCreateMat( 2, 1, CV_32FC1 ); /* only phi (angle) is measured */ CvMat* measurement = cvCreateMat( 1, 1, CV_32FC1 ); CvRandState rng; int code = -1; cvRandInit( &rng, 0, 1, -1, CV_RAND_UNI ); cvZero( measurement ); cvNamedWindow( "Kalman", 1 ); for(;;) { cvRandSetRange( &rng, 0, 0.1, 0 ); rng.disttype = CV_RAND_NORMAL; 6.1. MOTION ANALYSIS AND OBJECT TRACKING 383 cvRand( &rng, state ); memcpy( kalman->transition_matrix->data.fl, A, sizeof(A)); cvSetIdentity( kalman->measurement_matrix, cvRealScalar(1) ); cvSetIdentity( kalman->process_noise_cov, cvRealScalar(1e-5) ); cvSetIdentity( kalman->measurement_noise_cov, cvRealScalar(1e-1) ); cvSetIdentity( kalman->error_cov_post, cvRealScalar(1)); /* choose random initial state */ cvRand( &rng, kalman->state_post ); rng.disttype = CV_RAND_NORMAL; for(;;) { #define calc_point(angle) \ cvPoint( cvRound(img->width/2 + img->width/3*cos(angle)), \ cvRound(img->height/2 - img->width/3*sin(angle))) float state_angle = state->data.fl[0]; CvPoint state_pt = calc_point(state_angle); /* predict point position */ const CvMat* prediction = cvKalmanPredict( kalman, 0 ); float predict_angle = prediction->data.fl[0]; CvPoint predict_pt = calc_point(predict_angle); float measurement_angle; CvPoint measurement_pt; cvRandSetRange( &rng, 0, sqrt(kalman->measurement_noise_cov->data.fl[0]), 0 ); cvRand( &rng, measurement ); /* generate measurement */ cvMatMulAdd( kalman->measurement_matrix, state, measurement, measurement ); measurement_angle = measurement->data.fl[0]; measurement_pt = calc_point(measurement_angle); /* plot points */ #define draw_cross( center, color, d ) \ cvLine( img, cvPoint( center.x - d, center.y - d ), \ cvPoint( center.x + d, center.y + d ), \ 384 CHAPTER 6. VIDEO. VIDEO ANALYSIS color, 1, 0 ); \ cvLine( img, cvPoint( center.x + d, center.y - d ), \ cvPoint( center.x - d, center.y + d ), \ color, 1, 0 ) cvZero( img ); draw_cross( state_pt, CV_RGB(255,255,255), 3 ); draw_cross( measurement_pt, CV_RGB(255,0,0), 3 ); draw_cross( predict_pt, CV_RGB(0,255,0), 3 ); cvLine( img, state_pt, predict_pt, CV_RGB(255,255,0), 3, 0 ); /* adjust Kalman filter state */ cvKalmanCorrect( kalman, measurement ); cvRandSetRange( &rng, 0, sqrt(kalman->process_noise_cov->data.fl[0]), 0 ); cvRand( &rng, process_noise ); cvMatMulAdd( kalman->transition_matrix, state, process_noise, state ); cvShowImage( "Kalman", img ); code = cvWaitKey( 100 ); if( code > 0 ) /* break current simulation by pressing a key */ break; } if( code == 27 ) /* exit by ESCAPE */ break; } return 0; } cvKalmanPredict (view/add comments) Estimates the subsequent model state. 6.1. MOTION ANALYSIS AND OBJECT TRACKING 385 const CvMat* cvKalmanPredict( CvKalman* kalman, const CvMat* control=NULL); kalman Kalman filter state control Control vector uk, should be NULL iff there is no external control (control params =0) The function estimates the subsequent stochastic model state by its current state and stores it at kalman->state pre: x0 k = Axk−1 + Buk P 0 k = APk−1AT + Q where x0 k is predicted state kalman->state pre, xk−1 is corrected state on the previous step kalman->state post (should be initialized somehow in the beginning, zero vector by default), uk is external control (control parameter), P 0 k is priori error covariance matrix kalman->error cov pre Pk−1 is posteriori error covariance matrix on the previous step kalman->error cov post (should be initialized somehow in the beginning, identity matrix by default), The function returns the estimated state. KalmanUpdateByMeasurement Synonym for KalmanCorrect KalmanUpdateByTime Synonym for KalmanPredict cvMeanShift (view/add comments) Finds the object center on back projection. 386 CHAPTER 6. VIDEO. VIDEO ANALYSIS int cvMeanShift( const CvArr* prob image, CvRect window, CvTermCriteria criteria, CvConnectedComp* comp ); prob image Back projection of the object histogram (see cvCalcBackProject) window Initial search window criteria Criteria applied to determine when the window search should be finished comp Resultant structure that contains the converged search window coordinates (comp->rect field) and the sum of all of the pixels inside the window (comp->area field) The function iterates to find the object center given its back projection and initial position of search window. The iterations are made until the search window center moves by less than the given value and/or until the function has done the maximum number of iterations. The function returns the number of iterations made. cvReleaseConDensation (view/add comments) Deallocates the ConDensation filter structure. void cvReleaseConDensation( CvConDensation** condens ); condens Pointer to the pointer to the structure to be released The function releases the structure condens) and frees all memory previously allocated for the structure. cvReleaseKalman (view/add comments) Deallocates the Kalman filter structure. 6.1. MOTION ANALYSIS AND OBJECT TRACKING 387 void cvReleaseKalman( CvKalman** kalman ); kalman double pointer to the Kalman filter structure The function releases the structure cvCvKalman and all of the underlying matrices. cvSegmentMotion (view/add comments) Segments a whole motion into separate moving parts. CvSeq* cvSegmentMotion( const CvArr* mhi, CvArr* seg mask, CvMemStorage* storage, double timestamp, double seg thresh ); mhi Motion history image seg mask Image where the mask found should be stored, single-channel, 32-bit floating-point storage Memory storage that will contain a sequence of motion connected components timestamp Current time in milliseconds or other units seg thresh Segmentation threshold; recommended to be equal to the interval between motion history ”steps” or greater The function finds all of the motion segments and marks them in seg mask with individual values (1,2,...). It also returns a sequence of cvCvConnectedComp structures, one for each motion component. After that the motion direction for every component can be calculated with cvCalcGlobalOrientation using the extracted mask of the particular component cvCmp. 388 CHAPTER 6. VIDEO. VIDEO ANALYSIS cvSnakeImage (view/add comments) Changes the contour position to minimize its energy. void cvSnakeImage( const IplImage* image, CvPoint* points, int length, float* alpha, float* beta, float* gamma, int coeff usage, CvSize win, CvTermCriteria criteria, int calc gradient=1 ); image The source image or external energy field points Contour points (snake) length Number of points in the contour alpha Weight[s] of continuity energy, single float or array of length floats, one for each contour point beta Weight[s] of curvature energy, similar to alpha gamma Weight[s] of image energy, similar to alpha coeff usage Different uses of the previous three parameters: CV VALUE indicates that each of alpha, beta, gamma is a pointer to a single value to be used for all points; CV ARRAY indicates that each of alpha, beta, gamma is a pointer to an array of coeffi- cients different for all the points of the snake. All the arrays must have the size equal to the contour size. win Size of neighborhood of every point used to search the minimum, both win.width and win.height must be odd 6.1. MOTION ANALYSIS AND OBJECT TRACKING 389 criteria Termination criteria calc gradient Gradient flag; if not 0, the function calculates the gradient magnitude for every image pixel and consideres it as the energy field, otherwise the input image itself is consid- ered The function updates the snake in order to minimize its total energy that is a sum of internal energy that depends on the contour shape (the smoother contour is, the smaller internal energy is) and external energy that depends on the energy field and reaches minimum at the local energy extremums that correspond to the image edges in the case of using an image gradient. The parameter criteria.epsilon is used to define the minimal number of points that must be moved during any iteration to keep the iteration process running. If at some iteration the number of moved points is less than criteria.epsilon or the func- tion performed criteria.max iter iterations, the function terminates. cvUpdateMotionHistory (view/add comments) Updates the motion history image by a moving silhouette. void cvUpdateMotionHistory( const CvArr* silhouette, CvArr* mhi, double timestamp, double duration ); silhouette Silhouette mask that has non-zero pixels where the motion occurs mhi Motion history image, that is updated by the function (single-channel, 32-bit floating-point) timestamp Current time in milliseconds or other units duration Maximal duration of the motion track in the same units as timestamp The function updates the motion history image as following: mhi(x, y) =    timestamp if silhouette(x, y) 6= 0 0 if silhouette(x, y) = 0 and mhi < (timestamp − duration) mhi(x, y) otherwise That is, MHI pixels where motion occurs are set to the current timestamp, while the pixels where motion happened far ago are cleared. 390 CHAPTER 6. VIDEO. VIDEO ANALYSIS Chapter 7 highgui. High-level GUI and Media I/O While OpenCV was designed for use in full-scale applications and can be used within functionally rich UI frameworks (such as Qt, WinForms or Cocoa) or without any UI at all, sometimes there is a need to try some functionality quickly and visualize the results. This is what the HighGUI module has been designed for. It provides easy interface to: • create and manipulate windows that can display images and ”remember” their content (no need to handle repaint events from OS) • add trackbars to the windows, handle simple mouse events as well as keyboard commmands • read and write images to/from disk or memory. • read video from camera or file and write video to a file. 7.1 User Interface cvConvertImage (view/add comments) Converts one image to another with an optional vertical flip. void cvConvertImage( const CvArr* src, CvArr* dst, int flags=0 ); src Source image. 391 392 CHAPTER 7. HIGHGUI. HIGH-LEVEL GUI AND MEDIA I/O dst Destination image. Must be single-channel or 3-channel 8-bit image. flags The operation flags: CV CVTIMG FLIP Flips the image vertically CV CVTIMG SWAP RB Swaps the red and blue channels. In OpenCV color images have BGR channel order, however on some systems the order needs to be reversed before displaying the image ( ShowImage does this automatically). The function cvConvertImage converts one image to another and flips the result vertically if desired. The function is used by ShowImage. cvCreateTrackbar (view/add comments) Creates a trackbar and attaches it to the specified window int cvCreateTrackbar( const char* trackbarName, const char* windowName, int* value, int count, CvTrackbarCallback onChange ); trackbarName Name of the created trackbar. windowName Name of the window which will be used as a parent for created trackbar. value Pointer to an integer variable, whose value will reflect the position of the slider. Upon creation, the slider position is defined by this variable. count Maximal position of the slider. Minimal position is always 0. onChange Pointer to the function to be called every time the slider changes position. This function should be prototyped as void Foo(int); Can be NULL if callback is not required. The function cvCreateTrackbar creates a trackbar (a.k.a. slider or range control) with the specified name and range, assigns a variable to be syncronized with trackbar position and speci- fies a callback function to be called on trackbar position change. The created trackbar is displayed on the top of the given window. 7.1. USER INTERFACE 393 [Qt Backend Only] qt-specific details: windowName Name of the window which will be used as a parent for created trackbar. Can be NULL if the trackbar should be attached to the control panel. The created trackbar is displayed at the bottom of the given window if windowName is correctly provided, or displayed on the control panel if windowName is NULL. By clicking on the label of each trackbar, it is possible to edit the trackbar’s value manually for a more accurate control of it. CV_EXTERN_C_FUNCPTR( void (*CvTrackbarCallback)(int pos) ); cvDestroyAllWindows (view/add comments) Destroys all of the HighGUI windows. void cvDestroyAllWindows(void); The function cvDestroyAllWindows destroys all of the opened HighGUI windows. cvDestroyWindow (view/add comments) Destroys a window. void cvDestroyWindow( const char* name ); name Name of the window to be destroyed. The function cvDestroyWindow destroys the window with the given name. 394 CHAPTER 7. HIGHGUI. HIGH-LEVEL GUI AND MEDIA I/O cvGetTrackbarPos (view/add comments) Returns the trackbar position. int cvGetTrackbarPos( const char* trackbarName, const char* windowName ); trackbarName Name of the trackbar. windowName Name of the window which is the parent of the trackbar. The function cvGetTrackbarPos returns the current position of the specified trackbar. [Qt Backend Only] qt-specific details: windowName Name of the window which is the parent of the trackbar. Can be NULL if the trackbar is attached to the control panel. cvGetWindowHandle (view/add comments) Gets the window’s handle by its name. void* cvGetWindowHandle( const char* name ); name Name of the window . The function cvGetWindowHandle returns the native window handle (HWND in case of Win32 and GtkWidget in case of GTK+). [Qt Backend Only] qt-specific details: The function cvGetWindowHandle returns the native window handle inheriting from the Qt class QWidget. 7.1. USER INTERFACE 395 cvGetWindowName (view/add comments) Gets the window’s name by its handle. const char* cvGetWindowName( void* windowHandle ); windowHandle Handle of the window. The function cvGetWindowName returns the name of the window given its native handle (HWND in case of Win32 and GtkWidget in case of GTK+). [Qt Backend Only] qt-specific details: The function cvGetWindowName returns the name of the window given its native handle (QWidget). cvInitSystem (view/add comments) Initializes HighGUI. int cvInitSystem( int argc, char** argv ); argc Number of command line arguments argv Array of command line arguments The function cvInitSystem initializes HighGUI. If it wasn’t called explicitly by the user before the first window was created, it is called implicitly then with argc=0, argv=NULL. Under Win32 there is no need to call it explicitly. Under X Window the arguments may be used to customize a look of HighGUI windows and controls. [Qt Backend Only] qt-specific details: The function cvInitSystem is automatically called at the first cvNameWindow call. 396 CHAPTER 7. HIGHGUI. HIGH-LEVEL GUI AND MEDIA I/O cvMoveWindow (view/add comments) Sets the position of the window. void cvMoveWindow( const char* name, int x, int y ); name Name of the window to be moved. x New x coordinate of the top-left corner y New y coordinate of the top-left corner The function cvMoveWindow changes the position of the window. cvNamedWindow (view/add comments) Creates a window. int cvNamedWindow( const char* name, int flags ); name Name of the window in the window caption that may be used as a window identifier. flags Flags of the window. Currently the only supported flag is CV WINDOW AUTOSIZE. If this is set, window size is automatically adjusted to fit the displayed image (see ShowImage ), and the user can not change the window size manually. The function cvNamedWindow creates a window which can be used as a placeholder for im- ages and trackbars. Created windows are referred to by their names. If a window with the same name already exists, the function does nothing. [Qt Backend Only] qt-specific details: flags Flags of the window. Currently the supported flags are: 7.1. USER INTERFACE 397 CV WINDOW NORMAL or CV WINDOW AUTOSIZE: CV WINDOW NORMAL let the user resize the window, whereas CV WINDOW AUTOSIZE adjusts automatically the window’s size to fit the displayed image (see ShowImage ), and the user can not change the window size manually. CV WINDOW FREERATIO or CV WINDOW KEEPRATIO: CV WINDOW FREERATIO adjust the image without respect the its ration, whereas CV WINDOW KEEPRATIO keep the image’s ratio. CV GUI NORMAL or CV GUI EXPANDED: CV GUI NORMAL is the old way to draw the win- dow without statusbar and toolbar, whereas CV GUI EXPANDED is the new enhance GUI. This parameter is optional. The default flags set for a new window are CV WINDOW AUTOSIZE, CV WINDOW KEEPRATIO, and CV GUI EXPANDED. However, if you want to modify the flags, you can combine them using OR operator, ie: V WINDOW NORMALV GUI NORMAL cvResizeWindow (view/add comments) Sets the window size. void cvResizeWindow( const char* name, int width, int height ); name Name of the window to be resized. width New width height New height The function cvResizeWindow changes the size of the window. cvSetMouseCallback (view/add comments) Assigns callback for mouse events. void cvSetMouseCallback( const char* windowName, CvMouseCallback onMouse, void* param=NULL ); 398 CHAPTER 7. HIGHGUI. HIGH-LEVEL GUI AND MEDIA I/O windowName Name of the window. onMouse Pointer to the function to be called every time a mouse event occurs in the specified window. This function should be prototyped as void Foo(int event, int x, int y, int flags, void* param); where event is one of CV EVENT *, x and y are the co- ordinates of the mouse pointer in image coordinates (not window coordinates), flags is a combination of CV EVENT FLAG *, and param is a user-defined parameter passed to the cvSetMouseCallback function call. param User-defined parameter to be passed to the callback function. The function cvSetMouseCallback sets the callback function for mouse events occuring within the specified window. The event parameter is one of: CV EVENT MOUSEMOVE Mouse movement CV EVENT LBUTTONDOWN Left button down CV EVENT RBUTTONDOWN Right button down CV EVENT MBUTTONDOWN Middle button down CV EVENT LBUTTONUP Left button up CV EVENT RBUTTONUP Right button up CV EVENT MBUTTONUP Middle button up CV EVENT LBUTTONDBLCLK Left button double click CV EVENT RBUTTONDBLCLK Right button double click CV EVENT MBUTTONDBLCLK Middle button double click The flags parameter is a combination of : CV EVENT FLAG LBUTTON Left button pressed CV EVENT FLAG RBUTTON Right button pressed CV EVENT FLAG MBUTTON Middle button pressed CV EVENT FLAG CTRLKEY Control key pressed CV EVENT FLAG SHIFTKEY Shift key pressed CV EVENT FLAG ALTKEY Alt key pressed 7.1. USER INTERFACE 399 cvSetTrackbarPos (view/add comments) Sets the trackbar position. void cvSetTrackbarPos( const char* trackbarName, const char* windowName, int pos ); trackbarName Name of the trackbar. windowName Name of the window which is the parent of trackbar. pos New position. The function cvSetTrackbarPos sets the position of the specified trackbar. [Qt Backend Only] qt-specific details: windowName Name of the window which is the parent of trackbar. Can be NULL if the trackbar is attached to the control panel. cvShowImage (view/add comments) Displays the image in the specified window void cvShowImage( const char* name, const CvArr* image ); name Name of the window. image Image to be shown. The function cvShowImage displays the image in the specified window. If the window was created with the CV WINDOW AUTOSIZE flag then the image is shown with its original size, other- wise the image is scaled to fit in the window. The function may scale the image, depending on its depth: 400 CHAPTER 7. HIGHGUI. HIGH-LEVEL GUI AND MEDIA I/O • If the image is 8-bit unsigned, it is displayed as is. • If the image is 16-bit unsigned or 32-bit integer, the pixels are divided by 256. That is, the value range [0,255*256] is mapped to [0,255]. • If the image is 32-bit floating-point, the pixel values are multiplied by 255. That is, the value range [0,1] is mapped to [0,255]. cvWaitKey (view/add comments) Waits for a pressed key. int cvWaitKey( int delay=0 ); delay Delay in milliseconds. The function cvWaitKey waits for key event infinitely (delay <= 0) or for delay milliseconds. Returns the code of the pressed key or -1 if no key was pressed before the specified time had elapsed. Note: This function is the only method in HighGUI that can fetch and handle events, so it needs to be called periodically for normal event processing, unless HighGUI is used within some environment that takes care of event processing. [Qt Backend Only] qt-specific details: With this current Qt implementation, this is the only way to process event such as repaint for the windows, and so on . . . 7.2 Reading and Writing Images and Video cvLoadImage (view/add comments) Loads an image from a file as an IplImage. IplImage* cvLoadImage( const char* filename, int iscolor=CV LOAD IMAGE COLOR ); 7.2. READING AND WRITING IMAGES AND VIDEO 401 filename Name of file to be loaded. iscolor Specific color type of the loaded image: CV LOAD IMAGE COLOR the loaded image is forced to be a 3-channel color image CV LOAD IMAGE GRAYSCALE the loaded image is forced to be grayscale CV LOAD IMAGE UNCHANGED the loaded image will be loaded as is. The function cvLoadImage loads an image from the specified file and returns the pointer to the loaded image. Currently the following file formats are supported: • Windows bitmaps - BMP, DIB • JPEG files - JPEG, JPG, JPE • Portable Network Graphics - PNG • Portable image format - PBM, PGM, PPM • Sun rasters - SR, RAS • TIFF files - TIFF, TIF Note that in the current implementation the alpha channel, if any, is stripped from the output image, e.g. 4-channel RGBA image will be loaded as RGB. cvLoadImageM (view/add comments) Loads an image from a file as a CvMat. CvMat* cvLoadImageM( const char* filename, int iscolor=CV LOAD IMAGE COLOR ); filename Name of file to be loaded. iscolor Specific color type of the loaded image: CV LOAD IMAGE COLOR the loaded image is forced to be a 3-channel color image CV LOAD IMAGE GRAYSCALE the loaded image is forced to be grayscale 402 CHAPTER 7. HIGHGUI. HIGH-LEVEL GUI AND MEDIA I/O CV LOAD IMAGE UNCHANGED the loaded image will be loaded as is. The function cvLoadImageM loads an image from the specified file and returns the pointer to the loaded image. urrently the following file formats are supported: • Windows bitmaps - BMP, DIB • JPEG files - JPEG, JPG, JPE • Portable Network Graphics - PNG • Portable image format - PBM, PGM, PPM • Sun rasters - SR, RAS • TIFF files - TIFF, TIF Note that in the current implementation the alpha channel, if any, is stripped from the output image, e.g. 4-channel RGBA image will be loaded as RGB. cvSaveImage (view/add comments) Saves an image to a specified file. int cvSaveImage( const char* filename, const CvArr* image ); filename Name of the file. image Image to be saved. The function cvSaveImage saves the image to the specified file. The image format is chosen based on the filename extension, see LoadImage . Only 8-bit single-channel or 3-channel (with ’BGR’ channel order) images can be saved using this function. If the format, depth or channel order is different, use cvCvtScale and cvCvtColor to convert it before saving, or use universal cvSave to save the image to XML or YAML format. CvCapture (view/add comments) Video capturing structure. 7.2. READING AND WRITING IMAGES AND VIDEO 403 typedef struct CvCapture CvCapture; The structure CvCapture does not have a public interface and is used only as a parameter for video capturing functions. cvCaptureFromCAM (view/add comments) Initializes capturing a video from a camera. CvCapture* cvCaptureFromCAM( int index ); index Index of the camera to be used. If there is only one camera or it does not matter what camera is used -1 may be passed. The function cvCaptureFromCAM allocates and initializes the CvCapture structure for reading a video stream from the camera. Currently two camera interfaces can be used on Windows: Video for Windows (VFW) and Matrox Imaging Library (MIL); and two on Linux: V4L and FireWire (IEEE1394). To release the structure, use ReleaseCapture. cvCaptureFromFile (view/add comments) Initializes capturing a video from a file. CvCapture* cvCaptureFromFile( const char* filename ); filename Name of the video file. The function cvCaptureFromFile allocates and initializes the CvCapture structure for read- ing the video stream from the specified file. Which codecs and file formats are supported depends on the back end library. On Windows HighGui uses Video for Windows (VfW), on Linux ffmpeg 404 CHAPTER 7. HIGHGUI. HIGH-LEVEL GUI AND MEDIA I/O is used and on Mac OS X the back end is QuickTime. See VideoCodecs for some discussion on what to expect and how to prepare your video files. After the allocated structure is not used any more it should be released by the ReleaseCapture function. cvGetCaptureProperty (view/add comments) Gets video capturing properties. double cvGetCaptureProperty( CvCapture* capture, int property id ); capture video capturing structure. property id Property identifier. Can be one of the following: CV CAP PROP POS MSEC Film current position in milliseconds or video capture timestamp CV CAP PROP POS FRAMES 0-based index of the frame to be decoded/captured next CV CAP PROP POS AVI RATIO Relative position of the video file (0 - start of the film, 1 - end of the film) CV CAP PROP FRAME WIDTH Width of the frames in the video stream CV CAP PROP FRAME HEIGHT Height of the frames in the video stream CV CAP PROP FPS Frame rate CV CAP PROP FOURCC 4-character code of codec CV CAP PROP FRAME COUNT Number of frames in the video file CV CAP PROP FORMAT The format of the Mat objects returned by retrieve() CV CAP PROP MODE A backend-specific value indicating the current capture mode CV CAP PROP BRIGHTNESS Brightness of the image (only for cameras) CV CAP PROP CONTRAST Contrast of the image (only for cameras) CV CAP PROP SATURATION Saturation of the image (only for cameras) CV CAP PROP HUE Hue of the image (only for cameras) CV CAP PROP GAIN Gain of the image (only for cameras) CV CAP PROP EXPOSURE Exposure (only for cameras) CV CAP PROP CONVERT RGB Boolean flags indicating whether images should be converted to RGB 7.2. READING AND WRITING IMAGES AND VIDEO 405 CV CAP PROP WHITE BALANCE Currently unsupported CV CAP PROP RECTIFICATION TOWRITE (note: only supported by DC1394 v 2.x backend currently) The function cvGetCaptureProperty retrieves the specified property of the camera or video file. cvGrabFrame (view/add comments) Grabs the frame from a camera or file. int cvGrabFrame( CvCapture* capture ); capture video capturing structure. The function cvGrabFrame grabs the frame from a camera or file. The grabbed frame is stored internally. The purpose of this function is to grab the frame quickly so that syncronization can occur if it has to read from several cameras simultaneously. The grabbed frames are not exposed because they may be stored in a compressed format (as defined by the camera/driver). To retrieve the grabbed frame, RetrieveFrame should be used. cvQueryFrame (view/add comments) Grabs and returns a frame from a camera or file. IplImage* cvQueryFrame( CvCapture* capture ); capture video capturing structure. The function cvQueryFrame grabs a frame from a camera or video file, decompresses it and returns it. This function is just a combination of GrabFrame and RetrieveFrame , but in one call. The returned image should not be released or modified by the user. In the event of an error, the return value may be NULL. 406 CHAPTER 7. HIGHGUI. HIGH-LEVEL GUI AND MEDIA I/O cvReleaseCapture (view/add comments) Releases the CvCapture structure. void cvReleaseCapture( CvCapture** capture ); capture Pointer to video the capturing structure. The function cvReleaseCapture releases the CvCapture structure allocated by Capture- FromFile or CaptureFromCAM. cvRetrieveFrame (view/add comments) Gets the image grabbed with cvGrabFrame. IplImage* cvRetrieveFrame( CvCapture* capture ); capture video capturing structure. The function cvRetrieveFrame returns the pointer to the image grabbed with the GrabFrame function. The returned image should not be released or modified by the user. In the event of an error, the return value may be NULL. cvSetCaptureProperty (view/add comments) Sets video capturing properties. int cvSetCaptureProperty( CvCapture* capture, int property id, double value ); 7.2. READING AND WRITING IMAGES AND VIDEO 407 capture video capturing structure. property id property identifier. Can be one of the following: CV CAP PROP POS MSEC Film current position in milliseconds or video capture timestamp CV CAP PROP POS FRAMES 0-based index of the frame to be decoded/captured next CV CAP PROP POS AVI RATIO Relative position of the video file (0 - start of the film, 1 - end of the film) CV CAP PROP FRAME WIDTH Width of the frames in the video stream CV CAP PROP FRAME HEIGHT Height of the frames in the video stream CV CAP PROP FPS Frame rate CV CAP PROP FOURCC 4-character code of codec CV CAP PROP FRAME COUNT Number of frames in the video file CV CAP PROP FORMAT The format of the Mat objects returned by retrieve() CV CAP PROP MODE A backend-specific value indicating the current capture mode CV CAP PROP BRIGHTNESS Brightness of the image (only for cameras) CV CAP PROP CONTRAST Contrast of the image (only for cameras) CV CAP PROP SATURATION Saturation of the image (only for cameras) CV CAP PROP HUE Hue of the image (only for cameras) CV CAP PROP GAIN Gain of the image (only for cameras) CV CAP PROP EXPOSURE Exposure (only for cameras) CV CAP PROP CONVERT RGB Boolean flags indicating whether images should be converted to RGB CV CAP PROP WHITE BALANCE Currently unsupported CV CAP PROP RECTIFICATION TOWRITE (note: only supported by DC1394 v 2.x backend currently) value value of the property. The function cvSetCaptureProperty sets the specified property of video capturing. Cur- rently the function supports only video files: CV CAP PROP POS MSEC, CV CAP PROP POS FRAMES, CV CAP PROP POS AVI RATIO. NB This function currently does nothing when using the latest CVS download on linux with FFMPEG (the function contents are hidden if 0 is used and returned). 408 CHAPTER 7. HIGHGUI. HIGH-LEVEL GUI AND MEDIA I/O cvCreateVideoWriter (view/add comments) Creates the video file writer. typedef struct CvVideoWriter CvVideoWriter; CvVideoWriter* cvCreateVideoWriter( const char* filename, int fourcc, double fps, CvSize frame size, int is color=1 ); filename Name of the output video file. fourcc 4-character code of codec used to compress the frames. For example, CV FOURCC(’P’,’I’,’M,’1’) is a MPEG-1 codec, CV FOURCC(’M’,’J’,’P’,’G’) is a motion-jpeg codec etc. Under Win32 it is possible to pass -1 in order to choose compression method and additional com- pression parameters from dialog. Under Win32 if 0 is passed while using an avi filename it will create a video writer that creates an uncompressed avi file. fps Framerate of the created video stream. frame size Size of the video frames. is color If it is not zero, the encoder will expect and encode color frames, otherwise it will work with grayscale frames (the flag is currently supported on Windows only). The function cvCreateVideoWriter creates the video writer structure. Which codecs and file formats are supported depends on the back end library. On Windows HighGui uses Video for Windows (VfW), on Linux ffmpeg is used and on Mac OS X the back end is QuickTime. See VideoCodecs for some discussion on what to expect. cvReleaseVideoWriter (view/add comments) Releases the AVI writer. void cvReleaseVideoWriter( CvVideoWriter** writer ); 7.2. READING AND WRITING IMAGES AND VIDEO 409 writer Pointer to the video file writer structure. The function cvReleaseVideoWriter finishes writing to the video file and releases the struc- ture. cvWriteFrame (view/add comments) Writes a frame to a video file. int cvWriteFrame( CvVideoWriter* writer, const IplImage* image ); writer Video writer structure image The written frame The function cvWriteFrame writes/appends one frame to a video file. 410 CHAPTER 7. HIGHGUI. HIGH-LEVEL GUI AND MEDIA I/O 7.3 Qt new functions This figure explains the new functionalities implemented with Qt GUI. As we can see, the new GUI provides a statusbar, a toolbar, and a control panel. The control panel can have trackbars and buttonbars attached to it. • To attach a trackbar, the window name parameter must be NULL. • To attach a buttonbar, a button must be created. If the last bar attached to the control panel is a buttonbar, the new button is added on the right of the last button. If the last bar attached to the control panel is a trackbar, or the control panel is empty, a new buttonbar is created. Then a new button is attached to it. The following code is an example used to generate the figure. int main(int argc, char *argv[]) int value = 50; int value2 = 0; 7.3. QT NEW FUNCTIONS 411 cvNamedWindow("main1",CV_WINDOW_NORMAL); cvNamedWindow("main2",CV_WINDOW_AUTOSIZE | CV_GUI_NORMAL); cvCreateTrackbar( "track1", "main1", &value, 255, NULL);//OK tested char* nameb1 = "button1"; char* nameb2 = "button2"; cvCreateButton(nameb1,callbackButton,nameb1,CV_CHECKBOX,1); cvCreateButton(nameb2,callbackButton,nameb2,CV_CHECKBOX,0); cvCreateTrackbar( "track2", NULL, &value2, 255, NULL); cvCreateButton("button5",callbackButton1,NULL,CV_RADIOBOX,0); cvCreateButton("button6",callbackButton2,NULL,CV_RADIOBOX,1); cvSetMouseCallback( "main2",on_mouse,NULL ); IplImage* img1 = cvLoadImage("files/flower.jpg"); IplImage* img2 = cvCreateImage(cvGetSize(img1),8,3); CvCapture* video = cvCaptureFromFile("files/hockey.avi"); IplImage* img3 = cvCreateImage(cvGetSize(cvQueryFrame(video)),8,3); while(cvWaitKey(33) != 27) { cvAddS(img1,cvScalarAll(value),img2); cvAddS(cvQueryFrame(video),cvScalarAll(value2),img3); cvShowImage("main1",img2); cvShowImage("main2",img3); } cvDestroyAllWindows(); cvReleaseImage(&img1); cvReleaseImage(&img2); cvReleaseImage(&img3); cvReleaseCapture(&video); return 0; } cvSetWindowProperty (view/add comments) Change the parameters of the window dynamically. void cvSetWindowProperty(const char* name, int prop id, double prop value); 412 CHAPTER 7. HIGHGUI. HIGH-LEVEL GUI AND MEDIA I/O name Name of the window. prop id Window’s property to edit. The operation flags: CV WND PROP FULLSCREEN Change if the window is fullscreen (CV WINDOW NORMAL or CV WINDOW FULLSCREEN). CV WND PROP AUTOSIZE Change if the user can resize the window (textttCV WINDOW NORMAL or CV WINDOW AUTOSIZE). CV WND PROP ASPECTRATIO Change if the image’s aspect ratio is preserved (textttCV WINDOW FREERATIO or CV WINDOW KEEPRATIO). prop value New value of the Window’s property. The operation flags: CV WINDOW NORMAL Change the window in normal size, or allows the user to resize the window. CV WINDOW AUTOSIZE The user cannot resize the window, the size is constrainted by the image displayed. CV WINDOW FULLSCREEN Change the window to fullscreen. CV WINDOW FREERATIO The image expends as much as it can (no ratio constraint) CV WINDOW KEEPRATIO The ration image is respected. The function cvSetWindowProperty allows to change the window’s properties. cvGetWindowProperty (view/add comments) Get the parameters of the window. void cvGetWindowProperty(const char* name, int prop id); name Name of the window. prop id Window’s property to retrive. The operation flags: CV WND PROP FULLSCREEN Change if the window is fullscreen (CV WINDOW NORMAL or CV WINDOW FULLSCREEN). 7.3. QT NEW FUNCTIONS 413 CV WND PROP AUTOSIZE Change if the user can resize the window (textttCV WINDOW NORMAL or CV WINDOW AUTOSIZE). CV WND PROP ASPECTRATIO Change if the image’s aspect ratio is preserved (textttCV WINDOW FREERATIO or CV WINDOW KEEPRATIO). See SetWindowProperty to know the meaning of the returned values. The function cvGetWindowProperty return window’s properties. cvFontQt (view/add comments) Create the font to be used to draw text on an image (with addText). CvFont cvFontQt(const char* nameFont, int pointSize = -1, CvScalar color = cvScalarAll(0), int weight = CV FONT NORMAL, int style = CV STYLE NORMAL, int spacing = 0); nameFont Name of the font. The name should match the name of a system font (such as “Times”). If the font is not found, a default one will be used. pointSize Size of the font. If not specified, equal zero or negative, the point size of the font is set to a system-dependent default value. Generally, this is 12 points. color Color of the font in BGRA – A = 255 is fully transparent. Use the macro CV RGB for simplicity. weight The operation flags: CV FONT LIGHT Weight of 25 CV FONT NORMAL Weight of 50 CV FONT DEMIBOLD Weight of 63 CV FONT BOLD Weight of 75 CV FONT BLACK Weight of 87 You can also specify a positive integer for more control. style The operation flags: CV STYLE NORMAL Font is normal CV STYLE ITALIC Font is in italic 414 CHAPTER 7. HIGHGUI. HIGH-LEVEL GUI AND MEDIA I/O CV STYLE OBLIQUE Font is oblique spacing Spacing between characters. Can be negative or positive The function cvFontQt creates a CvFont object to be used with addText . This CvFont is not compatible with cvPutText. A basic usage of this function is: CvFont font = cvFontQt(’’Times’’); cvAddText( img1, ‘‘Hello World !’’, cvPoint(50,50), font); cvAddText (view/add comments) Create the font to be used to draw text on an image void cvAddText(const CvArr* img, const char* text, CvPoint location, CvFont *font); img Image where the text should be drawn text Text to write on the image location Point(x,y) where the text should start on the image font Font to use to draw the text The function cvAddText draw text on the image img using a specific font font (see example FontQt) cvDisplayOverlay (view/add comments) Display text on the window’s image as an overlay for delay milliseconds. This is not editing the image’s data. The text is display on the top of the image. void cvDisplayOverlay(const char* name, const char* text, int delay); 7.3. QT NEW FUNCTIONS 415 name Name of the window text Overlay text to write on the window’s image delay Delay to display the overlay text. If this function is called before the previous overlay text time out, the timer is restarted and the text updated. . If this value is zero, the text never disapers. The function cvDisplayOverlay aims at displaying useful information/tips on the window for a certain amount of time delay. This information is display on the top of the window. cvDisplayStatusBar (view/add comments) Display text on the window’s statusbar as for delay milliseconds. void cvDisplayStatusBar(const char* name, const char* text, int delayms); name Name of the window text Text to write on the window’s statusbar delay Delay to display the text. If this function is called before the previous text time out, the timer is restarted and the text updated. If this value is zero, the text never disapers. The function cvDisplayOverlay aims at displaying useful information/tips on the window for a certain amount of time delay. This information is displayed on the window’s statubar (the window must be created with CV GUI EXPANDED flags). cvCreateOpenGLCallback (view/add comments) Create a callback function called to draw OpenGL on top the the image display by window name. void cvCreateOpenGLCallback( const char* window name, CvOpenGLCallback callbackOpenGL, void* userdata CV DEFAULT(NULL), double angle CV DEFAULT(-1), double zmin CV DEFAULT(-1), double zmax CV DEFAULT(-1); 416 CHAPTER 7. HIGHGUI. HIGH-LEVEL GUI AND MEDIA I/O window name Name of the window callbackOpenGL Pointer to the function to be called every frame. This function should be pro- totyped as void Foo(*void);. userdata pointer passed to the callback function. (Optional) angle Specifies the field of view angle, in degrees, in the y direction.. (Optional - Default 45 degree) zmin Specifies the distance from the viewer to the near clipping plane (always positive). (Optional - Default 0.01) zmax Specifies the distance from the viewer to the far clipping plane (always positive). (Optional - Default 1000) The function cvCreateOpenGLCallback can be used to draw 3D data on the window. An example of callback could be: void on_opengl(void* param) { //draw scene here glLoadIdentity(); glTranslated(0.0, 0.0, -1.0); glRotatef( 55, 1, 0, 0 ); glRotatef( 45, 0, 1, 0 ); glRotatef( 0, 0, 0, 1 ); static const int coords[6][4][3] = { { { +1, -1, -1 }, { -1, -1, -1 }, { -1, +1, -1 }, { +1, +1, -1 } }, { { +1, +1, -1 }, { -1, +1, -1 }, { -1, +1, +1 }, { +1, +1, +1 } }, { { +1, -1, +1 }, { +1, -1, -1 }, { +1, +1, -1 }, { +1, +1, +1 } }, { { -1, -1, -1 }, { -1, -1, +1 }, { -1, +1, +1 }, { -1, +1, -1 } }, { { +1, -1, +1 }, { -1, -1, +1 }, { -1, -1, -1 }, { +1, -1, -1 } }, { { -1, -1, +1 }, { +1, -1, +1 }, { +1, +1, +1 }, { -1, +1, +1 } } }; for (int i = 0; i < 6; ++i) { glColor3ub( i*20, 100+i*10, i*42 ); glBegin(GL_QUADS); for (int j = 0; j < 4; ++j) { glVertex3d(0.2 * coords[i][j][0], 0.2 * coords[i][j][1], 0.2 * coords[i][j][2]); } 7.3. QT NEW FUNCTIONS 417 glEnd(); } } CV_EXTERN_C_FUNCPTR( *CvOpenGLCallback)(void* userdata)); cvSaveWindowParameters (view/add comments) Save parameters of the window window name. void cvSaveWindowParameters(const char* name); name Name of the window The function cvSaveWindowParameters saves size, location, flags, trackbars’ value, zoom and panning location of the window window name cvLoadWindowParameters (view/add comments) Load parameters of the window window name. void cvLoadWindowParameters(const char* name); name Name of the window The function cvLoadWindowParameters load size, location, flags, trackbars’ value, zoom and panning location of the window window name cvCreateButton (view/add comments) Create a callback function called to draw OpenGL on top the the image display by window name. 418 CHAPTER 7. HIGHGUI. HIGH-LEVEL GUI AND MEDIA I/O cvCreateButton( const char* button name CV DEFAULT(NULL),CvButtonCallback on change CV DEFAULT(NULL), void* userdata CV DEFAULT(NULL) , int button type CV DEFAULT(CV PUSH BUTTON), int initial button state CV DEFAULT(0); button name Name of the button ( if NULL, the name will be ”button ¡number of boutton¿”) on change Pointer to the function to be called every time the button changed its state. This function should be prototyped as void Foo(int state,*void);. state is the current state of the button. It could be -1 for a push button, 0 or 1 for a check/radio box button. userdata pointer passed to the callback function. (Optional) The button type parameter can be : (Optional – Will be a push button by default.) CV PUSH BUTTON The button will be a push button. CV CHECKBOX The button will be a checkbox button. CV RADIOBOX The button will be a radiobox button. The radiobox on the same buttonbar (same line) are exclusive; one on can be select at the time. initial button state Default state of the button. Use for checkbox and radiobox, its value could be 0 or 1. (Optional) The function cvCreateButton attach button to the control panel. Each button is added to a buttonbar on the right of the last button. A new buttonbar is create if nothing was attached to the control panel before, or if the last element attached to the control panel was a trackbar. Here are various example of cvCreateButton function call: cvCreateButton(NULL,callbackButton);//create a push button "button 0", that will call callbackButton. cvCreateButton("button2",callbackButton,NULL,CV\_CHECKBOX,0); cvCreateButton("button3",callbackButton,&value); cvCreateButton("button5",callbackButton1,NULL,CV\_RADIOBOX); cvCreateButton("button6",callbackButton2,NULL,CV\_PUSH\_BUTTON,1); CV_EXTERN_C_FUNCPTR( *CvButtonCallback)(int state, void* userdata)); Chapter 8 calib3d. Camera Calibration, Pose Estimation and Stereo 8.1 Camera Calibration and 3d Reconstruction The functions in this section use the so-called pinhole camera model. That is, a scene view is formed by projecting 3D points into the image plane using a perspective transformation. s m0 = A[R|t]M0 or s   u v 1   =   fx 0 cx 0 fy cy 0 0 1     r11 r12 r13 t1 r21 r22 r23 t2 r31 r32 r33 t3     X Y Z 1   Where (X,Y,Z) are the coordinates of a 3D point in the world coordinate space, (u, v) are the coordinates of the projection point in pixels. A is called a camera matrix, or a matrix of intrinsic parameters. (cx, cy) is a principal point (that is usually at the image center), and fx, fy are the focal lengths expressed in pixel-related units. Thus, if an image from camera is scaled by some factor, all of these parameters should be scaled (multiplied/divided, respectively) by the same factor. The matrix of intrinsic parameters does not depend on the scene viewed and, once estimated, can be re-used (as long as the focal length is fixed (in case of zoom lens)). The joint rotation-translation matrix [R|t] is called a matrix of extrinsic parameters. It is used to describe the camera motion around a static scene, or vice versa, rigid motion of an object in front of still camera. That is, [R|t] translates coordinates of a point (X,Y,Z) to some coordinate system, fixed with respect to the camera. The transformation above is equivalent to the following (when z 6= 0): 419 420 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO   x y z   = R   X Y Z   + t x0 = x/z y0 = y/z u = fx ∗ x0 + cx v = fy ∗ y0 + cy Real lenses usually have some distortion, mostly radial distortion and slight tangential distor- tion. So, the above model is extended as:   x y z   = R   X Y Z   + t x0 = x/z y0 = y/z x00 = x0 1+k1r2+k2r4+k3r6 1+k4r2+k5r4+k6r6 + 2p1x0y0 + p2(r2 + 2x02) y00 = y0 1+k1r2+k2r4+k3r6 1+k4r2+k5r4+k6r6 + p1(r2 + 2y02) + 2p2x0y0 where r2 = x02 + y02 u = fx ∗ x00 + cx v = fy ∗ y00 + cy k1, k2, k3, k4, k5, k6 are radial distortion coefficients, p1, p2 are tangential distortion coefficients. Higher-order coefficients are not considered in OpenCV. In the functions below the coefficients are passed or returned as (k1, k2, p1, p2[, k3[, k4, k5, k6]]) vector. That is, if the vector contains 4 elements, it means that k3 = 0. The distortion coefficients do not depend on the scene viewed, thus they also belong to the intrinsic camera parameters. And they remain the same regardless of the captured image resolution. That is, if, for example, a camera has been calibrated on images of 320 × 240 resolution, absolutely the same distortion coefficients can be used for images of 640 × 480 resolution from the same camera (while fx, fy, cx and cy need to be scaled appropriately). The functions below use the above model to • Project 3D points to the image plane given intrinsic and extrinsic parameters • Compute extrinsic parameters given intrinsic parameters, a few 3D points and their projec- tions. • Estimate intrinsic and extrinsic camera parameters from several views of a known calibration pattern (i.e. every view is described by several 3D-2D point correspondences). 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 421 • Estimate the relative position and orientation of the stereo camera ”heads” and compute the rectification transformation that makes the camera optical axes parallel. cvCalcImageHomography (view/add comments) Calculates the homography matrix for an oblong planar object (e.g. arm). void cvCalcImageHomography( float* line, CvPoint3D32f* center, float* intrinsic, float* homography ); line the main object axis direction (vector (dx,dy,dz)) center object center ((cx,cy,cz)) intrinsic intrinsic camera parameters (3x3 matrix) homography output homography matrix (3x3) The function calculates the homography matrix for the initial image transformation from image plane to the plane, defined by a 3D oblong object line (See Figure 6-10 in the OpenCV Guide 3D Reconstruction Chapter). cvCalibrateCamera2 (view/add comments) Finds the camera intrinsic and extrinsic parameters from several views of a calibration pattern. double cvCalibrateCamera2( const CvMat* objectPoints, const CvMat* imagePoints, const CvMat* pointCounts, CvSize imageSize, CvMat* cameraMatrix, CvMat* distCoeffs, 422 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO CvMat* rvecs=NULL, CvMat* tvecs=NULL, int flags=0 ); objectPoints The joint matrix of object points - calibration pattern features in the model coordi- nate space. It is floating-point 3xN or Nx3 1-channel, or 1xN or Nx1 3-channel array, where N is the total number of points in all views. imagePoints The joint matrix of object points projections in the camera views. It is floating-point 2xN or Nx2 1-channel, or 1xN or Nx1 2-channel array, where N is the total number of points in all views pointCounts Integer 1xM or Mx1 vector (where M is the number of calibration pattern views) containing the number of points in each particular view. The sum of vector elements must match the size of objectPoints and imagePoints (=N). imageSize Size of the image, used only to initialize the intrinsic camera matrix cameraMatrix The output 3x3 floating-point camera matrix A =   fx 0 cx 0 fy cy 0 0 1  . If CV CALIB USE INTRINSIC GUESS and/or CV CALIB FIX ASPECT RATIO are specified, some or all of fx, fy, cx, cy must be initialized before calling the function distCoeffs The output vector of distortion coefficients (k1, k2, p1, p2[, k3[, k4, k5, k6]]) of 4, 5 or 8 elements rvecs The output 3xM or Mx3 1-channel, or 1xM or Mx1 3-channel array of rotation vectors (see cvRodrigues2), estimated for each pattern view. That is, each k-th rotation vector to- gether with the corresponding k-th translation vector (see the next output parameter descrip- tion) brings the calibration pattern from the model coordinate space (in which object points are specified) to the world coordinate space, i.e. real position of the calibration pattern in the k-th pattern view (k=0..M-1) tvecs The output 3xM or Mx3 1-channel, or 1xM or Mx1 3-channel array of translation vectors, estimated for each pattern view. flags Different flags, may be 0 or combination of the following values: CV CALIB USE INTRINSIC GUESS cameraMatrix contains the valid initial values of fx, fy, cx, cy that are optimized further. Otherwise, (cx, cy) is initially set to the 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 423 image center (imageSize is used here), and focal distances are computed in some least-squares fashion. Note, that if intrinsic parameters are known, there is no need to use this function just to estimate the extrinsic parameters. Use cvFindExtrinsicCamer- aParams2 instead. CV CALIB FIX PRINCIPAL POINT The principal point is not changed during the global op- timization, it stays at the center or at the other location specified when CV CALIB USE INTRINSIC GUESS is set too. CV CALIB FIX ASPECT RATIO The functions considers only fy as a free parameter, the ratio fx/fy stays the same as in the input cameraMatrix. When CV CALIB USE INTRINSIC GUESS is not set, the actual input values of fx and fy are ignored, only their ratio is computed and used further. CV CALIB ZERO TANGENT DIST Tangential distortion coefficients (p1, p2) will be set to ze- ros and stay zero. CV CALIB FIX K1,...,CV CALIB FIX K6 Do not change the corresponding radial distor- tion coefficient during the optimization. If CV CALIB USE INTRINSIC GUESS is set, the coefficient from the supplied distCoeffs matrix is used, otherwise it is set to 0. CV CALIB RATIONAL MODEL Enable coefficients k4, k5 and k6. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the rational model and return 8 coefficients. If the flag is not set, the function will compute only 5 distortion coefficients. The function estimates the intrinsic camera parameters and extrinsic parameters for each of the views. The coordinates of 3D object points and their correspondent 2D projections in each view must be specified. That may be achieved by using an object with known geometry and easily de- tectable feature points. Such an object is called a calibration rig or calibration pattern, and OpenCV has built-in support for a chessboard as a calibration rig (see cvFindChessboardCorners). Cur- rently, initialization of intrinsic parameters (when CV CALIB USE INTRINSIC GUESS is not set) is only implemented for planar calibration patterns (where z-coordinates of the object points must be all 0’s). 3D calibration rigs can also be used as long as initial cameraMatrix is provided. The algorithm does the following: 1. First, it computes the initial intrinsic parameters (the option only available for planar calibra- tion patterns) or reads them from the input parameters. The distortion coefficients are all set to zeros initially (unless some of CV CALIB FIX K? are specified). 2. The initial camera pose is estimated as if the intrinsic parameters have been already known. This is done using cvFindExtrinsicCameraParams2 3. After that the global Levenberg-Marquardt optimization algorithm is run to minimize the re- projection error, i.e. the total sum of squared distances between the observed feature points 424 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO imagePoints and the projected (using the current estimates for camera parameters and the poses) object points objectPoints; see cvProjectPoints2. The function returns the final re-projection error. Note: if you’re using a non-square (=non-NxN) grid and cv for calibration, and calibrateCamera returns bad values (i.e. zero distortion coefficients, an image center very far from (w/2−0.5, h/2− 0.5), and / or large differences between fx and fy (ratios of 10:1 or more)), then you’ve probably used patternSize=cvSize(rows,cols), but should use patternSize=cvSize(cols,rows) in cvFindChessboardCorners. See also: cvFindChessboardCorners, cvFindExtrinsicCameraParams2, cv, cvStereoCali- brate, cvUndistort2 cvComputeCorrespondEpilines (view/add comments) For points in one image of a stereo pair, computes the corresponding epilines in the other image. void cvComputeCorrespondEpilines( const CvMat* points, int whichImage, const CvMat* F, CvMat* lines); points The input points. 2xN, Nx2, 3xN or Nx3 array (where N number of points). Multi- channel 1xN or Nx1 array is also acceptable whichImage Index of the image (1 or 2) that contains the points F The fundamental matrix that can be estimated using cvFindFundamentalMat or cvStereoRec- tify. lines The output epilines, a 3xN or Nx3 array. Each line ax + by + c = 0 is encoded by 3 numbers (a, b, c) For every point in one of the two images of a stereo-pair the function finds the equation of the corresponding epipolar line in the other image. From the fundamental matrix definition (see cvFindFundamentalMat), line l(2) i in the second image for the point p(1) i in the first image (i.e. when whichImage=1) is computed as: l(2) i = F p(1) i 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 425 and, vice versa, when whichImage=2, l(1) i is computed from p(2) i as: l(1) i = FT p(2) i Line coefficients are defined up to a scale. They are normalized, such that a2 i + b2 i = 1. cvConvertPointsHomogeneous (view/add comments) Convert points to/from homogeneous coordinates. void cvConvertPointsHomogeneous( const CvMat* src, CvMat* dst ); src The input point array, 2xN, Nx2, 3xN, Nx3, 4xN or Nx4 (where N is the number of points). Multi-channel 1xN or Nx1 array is also acceptable dst The output point array, must contain the same number of points as the input; The dimension- ality must be the same, 1 less or 1 more than the input, and also within 2 to 4 The function converts 2D or 3D points from/to homogeneous coordinates, or simply copies or transposes the array. If the input array dimensionality is larger than the output, each coordinate is divided by the last coordinate: (x, y[, z], w)− > (x0, y0[, z0]) where x0 = x/w y0 = y/w z0 = z/w (if output is 3D) If the output array dimensionality is larger, an extra 1 is appended to each point. Otherwise, the input array is simply copied (with optional transposition) to the output. Note because the function accepts a large variety of array layouts, it may report an error when input/output array dimensionality is ambiguous. It is always safe to use the function with number of points N ≥ 5, or to use multi-channel Nx1 or 1xN arrays. 426 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO cvCreatePOSITObject (view/add comments) Initializes a structure containing object information. CvPOSITObject* cvCreatePOSITObject( CvPoint3D32f* points, int point count ); points Pointer to the points of the 3D object model point count Number of object points The function allocates memory for the object structure and computes the object inverse matrix. The preprocessed object data is stored in the structure cvCvPOSITObject, internal for OpenCV, which means that the user cannot directly access the structure data. The user may only create this structure and pass its pointer to the function. An object is defined as a set of points given in a coordinate system. The function cvPOSIT computes a vector that begins at a camera-related coordinate system center and ends at the points[0] of the object. Once the work with a given object is finished, the function cvReleasePOSITObject must be called to free memory. cvCreateStereoBMState (view/add comments) Creates block matching stereo correspondence structure. CvStereoBMState* cvCreateStereoBMState( int preset=CV STEREO BM BASIC, int numberOfDisparities=0 ); preset ID of one of the pre-defined parameter sets. Any of the parameters can be overridden after creating the structure. Values are CV STEREO BM BASIC Parameters suitable for general cameras CV STEREO BM FISH EYE Parameters suitable for wide-angle cameras CV STEREO BM NARROW Parameters suitable for narrow-angle cameras 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 427 numberOfDisparities The number of disparities. If the parameter is 0, it is taken from the preset, otherwise the supplied value overrides the one from preset. The function creates the stereo correspondence structure and initializes it. It is possible to override any of the parameters at any time between the calls to cvFindStereoCorrespondenceBM. cvCreateStereoGCState (view/add comments) Creates the state of graph cut-based stereo correspondence algorithm. CvStereoGCState* cvCreateStereoGCState( int numberOfDisparities, int maxIters ); numberOfDisparities The number of disparities. The disparity search range will be state->minDisparity ≤ disparity < state->minDisparity + state->numberOfDisparities maxIters Maximum number of iterations. On each iteration all possible (or reasonable) alpha- expansions are tried. The algorithm may terminate earlier if it could not find an alpha- expansion that decreases the overall cost function value. See [13] for details. The function creates the stereo correspondence structure and initializes it. It is possible to override any of the parameters at any time between the calls to cvFindStereoCorrespondenceGC. CvStereoBMState (view/add comments) The structure for block matching stereo correspondence algorithm. typedef struct CvStereoBMState { //pre filters (normalize input images): int preFilterType; // 0 for now int preFilterSize; // ˜5x5..21x21 int preFilterCap; // up to ˜31 //correspondence using Sum of Absolute Difference (SAD): int SADWindowSize; // Could be 5x5..21x21 int minDisparity; // minimum disparity (=0) int numberOfDisparities; // maximum disparity - minimum disparity //post filters (knock out bad matches): int textureThreshold; // areas with no texture are ignored int uniquenessRatio;// invalidate disparity at pixels where there are other close matches 428 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO // with different disparity int speckleWindowSize; // the maximum area of speckles to remove // (set to 0 to disable speckle filtering) int speckleRange; // acceptable range of disparity variation in each connected component int trySmallerWindows; // not used CvRect roi1, roi2; // clipping ROIs int disp12MaxDiff; // maximum allowed disparity difference in the left-right check // internal data ... } CvStereoBMState; preFilterType type of the prefilter, CV STEREO BM NORMALIZED RESPONSE or the default and the recommended CV STEREO BM XSOBEL, int preFilterSize 5x5..21x21, int preFilterCap up to 31, int SADWindowSize Could be 5x5..21x21 or higher, but with 21x21 or smaller windows the process- ing speed is much higher, int minDisparity minimum disparity (=0), int numberOfDisparities maximum disparity - minimum disparity, int textureThreshold the textureness threshold. That is, if the sum of absolute values of x- derivatives computed over SADWindowSize by SADWindowSize pixel neighborhood is smaller than the parameter, no disparity is computed at the pixel, int uniquenessRatio the minimum margin in percents between the best (minimum) cost function value and the second best value to accept the computed disparity, int speckleWindowSize the maximum area of speckles to remove (set to 0 to disable speckle filtering), int speckleRange acceptable range of disparity variation in each connected component, int trySmallerWindows not used currently (0), int 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 429 roi1, roi2 These are the clipping ROIs for the left and the right images. The function cvStere- oRectify returns the largest rectangles in the left and right images where after the rectification all the pixels are valid. If you copy those rectangles to the CvStereoBMState structure, the stereo correspondence function will automatically clear out the pixels outside of the ”valid” disparity rectangle computed by cvGetValidDisparityROI. Thus you will get more ”invalid disparity” pixels than usual, but the remaining pixels are more probable to be valid. disp12MaxDiff The maximum allowed difference between the explicitly computed left-to-right disparity map and the implicitly (by cvValidateDisparity) computed right-to-left disparity. If for some pixel the difference is larger than the specified threshold, the disparity at the pixel is invalidated. By default this parameter is set to (-1), which means that the left-right check is not performed. The block matching stereo correspondence algorithm, by Kurt Konolige, is very fast single- pass stereo matching algorithm that uses sliding sums of absolute differences between pixels in the left image and the pixels in the right image, shifted by some varying amount of pixels (from minDisparity to minDisparity+numberOfDisparities). On a pair of images WxH the al- gorithm computes disparity in O(W*H*numberOfDisparities) time. In order to improve quality and readability of the disparity map, the algorithm includes pre-filtering and post-filtering proce- dures. Note that the algorithm searches for the corresponding blocks in x direction only. It means that the supplied stereo pair should be rectified. Vertical stereo layout is not directly supported, but in such a case the images could be transposed by user. CvStereoGCState (view/add comments) The structure for graph cuts-based stereo correspondence algorithm typedef struct CvStereoGCState { int Ithreshold; // threshold for piece-wise linear data cost function (5 by default) int interactionRadius; // radius for smoothness cost function (1 by default; means Potts model) float K, lambda, lambda1, lambda2; // parameters for the cost function // (usually computed adaptively from the input data) int occlusionCost; // 10000 by default int minDisparity; // 0 by default; see CvStereoBMState int numberOfDisparities; // defined by user; see CvStereoBMState int maxIters; // number of iterations; defined by user. // internal buffers CvMat* left; CvMat* right; 430 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO CvMat* dispLeft; CvMat* dispRight; CvMat* ptrLeft; CvMat* ptrRight; CvMat* vtxBuf; CvMat* edgeBuf; } CvStereoGCState; The graph cuts stereo correspondence algorithm, described in [13] (as KZ1), is non-realtime stereo correspondence algorithm that usually gives very accurate depth map with well-defined object boundaries. The algorithm represents stereo problem as a sequence of binary optimization problems, each of those is solved using maximum graph flow algorithm. The state structure above should not be allocated and initialized manually; instead, use cvCreateStereoGCState and then override necessary parameters if needed. cvDecomposeProjectionMatrix (view/add comments) Decomposes the projection matrix into a rotation matrix and a camera matrix. void cvDecomposeProjectionMatrix( const CvMat *projMatrix, CvMat *cameraMatrix, CvMat *rotMatrix, CvMat *transVect, CvMat *rotMatrX=NULL, CvMat *rotMatrY=NULL, CvMat *rotMatrZ=NULL, CvPoint3D64f *eulerAngles=NULL); projMatrix The 3x4 input projection matrix P cameraMatrix The output 3x3 camera matrix K rotMatrix The output 3x3 external rotation matrix R transVect The output 4x1 translation vector T rotMatrX Optional 3x3 rotation matrix around x-axis 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 431 rotMatrY Optional 3x3 rotation matrix around y-axis rotMatrZ Optional 3x3 rotation matrix around z-axis eulerAngles Optional 3 points containing the three Euler angles of rotation The function computes a decomposition of a projection matrix into a calibration and a rotation matrix and the position of the camera. It optionally returns three rotation matrices, one for each axis, and the three Euler angles that could be used in OpenGL. The function is based on cvRQDecomp3x3. cvDrawChessboardCorners (view/add comments) Renders the detected chessboard corners. void cvDrawChessboardCorners( CvArr* image, CvSize patternSize, CvPoint2D32f* corners, int count, int patternWasFound ); image The destination image; it must be an 8-bit color image patternSize The number of inner corners per chessboard row and column. (patternSize = cv::Size(points per row,points per column) = cv::Size(rows,columns) ) corners The array of corners detected, this should be the output from findChessboardCorners wrapped in a cv::Mat(). count The number of corners patternWasFound Indicates whether the complete board was found (6= 0) or not (= 0) . One may just pass the return value cvFindChessboardCornersfindChessboardCorners here The function draws the individual chessboard corners detected as red circles if the board was not found or as colored corners connected with lines if the board was found. 432 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO cvFindChessboardCorners (view/add comments) Finds the positions of the internal corners of the chessboard. int cvFindChessboardCorners( const void* image, CvSize patternSize, CvPoint2D32f* corners, int* cornerCount=NULL, int flags=CV CALIB CB ADAPTIVE THRESH ); image Source chessboard view; it must be an 8-bit grayscale or color image patternSize The number of inner corners per chessboard row and column ( patternSize = cvSize(points per row,points per colum) = cvSize(columns,rows) ) corners The output array of corners detected cornerCount The output corner counter. If it is not NULL, it stores the number of corners found flags Various operation flags, can be 0 or a combination of the following values: CV CALIB CB ADAPTIVE THRESH use adaptive thresholding to convert the image to black and white, rather than a fixed threshold level (computed from the average image bright- ness). CV CALIB CB NORMALIZE IMAGE normalize the image gamma with cvEqualizeHist before applying fixed or adaptive thresholding. CV CALIB CB FILTER QUADS use additional criteria (like contour area, perimeter, square- like shape) to filter out false quads that are extracted at the contour retrieval stage. CALIB CB FAST CHECK Runs a fast check on the image that looks for chessboard corners, and shortcuts the call if none are found. This can drastically speed up the call in the degenerate condition when no chessboard is observed. The function attempts to determine whether the input image is a view of the chessboard pattern and locate the internal chessboard corners. The function returns a non-zero value if all of the corners have been found and they have been placed in a certain order (row by row, left to right in every row), otherwise, if the function fails to find all the corners or reorder them, it returns 0. For example, a regular chessboard has 8 x 8 squares and 7 x 7 internal corners, that is, points, where 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 433 the black squares touch each other. The coordinates detected are approximate, and to determine their position more accurately, the user may use the function cvFindCornerSubPix. Sample usage of detecting and drawing chessboard corners: Size patternsize(8,6); //interior number of corners Mat gray = ....; //source image vector corners; //this will be filled by the detected corners //CALIB_CB_FAST_CHECK saves a lot of time on images //that don’t contain any chessboard corners bool patternfound = findChessboardCorners(gray, patternsize, corners, CALIB_CB_ADAPTIVE_THRESH + CALIB_CB_NORMALIZE_IMAGE + CALIB_CB_FAST_CHECK); if(patternfound) cornerSubPix(gray, corners, Size(11, 11), Size(-1, -1), TermCriteria(CV_TERMCRIT_EPS + CV_TERMCRIT_ITER, 30, 0.1)); drawChessboardCorners(img, patternsize, Mat(corners), patternfound); Note: the function requires some white space (like a square-thick border, the wider the better) around the board to make the detection more robust in various environment (otherwise if there is no border and the background is dark, the outer black squares could not be segmented properly and so the square grouping and ordering algorithm will fail). cvFindExtrinsicCameraParams2 (view/add comments) Finds the object pose from the 3D-2D point correspondences void cvFindExtrinsicCameraParams2( const CvMat* objectPoints, const CvMat* imagePoints, const CvMat* cameraMatrix, const CvMat* distCoeffs, CvMat* rvec, CvMat* tvec, int useExtrinsicGuess=0); objectPoints The array of object points in the object coordinate space, 3xN or Nx3 1-channel, or 1xN or Nx1 3-channel, where N is the number of points. 434 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO imagePoints The array of corresponding image points, 2xN or Nx2 1-channel or 1xN or Nx1 2-channel, where N is the number of points. cameraMatrix The input camera matrix A =   fx 0 cx 0 fy cy 0 0 1   distCoeffs The input vector of distortion coefficients (k1, k2, p1, p2[, k3[, k4, k5, k6]]) of 4, 5 or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed. rvec The output rotation vector (see cvRodrigues2) that (together with tvec) brings points from the model coordinate system to the camera coordinate system tvec The output translation vector useExtrinsicGuess If true (1), the function will use the provided rvec and tvec as the initial approximations of the rotation and translation vectors, respectively, and will further optimize them. The function estimates the object pose given a set of object points, their corresponding image projections, as well as the camera matrix and the distortion coefficients. This function finds such a pose that minimizes reprojection error, i.e. the sum of squared distances between the observed projections imagePoints and the projected (using cvProjectPoints2) objectPoints. The function’s counterpart in the C++ API is cv::solvePnP cvFindFundamentalMat (view/add comments) Calculates the fundamental matrix from the corresponding points in two images. int cvFindFundamentalMat( const CvMat* points1, const CvMat* points2, CvMat* fundamentalMatrix, int method=CV FM RANSAC, double param1=1., double param2=0.99, CvMat* status=NULL); 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 435 points1 Array of N points from the first image. It can be 2xN, Nx2, 3xN or Nx3 1-channel array or 1xN or Nx1 2- or 3-channel array . The point coordinates should be floating-point (single or double precision) points2 Array of the second image points of the same size and format as points1 fundamentalMatrix The output fundamental matrix or matrices. The size should be 3x3 or 9x3 (7-point method may return up to 3 matrices) method Method for computing the fundamental matrix CV FM 7POINT for a 7-point algorithm. N = 7 CV FM 8POINT for an 8-point algorithm. N ≥ 8 CV FM RANSAC for the RANSAC algorithm. N ≥ 8 CV FM LMEDS for the LMedS algorithm. N ≥ 8 param1 The parameter is used for RANSAC. It is the maximum distance from point to epipolar line in pixels, beyond which the point is considered an outlier and is not used for computing the final fundamental matrix. It can be set to something like 1-3, depending on the accuracy of the point localization, image resolution and the image noise param2 The parameter is used for RANSAC or LMedS methods only. It specifies the desirable level of confidence (probability) that the estimated matrix is correct status The optional output array of N elements, every element of which is set to 0 for outliers and to 1 for the other points. The array is computed only in RANSAC and LMedS methods. For other methods it is set to all 1’s The epipolar geometry is described by the following equation: [p2; 1]TF[p1; 1] = 0 where F is fundamental matrix, p1 and p2 are corresponding points in the first and the second images, respectively. The function calculates the fundamental matrix using one of four methods listed above and returns the number of fundamental matrices found (1 or 3) and 0, if no matrix is found . Normally just 1 matrix is found, but in the case of 7-point algorithm the function may return up to 3 solutions (9 × 3 matrix that stores all 3 matrices sequentially). The calculated fundamental matrix may be passed further to cvComputeCorrespondEpilines that finds the epipolar lines corresponding to the specified points. It can also be passed to cvStere- oRectifyUncalibrated to compute the rectification transformation. 436 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO int point_count = 100; CvMat* points1; CvMat* points2; CvMat* status; CvMat* fundamental_matrix; points1 = cvCreateMat(1,point_count,CV_32FC2); points2 = cvCreateMat(1,point_count,CV_32FC2); status = cvCreateMat(1,point_count,CV_8UC1); /* Fill the points here ... */ for( i = 0; i < point_count; i++ ) { points1->data.fl[i*2] = ; points1->data.fl[i*2+1] = ; points2->data.fl[i*2] = ; points2->data.fl[i*2+1] = ; } fundamental_matrix = cvCreateMat(3,3,CV_32FC1); int fm_count = cvFindFundamentalMat( points1,points2,fundamental_matrix, CV_FM_RANSAC,1.0,0.99,status ); cvFindHomography (view/add comments) Finds the perspective transformation between two planes. void cvFindHomography( const CvMat* srcPoints, const CvMat* dstPoints, CvMat*H int method=0, double ransacReprojThreshold=3, CvMat* status=NULL); srcPoints Coordinates of the points in the original plane, 2xN, Nx2, 3xN or Nx3 1-channel array (the latter two are for representation in homogeneous coordinates), where N is the number of points. 1xN or Nx1 2- or 3-channel array can also be passed. 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 437 dstPoints Point coordinates in the destination plane, 2xN, Nx2, 3xN or Nx3 1-channel, or 1xN or Nx1 2- or 3-channel array. H The output 3x3 homography matrix method The method used to computed homography matrix; one of the following: 0 a regular method using all the points CV RANSAC RANSAC-based robust method CV LMEDS Least-Median robust method ransacReprojThreshold The maximum allowed reprojection error to treat a point pair as an inlier (used in the RANSAC method only). That is, if kdstPointsi−convertPointsHomogeneous(HsrcPointsi)k > ransacReprojThreshold then the point i is considered an outlier. If srcPoints and dstPoints are measured in pixels, it usually makes sense to set this parameter somewhere in the range 1 to 10. status The optional output mask set by a robust method (CV RANSAC or CV LMEDS). Note that the input mask values are ignored. The function finds the perspective transformation H between the source and the destination planes: si   x0 i y0 i 1   ∼ H   xi yi 1   So that the back-projection error X i  x0 i − h11xi + h12yi + h13 h31xi + h32yi + h33 2 +  y0 i − h21xi + h22yi + h23 h31xi + h32yi + h33 2 is minimized. If the parameter method is set to the default value 0, the function uses all the point pairs to compute the initial homography estimate with a simple least-squares scheme. However, if not all of the point pairs (srcP ointsi, dstP ointsi) fit the rigid perspective transfor- mation (i.e. there are some outliers), this initial estimate will be poor. In this case one can use one of the 2 robust methods. Both methods, RANSAC and LMeDS, try many different random sub- sets of the corresponding point pairs (of 4 pairs each), estimate the homography matrix using this subset and a simple least-square algorithm and then compute the quality/goodness of the com- puted homography (which is the number of inliers for RANSAC or the median re-projection error 438 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO for LMeDs). The best subset is then used to produce the initial estimate of the homography matrix and the mask of inliers/outliers. Regardless of the method, robust or not, the computed homography matrix is refined further (using inliers only in the case of a robust method) with the Levenberg-Marquardt method in order to reduce the re-projection error even more. The method RANSAC can handle practically any ratio of outliers, but it needs the threshold to distinguish inliers from outliers. The method LMeDS does not need any threshold, but it works correctly only when there are more than 50% of inliers. Finally, if you are sure in the computed features, where can be only some small noise present, but no outliers, the default method could be the best choice. The function is used to find initial intrinsic and extrinsic matrices. Homography matrix is deter- mined up to a scale, thus it is normalized so that h33 = 1. See also: cvGetAffineTransform, cvGetPerspectiveTransform, cvEstimateRigidMotion, cvWarp- Perspective, cvPerspectiveTransform cvFindStereoCorrespondenceBM (view/add comments) Computes the disparity map using block matching algorithm. void cvFindStereoCorrespondenceBM( const CvArr* left, const CvArr* right, CvArr* disparity, CvStereoBMState* state ); left The left single-channel, 8-bit image. right The right image of the same size and the same type. disparity The output single-channel 16-bit signed, or 32-bit floating-point disparity map of the same size as input images. In the first case the computed disparities are represented as fixed-point numbers with 4 fractional bits (i.e. the computed disparity values are multiplied by 16 and rounded to integers). state Stereo correspondence structure. The function cvFindStereoCorrespondenceBM computes disparity map for the input rectified stereo pair. Invalid pixels (for which disparity can not be computed) are set to state->minDisparity - 1 (or to (state->minDisparity-1)*16 in the case of 16-bit fixed-point disparity map) 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 439 cvFindStereoCorrespondenceGC (view/add comments) Computes the disparity map using graph cut-based algorithm. void cvFindStereoCorrespondenceGC( const CvArr* left, const CvArr* right, CvArr* dispLeft, CvArr* dispRight, CvStereoGCState* state, int useDisparityGuess = CV DEFAULT(0) ); left The left single-channel, 8-bit image. right The right image of the same size and the same type. dispLeft The optional output single-channel 16-bit signed left disparity map of the same size as input images. dispRight The optional output single-channel 16-bit signed right disparity map of the same size as input images. state Stereo correspondence structure. useDisparityGuess If the parameter is not zero, the algorithm will start with pre-defined dis- parity maps. Both dispLeft and dispRight should be valid disparity maps. Otherwise, the function starts with blank disparity maps (all pixels are marked as occlusions). The function computes disparity maps for the input rectified stereo pair. Note that the left disparity image will contain values in the following range: −state->numberOfDisparities−state->minDisparity < dispLeft(x, y) ≤ −state->minDisparity, or dispLeft(x, y) == CV STEREO GC OCCLUSION and for the right disparity image the following will be true: state->minDisparity ≤ dispRight(x, y) < state->minDisparity+state->numberOfDisparities 440 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO or dispRight(x, y) == CV STEREO GC OCCLUSION that is, the range for the left disparity image will be inversed, and the pixels for which no good match has been found, will be marked as occlusions. Here is how the function can be used: // image_left and image_right are the input 8-bit single-channel images // from the left and the right cameras, respectively CvSize size = cvGetSize(image_left); CvMat* disparity_left = cvCreateMat( size.height, size.width, CV_16S ); CvMat* disparity_right = cvCreateMat( size.height, size.width, CV_16S ); CvStereoGCState* state = cvCreateStereoGCState( 16, 2 ); cvFindStereoCorrespondenceGC( image_left, image_right, disparity_left, disparity_right, state, 0 ); cvReleaseStereoGCState( &state ); // now process the computed disparity images as you want ... and this is the output left disparity image computed from the well-known Tsukuba stereo pair and multiplied by -16 (because the values in the left disparity images are usually negative): CvMat* disparity_left_visual = cvCreateMat( size.height, size.width, CV_8U ); cvConvertScale( disparity_left, disparity_left_visual, -16 ); cvSave( "disparity.pgm", disparity_left_visual ); 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 441 cvGetOptimalNewCameraMatrix (view/add comments) Returns the new camera matrix based on the free scaling parameter void cvGetOptimalNewCameraMatrix( const CvMat* cameraMatrix, const CvMat* distCoeffs, CvSize imageSize, double alpha, CvMat* newCameraMatrix, CvSize newImageSize=cvSize(0,0), CvRect* validPixROI=0 ); cameraMatrix The input camera matrix distCoeffs The input vector of distortion coefficients (k1, k2, p1, p2[, k3[, k4, k5, k6]]) of 4, 5 or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed. 442 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO imageSize The original image size alpha The free scaling parameter between 0 (when all the pixels in the undistorted image will be valid) and 1 (when all the source image pixels will be retained in the undistorted image); see cvStereoRectify newCameraMatrix The output new camera matrix. newImageSize The image size after rectification. By default it will be set to imageSize. validPixROI The optional output rectangle that will outline all-good-pixels region in the undis- torted image. See roi1, roi2 description in cvStereoRectify The function computes the optimal new camera matrix based on the free scaling parame- ter. By varying this parameter the user may retrieve only sensible pixels alpha=0, keep all the original image pixels if there is valuable information in the corners alpha=1, or get something in between. When alpha>0, the undistortion result will likely have some black pixels corresponding to ”virtual” pixels outside of the captured distorted image. The original camera matrix, distor- tion coefficients, the computed new camera matrix and the newImageSize should be passed to cvInitUndistortRectifyMap to produce the maps for cvRemap. cvInitIntrinsicParams2D (view/add comments) Finds the initial camera matrix from the 3D-2D point correspondences void cvInitIntrinsicParams2D( const CvMat* objectPoints, const CvMat* imagePoints, const CvMat* npoints, CvSize imageSize, CvMat* cameraMatrix, double aspectRatio=1.); objectPoints The joint array of object points; see cvCalibrateCamera2 imagePoints The joint array of object point projections; see cvCalibrateCamera2 npoints The array of point counts; see cvCalibrateCamera2 imageSize The image size in pixels; used to initialize the principal point 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 443 cameraMatrix The output camera matrix   fx 0 cx 0 fy cy 0 0 1   aspectRatio If it is zero or negative, both fx and fy are estimated independently. Otherwise fx = fy ∗ aspectRatio The function estimates and returns the initial camera matrix for camera calibration process. Currently, the function only supports planar calibration patterns, i.e. patterns where each object point has z-coordinate =0. cvInitUndistortMap (view/add comments) Computes an undistortion map. void cvInitUndistortMap( const CvMat* cameraMatrix, const CvMat* distCoeffs, CvArr* map1, CvArr* map2 ); cameraMatrix The input camera matrix A =   fx 0 cx 0 fy cy 0 0 1   distCoeffs The input vector of distortion coefficients (k1, k2, p1, p2[, k3[, k4, k5, k6]]) of 4, 5 or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed. map1 The first output map of type CV 32FC1 or CV 16SC2 - the second variant is more efficient map2 The second output map of type CV 32FC1 or CV 16UC1 - the second variant is more efficient The function is a simplified variant of cvInitUndistortRectifyMap where the rectification trans- formation R is identity matrix and newCameraMatrix=cameraMatrix. 444 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO cvInitUndistortRectifyMap (view/add comments) Computes the undistortion and rectification transformation map. void cvInitUndistortRectifyMap( const CvMat* cameraMatrix, const CvMat* distCoeffs, const CvMat* R, const CvMat* newCameraMatrix, CvArr* map1, CvArr* map2 ); cameraMatrix The input camera matrix A =   fx 0 cx 0 fy cy 0 0 1   distCoeffs The input vector of distortion coefficients (k1, k2, p1, p2[, k3[, k4, k5, k6]]) of 4, 5 or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed. R The optional rectification transformation in object space (3x3 matrix). R1 or R2, computed by cvStereoRectify can be passed here. If the matrix is NULL , the identity transformation is assumed newCameraMatrix The new camera matrix A0 =   f0 x 0 c0 x 0 f0 y c0 y 0 0 1   map1 The first output map of type CV 32FC1 or CV 16SC2 - the second variant is more efficient map2 The second output map of type CV 32FC1 or CV 16UC1 - the second variant is more efficient The function computes the joint undistortion+rectification transformation and represents the result in the form of maps for cvRemap. The undistorted image will look like the original, as if it was captured with a camera with camera matrix =newCameraMatrix and zero distortion. In the case of monocular camera newCameraMatrix is usually equal to cameraMatrix, or it can be computed by cvGetOptimalNewCameraMatrix for a better control over scaling. In the case of stereo camera newCameraMatrix is normally set to P1 or P2 computed by cvStereoRectify. Also, this new camera will be oriented differently in the coordinate space, according to R. That, for example, helps to align two heads of a stereo camera so that the epipolar lines on both images 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 445 become horizontal and have the same y- coordinate (in the case of horizontally aligned stereo camera). The function actually builds the maps for the inverse mapping algorithm that is used by cvRemap. That is, for each pixel (u, v) in the destination (corrected and rectified) image the function com- putes the corresponding coordinates in the source image (i.e. in the original image from camera). The process is the following: x ← (u − c0x)/f0 x y ← (v − c0y)/f0 y [XYW]T ← R−1 ∗ [x y 1]T x0 ← X/W y0 ← Y/W x” ← x0(1 + k1r2 + k2r4 + k3r6) + 2p1x0y0 + p2(r2 + 2x02) y” ← y0(1 + k1r2 + k2r4 + k3r6) + p1(r2 + 2y02) + 2p2x0y0 mapx(u, v) ← x”fx + cx mapy(u, v) ← y”fy + cy where (k1, k2, p1, p2[, k3]) are the distortion coefficients. In the case of a stereo camera this function is called twice, once for each camera head, after cvStereoRectify, which in its turn is called after cvStereoCalibrate. But if the stereo camera was not calibrated, it is still possible to compute the rectification transformations directly from the fundamental matrix using cvStereoRectifyUncalibrated. For each camera the function computes homography H as the rectification transformation in pixel domain, not a rotation matrix R in 3D space. The R can be computed from H as R = cameraMatrix−1 ·H· cameraMatrix where the cameraMatrix can be chosen arbitrarily. cvPOSIT (view/add comments) Implements the POSIT algorithm. void cvPOSIT( CvPOSITObject* posit object, CvPoint2D32f* imagePoints, double focal length, CvTermCriteria criteria, CvMatr32f rotationMatrix, CvVect32f translation vector ); 446 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO posit object Pointer to the object structure imagePoints Pointer to the object points projections on the 2D image plane focal length Focal length of the camera used criteria Termination criteria of the iterative POSIT algorithm rotationMatrix Matrix of rotations translation vector Translation vector The function implements the POSIT algorithm. Image coordinates are given in a camera- related coordinate system. The focal length may be retrieved using the camera calibration func- tions. At every iteration of the algorithm a new perspective projection of the estimated pose is computed. Difference norm between two projections is the maximal distance between corresponding points. The parameter criteria.epsilon serves to stop the algorithm if the difference is small. cvProjectPoints2 (view/add comments) Project 3D points on to an image plane. void cvProjectPoints2( const CvMat* objectPoints, const CvMat* rvec, const CvMat* tvec, const CvMat* cameraMatrix, const CvMat* distCoeffs, CvMat* imagePoints, CvMat* dpdrot=NULL, CvMat* dpdt=NULL, CvMat* dpdf=NULL, CvMat* dpdc=NULL, CvMat* dpddist=NULL ); 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 447 objectPoints The array of object points, 3xN or Nx3 1-channel or 1xN or Nx1 3-channel , where N is the number of points in the view rvec The rotation vector, see cvRodrigues2 tvec The translation vector cameraMatrix The camera matrix A =   fx 0 cx 0 fy cy 0 0 1   distCoeffs The input vector of distortion coefficients (k1, k2, p1, p2[, k3[, k4, k5, k6]]) of 4, 5 or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed. imagePoints The output array of image points, 2xN or Nx2 1-channel or 1xN or Nx1 2-channel dpdrot Optional 2Nx3 matrix of derivatives of image points with respect to components of the rotation vector dpdt Optional 2Nx3 matrix of derivatives of image points with respect to components of the trans- lation vector dpdf Optional 2Nx2 matrix of derivatives of image points with respect to fx and fy dpdc Optional 2Nx2 matrix of derivatives of image points with respect to cx and cy dpddist Optional 2Nx4 matrix of derivatives of image points with respect to distortion coefficients The function computes projections of 3D points to the image plane given intrinsic and extrinsic camera parameters. Optionally, the function computes jacobians - matrices of partial derivatives of image points coordinates (as functions of all the input parameters) with respect to the particular parameters, intrinsic and/or extrinsic. The jacobians are used during the global optimization in cvCalibrateCamera2, cvFindExtrinsicCameraParams2 and cvStereoCalibrate. The function itself can also used to compute re-projection error given the current intrinsic and extrinsic parameters. Note, that by setting rvec=tvec=(0,0,0), or by setting cameraMatrix to 3x3 identity ma- trix, or by passing zero distortion coefficients, you can get various useful partial cases of the function, i.e. you can compute the distorted coordinates for a sparse set of points, or apply a perspective transformation (and also compute the derivatives) in the ideal zero-distortion setup etc. cvReprojectImageTo3D (view/add comments) Reprojects disparity image to 3D space. 448 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO void cvReprojectImageTo3D( const CvArr* disparity, CvArr* 3dImage, const CvMat* Q, int handleMissingValues=0); disparity The input single-channel 16-bit signed or 32-bit floating-point disparity image 3dImage The output 3-channel floating-point image of the same size as disparity. Each element of 3dImage(x,y) will contain the 3D coordinates of the point (x,y), computed from the disparity map. Q The 4 × 4 perspective transformation matrix that can be obtained with cvStereoRectify handleMissingValues If true, when the pixels with the minimal disparity (that corresponds to the outliers; see cvFindStereoCorrespondenceBM) will be transformed to 3D points with some very large Z value (currently set to 10000) The function transforms 1-channel disparity map to 3-channel image representing a 3D sur- face. That is, for each pixel (x,y) and the corresponding disparity d=disparity(x,y) it com- putes: [XYZW]T = Q ∗ [x y disparity(x, y) 1]T 3dImage(x, y) = (X/W, Y/W, Z/W) The matrix Q can be arbitrary 4 × 4 matrix, e.g. the one computed by cvStereoRectify. To reproject a sparse set of points (x,y,d),... to 3D space, use cvPerspectiveTransform. cvRQDecomp3x3 (view/add comments) Computes the ’RQ’ decomposition of 3x3 matrices. void cvRQDecomp3x3( const CvMat *M, CvMat *R, CvMat *Q, CvMat *Qx=NULL, CvMat *Qy=NULL, CvMat *Qz=NULL, CvPoint3D64f *eulerAngles=NULL); 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 449 M The 3x3 input matrix R The output 3x3 upper-triangular matrix Q The output 3x3 orthogonal matrix Qx Optional 3x3 rotation matrix around x-axis Qy Optional 3x3 rotation matrix around y-axis Qz Optional 3x3 rotation matrix around z-axis eulerAngles Optional three Euler angles of rotation The function computes a RQ decomposition using the given rotations. This function is used in cvDecomposeProjectionMatrix to decompose the left 3x3 submatrix of a projection matrix into a camera and a rotation matrix. It optionally returns three rotation matrices, one for each axis, and the three Euler angles that could be used in OpenGL. cvReleasePOSITObject (view/add comments) Deallocates a 3D object structure. void cvReleasePOSITObject( CvPOSITObject** posit object ); posit object Double pointer to CvPOSIT structure The function releases memory previously allocated by the function cvCreatePOSITObject. cvReleaseStereoBMState (view/add comments) Releases block matching stereo correspondence structure. void cvReleaseStereoBMState( CvStereoBMState** state ); 450 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO state Double pointer to the released structure. The function releases the stereo correspondence structure and all the associated internal buffers. cvReleaseStereoGCState (view/add comments) Releases the state structure of the graph cut-based stereo correspondence algorithm. void cvReleaseStereoGCState( CvStereoGCState** state ); state Double pointer to the released structure. The function releases the stereo correspondence structure and all the associated internal buffers. cvRodrigues2 (view/add comments) Converts a rotation matrix to a rotation vector or vice versa. int cvRodrigues2( const CvMat* src, CvMat* dst, CvMat* jacobian=0 ); src The input rotation vector (3x1 or 1x3) or rotation matrix (3x3) dst The output rotation matrix (3x3) or rotation vector (3x1 or 1x3), respectively jacobian Optional output Jacobian matrix, 3x9 or 9x3 - partial derivatives of the output array components with respect to the input array components θ ← norm(r) r ← r/θ R = cos θI + (1 − cos θ)rrT + sin θ   0 −rz ry rz 0 −rx −ry rx 0   8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 451 Inverse transformation can also be done easily, since sin(θ)   0 −rz ry rz 0 −rx −ry rx 0   = R − RT 2 A rotation vector is a convenient and most-compact representation of a rotation matrix (since any rotation matrix has just 3 degrees of freedom). The representation is used in the global 3D geometry optimization procedures like cvCalibrateCamera2, cvStereoCalibrate or cvFindExtrin- sicCameraParams2. cvStereoCalibrate (view/add comments) Calibrates stereo camera. double cvStereoCalibrate( const CvMat* objectPoints, const CvMat* imagePoints1, const CvMat* imagePoints2, const CvMat* pointCounts, CvMat* cameraMatrix1, CvMat* distCoeffs1, CvMat* cameraMatrix2, CvMat* distCoeffs2, CvSize imageSize, CvMat* R, CvMat* T, CvMat* E=0, CvMat* F=0, CvTermCriteria term crit=cvTermCriteria( CV TERMCRIT ITER+CV TERMCRIT EPS,30,1e-6), int flags=CV CALIB FIX INTRINSIC ); objectPoints The joint matrix of object points - calibration pattern features in the model coordi- nate space. It is floating-point 3xN or Nx3 1-channel, or 1xN or Nx1 3-channel array, where N is the total number of points in all views. 452 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO imagePoints1 The joint matrix of object points projections in the first camera views. It is floating- point 2xN or Nx2 1-channel, or 1xN or Nx1 2-channel array, where N is the total number of points in all views imagePoints2 The joint matrix of object points projections in the second camera views. It is floating-point 2xN or Nx2 1-channel, or 1xN or Nx1 2-channel array, where N is the total number of points in all views pointCounts Integer 1xM or Mx1 vector (where M is the number of calibration pattern views) containing the number of points in each particular view. The sum of vector elements must match the size of objectPoints and imagePoints*(=N). cameraMatrix1 The input/output first camera matrix:   f(j) x 0 c(j) x 0 f(j) y c(j) y 0 0 1  , j = 0, 1. If any of CV CALIB USE INTRINSIC GUESS, CV CALIB FIX ASPECT RATIO, CV CALIB FIX INTRINSIC or CV CALIB FIX FOCAL LENGTH are specified, some or all of the matrices’ components must be initialized; see the flags de- scription distCoeffs The input/output vector of distortion coefficients (k1, k2, p1, p2[, k3[, k4, k5, k6]]) of 4, 5 or 8 elements. cameraMatrix2 The input/output second camera matrix, as cameraMatrix1. distCoeffs2 The input/output lens distortion coefficients for the second camera, as distCoeffs1. imageSize Size of the image, used only to initialize intrinsic camera matrix. R The output rotation matrix between the 1st and the 2nd cameras’ coordinate systems. T The output translation vector between the cameras’ coordinate systems. E The optional output essential matrix. F The optional output fundamental matrix. term crit The termination criteria for the iterative optimization algorithm. flags Different flags, may be 0 or combination of the following values: CV CALIB FIX INTRINSIC If it is set, cameraMatrix?, as well as distCoeffs? are fixed, so that only R, T, E and F are estimated. 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 453 CV CALIB USE INTRINSIC GUESS The flag allows the function to optimize some or all of the intrinsic parameters, depending on the other flags, but the initial values are provided by the user. CV CALIB FIX PRINCIPAL POINT The principal points are fixed during the optimization. CV CALIB FIX FOCAL LENGTH f(j) x and f(j) y are fixed. CV CALIB FIX ASPECT RATIO f(j) y is optimized, but the ratio f(j) x /f(j) y is fixed. CV CALIB SAME FOCAL LENGTH Enforces f(0) x = f(1) x and f(0) y = f(1) y CV CALIB ZERO TANGENT DIST Tangential distortion coefficients for each camera are set to zeros and fixed there. CV CALIB FIX K1,...,CV CALIB FIX K6 Do not change the corresponding radial distor- tion coefficient during the optimization. If CV CALIB USE INTRINSIC GUESS is set, the coefficient from the supplied distCoeffs matrix is used, otherwise it is set to 0. CV CALIB RATIONAL MODEL Enable coefficients k4, k5 and k6. To provide the backward compatibility, this extra flag should be explicitly specified to make the calibration function use the rational model and return 8 coefficients. If the flag is not set, the function will compute only 5 distortion coefficients. The function estimates transformation between the 2 cameras making a stereo pair. If we have a stereo camera, where the relative position and orientation of the 2 cameras is fixed, and if we computed poses of an object relative to the fist camera and to the second camera, (R1, T1) and (R2, T2), respectively (that can be done with cvFindExtrinsicCameraParams2), obviously, those poses will relate to each other, i.e. given (R1,T1) it should be possible to compute (R2,T2) - we only need to know the position and orientation of the 2nd camera relative to the 1st camera. That’s what the described function does. It computes (R,T) such that: R2 = R ∗ R1T2 = R ∗ T1 + T, Optionally, it computes the essential matrix E: E =   0 −T2 T1 T2 0 −T0 −T1 T0 0   ∗ R where Ti are components of the translation vector T:T = [T0,T1,T2]T. And also the function can compute the fundamental matrix F: F = cameraMatrix2−T EcameraMatrix1−1 Besides the stereo-related information, the function can also perform full calibration of each of the 2 cameras. However, because of the high dimensionality of the parameter space and noise in 454 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO the input data the function can diverge from the correct solution. Thus, if intrinsic parameters can be estimated with high accuracy for each of the cameras individually (e.g. using cvCalibrateCam- era2), it is recommended to do so and then pass CV CALIB FIX INTRINSIC flag to the function along with the computed intrinsic parameters. Otherwise, if all the parameters are estimated at once, it makes sense to restrict some parameters, e.g. pass CV CALIB SAME FOCAL LENGTH and CV CALIB ZERO TANGENT DIST flags, which are usually reasonable assumptions. Similarly to cvCalibrateCamera2, the function minimizes the total re-projection error for all the points in all the available views from both cameras. The function returns the final value of the re-projection error. cvStereoRectify (view/add comments) Computes rectification transforms for each head of a calibrated stereo camera. void cvStereoRectify( const CvMat* cameraMatrix1, const CvMat* cameraMatrix2, const CvMat* distCoeffs1, const CvMat* distCoeffs2, CvSize imageSize, const CvMat* R, const CvMat* T, CvMat* R1, CvMat* R2, CvMat* P1, CvMat* P2, CvMat* Q=0, int flags=CV CALIB ZERO DISPARITY, double alpha=-1, CvSize newImageSize=cvSize(0,0), CvRect* roi1=0, CvRect* roi2=0); cameraMatrix1, cameraMatrix2 The camera matrices   f(j) x 0 c(j) x 0 f(j) y c(j) y 0 0 1  . distCoeffs1, distCoeffs2 distCoeffs The input vectors of distortion coefficients (k1, k2, p1, p2[, k3[, k4, k5, k6]]) of 4, 5 or 8 elements each. If the vectors are NULL/empty, the zero distortion coefficients are assumed. imageSize Size of the image used for stereo calibration. R The rotation matrix between the 1st and the 2nd cameras’ coordinate systems. T The translation vector between the cameras’ coordinate systems. R1, R2 The output 3 × 3 rectification transforms (rotation matrices) for the first and the second cameras, respectively. 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 455 P1, P2 The output 3 × 4 projection matrices in the new (rectified) coordinate systems. Q The output 4 × 4 disparity-to-depth mapping matrix, see cv. flags The operation flags; may be 0 or CV CALIB ZERO DISPARITY. If the flag is set, the func- tion makes the principal points of each camera have the same pixel coordinates in the rec- tified views. And if the flag is not set, the function may still shift the images in horizontal or vertical direction (depending on the orientation of epipolar lines) in order to maximize the useful image area. alpha The free scaling parameter. If it is -1 , the functions performs some default scaling. Otherwise the parameter should be between 0 and 1. alpha=0 means that the rectified images will be zoomed and shifted so that only valid pixels are visible (i.e. there will be no black areas after rectification). alpha=1 means that the rectified image will be decimated and shifted so that all the pixels from the original images from the cameras are retained in the rectified images, i.e. no source image pixels are lost. Obviously, any intermediate value yields some intermediate result between those two extreme cases. newImageSize The new image resolution after rectification. The same size should be passed to cvInitUndistortRectifyMap, see the stereo calib.cpp sample in OpenCV samples directory. By default, i.e. when (0,0) is passed, it is set to the original imageSize. Setting it to larger value can help you to preserve details in the original image, especially when there is big radial distortion. roi1, roi2 The optional output rectangles inside the rectified images where all the pixels are valid. If alpha=0, the ROIs will cover the whole images, otherwise they likely be smaller, see the picture below The function computes the rotation matrices for each camera that (virtually) make both camera image planes the same plane. Consequently, that makes all the epipolar lines parallel and thus simplifies the dense stereo correspondence problem. On input the function takes the matrices computed by cv and on output it gives 2 rotation matrices and also 2 projection matrices in the new coordinates. The 2 cases are distinguished by the function are: 1. Horizontal stereo, when 1st and 2nd camera views are shifted relative to each other mainly along the x axis (with possible small vertical shift). Then in the rectified images the cor- responding epipolar lines in left and right cameras will be horizontal and have the same y-coordinate. P1 and P2 will look as: P1 =   f 0 cx1 0 0 f cy 0 0 0 1 0   456 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO P2 =   f 0 cx2 Tx ∗ f 0 f cy 0 0 0 1 0   , where Tx is horizontal shift between the cameras and cx1 = cx2 if CV CALIB ZERO DISPARITY is set. 2. Vertical stereo, when 1st and 2nd camera views are shifted relative to each other mainly in vertical direction (and probably a bit in the horizontal direction too). Then the epipolar lines in the rectified images will be vertical and have the same x coordinate. P2 and P2 will look as: P1 =   f 0 cx 0 0 f cy1 0 0 0 1 0   P2 =   f 0 cx 0 0 f cy2 Ty ∗ f 0 0 1 0   , where Ty is vertical shift between the cameras and cy1 = cy2 if CALIB ZERO DISPARITY is set. As you can see, the first 3 columns of P1 and P2 will effectively be the new ”rectified” camera matrices. The matrices, together with R1 and R2, can then be passed to cvInitUndistortRectifyMap to initialize the rectification map for each camera. Below is the screenshot from stereo calib.cpp sample. Some red horizontal lines, as you can see, pass through the corresponding image regions, i.e. the images are well rectified (which is what most stereo correspondence algorithms rely on). The green rectangles are roi1 and roi2 - indeed, their interior are all valid pixels. 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 457 cvStereoRectifyUncalibrated (view/add comments) Computes rectification transform for uncalibrated stereo camera. void cvStereoRectifyUncalibrated( const CvMat* points1, const CvMat* points2, const CvMat* F, CvSize imageSize, CvMat* H1, CvMat* H2, double threshold=5 ); points1, points2 The 2 arrays of corresponding 2D points. The same formats as in cvFind- FundamentalMat are supported 458 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO F The input fundamental matrix. It can be computed from the same set of point pairs using cvFindFundamentalMat. imageSize Size of the image. H1, H2 The output rectification homography matrices for the first and for the second images. threshold The optional threshold used to filter out the outliers. If the parameter is greater than zero, then all the point pairs that do not comply the epipolar geometry well enough (that is, the points for which |points2[i]T ∗ F ∗ points1[i]| > threshold) are rejected prior to computing the homographies. Otherwise all the points are considered inliers. The function computes the rectification transformations without knowing intrinsic parameters of the cameras and their relative position in space, hence the suffix ”Uncalibrated”. Another related difference from cvStereoRectify is that the function outputs not the rectification transformations in the object (3D) space, but the planar perspective transformations, encoded by the homography matrices H1 and H2. The function implements the algorithm [10]. Note that while the algorithm does not need to know the intrinsic parameters of the cameras, it heavily depends on the epipolar geometry. Therefore, if the camera lenses have significant distor- tion, it would better be corrected before computing the fundamental matrix and calling this function. For example, distortion coefficients can be estimated for each head of stereo camera separately by using cvCalibrateCamera2 and then the images can be corrected using cvUndistort2, or just the point coordinates can be corrected with cvUndistortPoints. cvUndistort2 (view/add comments) Transforms an image to compensate for lens distortion. void cvUndistort2( const CvArr* src, CvArr* dst, const CvMat* cameraMatrix, const CvMat* distCoeffs, const CvMat* newCameraMatrix=0 ); src The input (distorted) image dst The output (corrected) image; will have the same size and the same type as src 8.1. CAMERA CALIBRATION AND 3D RECONSTRUCTION 459 cameraMatrix The input camera matrix A =   fx 0 cx 0 fy cy 0 0 1   distCoeffs The input vector of distortion coefficients (k1, k2, p1, p2[, k3[, k4, k5, k6]]) of 4, 5 or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed. The function transforms the image to compensate radial and tangential lens distortion. The function is simply a combination of cvInitUndistortRectifyMap (with unity R) and cvRemap (with bilinear interpolation). See the former function for details of the transformation being per- formed. Those pixels in the destination image, for which there is no correspondent pixels in the source image, are filled with 0’s (black color). The particular subset of the source image that will be visible in the corrected image can be regulated by newCameraMatrix. You can use cvGetOptimalNewCameraMatrix to compute the appropriate newCameraMatrix, depending on your requirements. The camera matrix and the distortion parameters can be determined using cvCalibrateCam- era2. If the resolution of images is different from the used at the calibration stage, fx, fy, cx and cy need to be scaled accordingly, while the distortion coefficients remain the same. cvUndistortPoints (view/add comments) Computes the ideal point coordinates from the observed point coordinates. void cvUndistortPoints( const CvMat* src, CvMat* dst, const CvMat* cameraMatrix, const CvMat* distCoeffs, const CvMat* R=NULL, const CvMat* P=NULL); src The observed point coordinates, 1xN or Nx1 2-channel (CV 32FC2 or CV 64FC2). dst The output ideal point coordinates, after undistortion and reverse perspective transformation , same format as src . cameraMatrix The camera matrix   fx 0 cx 0 fy cy 0 0 1   460 CHAPTER 8. CALIB3D. CAMERA CALIBRATION, POSE ESTIMATION AND STEREO distCoeffs distCoeffs The input vector of distortion coefficients (k1, k2, p1, p2[, k3[, k4, k5, k6]]) of 4, 5 or 8 elements. If the vector is NULL/empty, the zero distortion coefficients are assumed. R The rectification transformation in object space (3x3 matrix). R1 or R2, computed by cv can be passed here. If the matrix is empty, the identity transformation is used P The new camera matrix (3x3) or the new projection matrix (3x4). P1 or P2, computed by cv can be passed here. If the matrix is empty, the identity new camera matrix is used The function is similar to cvUndistort2 and cvInitUndistortRectifyMap, but it operates on a sparse set of points instead of a raster image. Also the function does some kind of reverse trans- formation to cvProjectPoints2 (in the case of 3D object it will not reconstruct its 3D coordinates, of course; but for a planar object it will, up to a translation vector, if the proper R is specified). // (u,v) is the input point, (u’, v’) is the output point // camera_matrix=[fx 0 cx; 0 fy cy; 0 0 1] // P=[fx’ 0 cx’ tx; 0 fy’ cy’ ty; 0 0 1 tz] x" = (u - cx)/fx y" = (v - cy)/fy (x’,y’) = undistort(x",y",dist_coeffs) [X,Y,W]T = R*[x’ y’ 1]T x = X/W, y = Y/W u’ = x*fx’ + cx’ v’ = y*fy’ + cy’, where undistort() is approximate iterative algorithm that estimates the normalized original point coordinates out of the normalized distorted point coordinates (”normalized” means that the coor- dinates do not depend on the camera matrix). The function can be used both for a stereo camera head or for monocular camera (when R is NULL ). Chapter 9 ml. Machine Learning The Machine Learning Library (MLL) is a set of classes and functions for statistical classification, regression and clustering of data. Most of the classification and regression algorithms are implemented as C++ classes. As the algorithms have different seta of features (like the ability to handle missing measurements, or categorical input variables etc.), there is a little common ground between the classes. This common ground is defined by the class ‘CvStatModel‘ that all the other ML classes are derived from. 461 462 CHAPTER 9. ML. MACHINE LEARNING Part II C++ API Reference 463 Chapter 10 Introduction Starting from OpenCV 2.0 the new modern C++ interface has been introduced. It is crisp (less typing is needed to code the same thing), type-safe (no more CvArr* a.k.a. void*) and, in general, more convenient to use. Here is a short example of what it looks like: // // Simple retro-style photo effect done by adding noise to // the luminance channel and reducing intensity of the chroma channels // // include standard OpenCV headers, same as before #include "cv.h" #include "highgui.h" // all the new API is put into "cv" namespace. Export its content using namespace cv; // enable/disable use of mixed API in the code below. #define DEMO_MIXED_API_USE 1 int main( int argc, char** argv ) { const char* imagename = argc > 1 ? argv[1] : "lena.jpg"; #if DEMO_MIXED_API_USE // Ptr is safe ref-conting pointer class Ptr iplimg = cvLoadImage(imagename); // cv::Mat replaces the CvMat and IplImage, but it’s easy to convert // between the old and the new data structures // (by default, only the header is converted and the data is shared) Mat img(iplimg); 465 466 CHAPTER 10. INTRODUCTION #else // the newer cvLoadImage alternative with MATLAB-style name Mat img = imread(imagename); #endif if( !img.data ) // check if the image has been loaded properly return -1; Mat img_yuv; // convert image to YUV color space. // The output image will be allocated automatically cvtColor(img, img_yuv, CV_BGR2YCrCb); // split the image into separate color planes vector planes; split(img_yuv, planes); // another Mat constructor; allocates a matrix of the specified // size and type Mat noise(img.size(), CV_8U); // fills the matrix with normally distributed random values; // there is also randu() for uniformly distributed random numbers. // Scalar replaces CvScalar, Scalar::all() replaces cvScalarAll(). randn(noise, Scalar::all(128), Scalar::all(20)); // blur the noise a bit, kernel size is 3x3 and both sigma’s // are set to 0.5 GaussianBlur(noise, noise, Size(3, 3), 0.5, 0.5); const double brightness_gain = 0; const double contrast_gain = 1.7; #if DEMO_MIXED_API_USE // it’s easy to pass the new matrices to the functions that // only work with IplImage or CvMat: // step 1) - convert the headers, data will not be copied IplImage cv_planes_0 = planes[0], cv_noise = noise; // step 2) call the function; do not forget unary "&" to form pointers cvAddWeighted(&cv_planes_0, contrast_gain, &cv_noise, 1, -128 + brightness_gain, &cv_planes_0); #else addWeighted(planes[0], constrast_gain, noise, 1, -128 + brightness_gain, planes[0]); #endif const double color_scale = 0.5; 467 // Mat::convertTo() replaces cvConvertScale. // One must explicitly specify the output matrix type // (we keep it intact, i.e. pass planes[1].type()) planes[1].convertTo(planes[1], planes[1].type(), color_scale, 128*(1-color_scale)); // alternative form of convertTo if we know the datatype // at compile time ("uchar" here). // This expression will not create any temporary arrays // and should be almost as fast as the above variant planes[2] = Mat_(planes[2]*color_scale + 128*(1-color_scale)); // Mat::mul replaces cvMul(). Again, no temporary arrays are // created in the case of simple expressions. planes[0] = planes[0].mul(planes[0], 1./255); // now merge the results back merge(planes, img_yuv); // and produce the output RGB image cvtColor(img_yuv, img, CV_YCrCb2BGR); // this is counterpart for cvNamedWindow namedWindow("image with grain", CV_WINDOW_AUTOSIZE); #if DEMO_MIXED_API_USE // this is to demonstrate that img and iplimg really share the data - // the result of the above processing is stored to img and thus // in iplimg too. cvShowImage("image with grain", iplimg); #else imshow("image with grain", img); #endif waitKey(); return 0; // all the memory will automatically be released // by vector<>, Mat and Ptr<> destructors. } Following a summary ”cheatsheet” below, the rest of the introduction will discuss the key fea- tures of the new interface in more detail. 468 CHAPTER 10. INTRODUCTION 10.1 C++ Cheatsheet The section is just a summary ”cheatsheet” of common things you may want to do with cv::Mat:. The code snippets below all assume the correct namespace is used: using namespace cv; using namespace std; Convert an IplImage or CvMat to an cv::Mat and a cv::Mat to an IplImage or CvMat: // Assuming somewhere IplImage *iplimg; exists // and has been allocated and cv::Mat Mimg has been defined Mat imgMat(iplimg); //Construct an Mat image "img" out of an IplImage Mimg = iplimg; //Or just set the header of pre existing cv::Mat //Ming to iplimg’s data (no copying is done) //Convert to IplImage or CvMat, no data copying IplImage ipl_img = img; CvMat cvmat = img; // convert cv::Mat -> CvMat A very simple way to operate on a rectanglular sub-region of an image (ROI – ”Region of Interest”): //Make a rectangle Rect roi(10, 20, 100, 50); //Point a cv::Mat header at it (no allocation is done) Mat image_roi = image(roi); A bit advanced, but should you want efficiently to sample from a circular region in an image (below, instead of sampling, we just draw into a BGR image) : // the function returns x boundary coordinates of // the circle for each y. RxV[y1] = x1 means that // when y=y1, -x1 <=x<=x1 is inside the circle void getCircularROI(int R, vector < int > & RxV) { RxV.resize(R+1); for( int y = 0; y <= R; y++ ) RxV[y] = cvRound(sqrt((double)R*R - y*y)); } // This draws a circle in the green channel // (note the "[1]" for a BGR" image, // blue and red channels are not modified), // but is really an example of how to *sample* from a circular region. void drawCircle(Mat &image, int R, Point center) { vector RxV; 10.2. NAMESPACE CV AND FUNCTION NAMING 469 getCircularROI(R, RxV); Mat_& img = (Mat_&)image; //3 channel pointer to image for( int dy = -R; dy <= R; dy++ ) { int Rx = RxV[abs(dy)]; for( int dx = -Rx; dx <= Rx; dx++ ) img(center.y+dy, center.x+dx)[1] = 255; } } 10.2 Namespace cv and Function Naming All the newly introduced classes and functions are placed into cv namespace. Therefore, to access this functionality from your code, use cv:: specifier or "using namespace cv;" direc- tive: #include "cv.h" ... cv::Mat H = cv::findHomography(points1, points2, cv::RANSAC, 5); ... or #include "cv.h" using namespace cv; ... Mat H = findHomography(points1, points2, RANSAC, 5 ); ... It is probable that some of the current or future OpenCV external names conflict with STL or other libraries, in this case use explicit namespace specifiers to resolve the name conflicts: Mat a(100, 100, CV_32F); randu(a, Scalar::all(1), Scalar::all(std::rand()%256+1)); cv::log(a, a); a /= std::log(2.); For the most of the C functions and structures from OpenCV 1.x you may find the direct coun- terparts in the new C++ interface. The name is usually formed by omitting cv or Cv prefix and turning the first letter to the low case (unless it’s a own name, like Canny, Sobel etc). In case when there is no the new-style counterpart, it’s possible to use the old functions with the new structures, as shown the first sample in the chapter. 470 CHAPTER 10. INTRODUCTION 10.3 Memory Management When using the new interface, the most of memory deallocation and even memory allocation operations are done automatically when needed. First of all, Mat, SparseMat and other classes have destructors that deallocate memory buffers occupied by the structures when needed. Secondly, this ”when needed” means that the destructors do not always deallocate the buffers, they take into account possible data sharing. That is, in a destructor the reference counter as- sociated with the underlying data is decremented and the data is deallocated if and only if the reference counter becomes zero, that is, when no other structures refer to the same buffer. When such a structure containing a reference counter is copied, usually just the header is duplicated, while the underlying data is not; instead, the reference counter is incremented to memorize that there is another owner of the same data. Also, some structures, such as Mat, can refer to the user- allocated data. In this case the reference counter is NULL pointer and then no reference counting is done - the data is not deallocated by the destructors and should be deallocated manually by the user. We saw this scheme in the first example in the chapter: // allocates IplImages and wraps it into shared pointer class. Ptr iplimg = cvLoadImage(...); // constructs Mat header for IplImage data; // does not copy the data; // the reference counter will be NULL Mat img(iplimg); ... // in the end of the block img destructor is called, // which does not try to deallocate the data because // of NULL pointer to the reference counter. // // Then Ptr destructor is called that decrements // the reference counter and, as the counter becomes 0 in this case, // the destructor calls cvReleaseImage(). The copying semantics was mentioned in the above paragraph, but deserves a dedicated dis- cussion. By default, the new OpenCV structures implement shallow, so called O(1) (i.e. constant- time) assignment operations. It gives user possibility to pass quite big data structures to functions (though, e.g. passing const Mat& is still faster than passing Mat), return them (e.g. see the example with findHomography above), store them in OpenCV and STL containers etc. - and do all of this very efficiently. On the other hand, most of the new data structures provide clone() method that creates a full copy of an object. Here is the sample: // create a big 8Mb matrix Mat A(1000, 1000, CV_64F); 10.4. MEMORY MANAGEMENT PART II. AUTOMATIC DATA ALLOCATION 471 // create another header for the same matrix; // this is instant operation, regardless of the matrix size. Mat B = A; // create another header for the 3-rd row of A; no data is copied either Mat C = B.row(3); // now create a separate copy of the matrix Mat D = B.clone(); // copy the 5-th row of B to C, that is, copy the 5-th row of A // to the 3-rd row of A. B.row(5).copyTo(C); // now let A and D share the data; after that the modified version // of A is still referenced by B and C. A = D; // now make B an empty matrix (which references no memory buffers), // but the modified version of A will still be referenced by C, // despite that C is just a single row of the original A B.release(); // finally, make a full copy of C. In result, the big modified // matrix will be deallocated, since it’s not referenced by anyone C = C.clone(); Memory management of the new data structures is automatic and thus easy. If, however, your code uses IplImage, CvMat or other C data structures a lot, memory management can still be automated without immediate migration to Mat by using the already mentioned template class Ptr , similar to shared ptr from Boost and C++ TR1. It wraps a pointer to an arbitrary object, provides transparent access to all the object fields and associates a reference counter with it. Instance of the class can be passed to any function that expects the original pointer. For correct deallocation of the object, you should specialize Ptr::delete obj() method. Such specialized methods already exist for the classical OpenCV structures, e.g.: // cxoperations.hpp: ... template<> inline Ptr::delete_obj() { cvReleaseImage(&obj); } ... See Ptr description for more details and other usage scenarios. 10.4 Memory Management Part II. Automatic Data Allocation With the new interface not only explicit memory deallocation is not needed anymore, but the mem- ory allocation is often done automatically too. That was demonstrated in the example in the be- 472 CHAPTER 10. INTRODUCTION ginning of the chapter when cvtColor was called, and here are some more details. Mat and other array classes provide method create that allocates a new buffer for array data if and only if the currently allocated array is not of the required size and type. If a new buffer is needed, the previously allocated buffer is released (by engaging all the reference counting mechanism described in the previous section). Now, since it is very quick to check whether the needed memory buffer is already allocated, most new OpenCV functions that have arrays as output parameters call the create method and this way the automatic data allocation concept is implemented. Here is the example: #include "cv.h" #include "highgui.h" using namespace cv; int main(int, char**) { VideoCapture cap(0); if(!cap.isOpened()) return -1; Mat edges; namedWindow("edges",1); for(;;) { Mat frame; cap >> frame; cvtColor(frame, edges, CV_BGR2GRAY); GaussianBlur(edges, edges, Size(7,7), 1.5, 1.5); Canny(edges, edges, 0, 30, 3); imshow("edges", edges); if(waitKey(30) >= 0) break; } return 0; } The matrix edges is allocated during the first frame processing and unless the resolution will suddenly change, the same buffer will be reused for every next frame’s edge map. In many cases the output array type and size can be inferenced from the input arrays’ respec- tive characteristics, but not always. In these rare cases the corresponding functions take separate input parameters that specify the data type and/or size of the output arrays, like resize . Anyway, a vast majority of the new-style array processing functions call create for each of the output array, with just a few exceptions like mixChannels, RNG::fill and some others. Note that this output array allocation semantic is only implemented in the new functions. If you want to pass the new structures to some old OpenCV function, you should first allocate the output arrays using create method, then make CvMat or IplImage headers and after that call 10.5. ALGEBRAIC OPERATIONS 473 the function. 10.5 Algebraic Operations Just like in v1.x, OpenCV 2.x provides some basic functions operating on matrices, like add, subtract, gemm etc. In addition, it introduces overloaded operators that give the user a conve- nient algebraic notation, which is nearly as fast as using the functions directly. For example, here is how the least squares problem Ax = b can be solved using normal equations: Mat x = (A.t()*A).inv()*(A.t()*b); The complete list of overloaded operators can be found in Matrix Expressions. 10.6 Fast Element Access Historically, OpenCV provided many different ways to access image and matrix elements, and none of them was both fast and convenient. With the new data structures, OpenCV 2.x introduces a few more alternatives, hopefully more convenient than before. For detailed description of the op- erations, please, check Mat and Mat description. Here is part of the retro-photo-styling example rewritten (in simplified form) using the element access operations: ... // split the image into separate color planes vector planes; split(img_yuv, planes); // method 1. process Y plane using an iterator MatIterator_ it = planes[0].begin(), it_end = planes[0].end(); for(; it != it_end; ++it) { double v = *it*1.7 + rand()%21-10; *it = saturate_cast(v*v/255.); } // method 2. process the first chroma plane using pre-stored row pointer. // method 3. process the second chroma plane using // individual element access operations for( int y = 0; y < img_yuv.rows; y++ ) { uchar* Uptr = planes[1].ptr(y); for( int x = 0; x < img_yuv.cols; x++ ) { Uptr[x] = saturate_cast((Uptr[x]-128)/2 + 128); 474 CHAPTER 10. INTRODUCTION uchar& Vxy = planes[2].at(y, x); Vxy = saturate_cast((Vxy-128)/2 + 128); } } merge(planes, img_yuv); ... 10.7 Saturation Arithmetics In the above sample you may have noticed saturate cast operator, and that’s how all the pixel processing is done in OpenCV. When a result of image operation is 8-bit image with pixel values ranging from 0 to 255, each output pixel value is clipped to this available range: I(x, y) = min(max(value, 0), 255) and the similar rules are applied to 8-bit signed and 16-bit signed and unsigned types. This ”saturation” semantics (different from usual C language ”wrapping” semantics, where lowest bits are taken, is implemented in every image processing function, from the simple cv::add to cv::cvtColor, cv::resize, cv::filter2D etc. It is not a new feature of OpenCV v2.x, it was there from very beginning. In the new version this special saturate cast template operator is introduced to simplify implementation of this semantic in your own functions. 10.8 Error handling The modern error handling mechanism in OpenCV uses exceptions, as opposite to the manual stack unrolling used in previous versions. If you to check some conditions in your code and raise an error if they are not satisfied, use CV Assert() orCV Error(). CV_Assert(mymat.type() == CV_32FC1); ... if( scaleValue < 0 || scaleValue > 1000 ) CV_Error(CV_StsOutOfRange, "The scale value is out of range"); There is alsoCV DbgAssert that yields no code in the Release configuration. To handle the errors, use the standard exception handling mechanism: try { ... } 10.9. THREADING AND REENTERABILITY 475 catch( cv::Exception& e ) { const char* err_msg = e.what(); ... } instead of cv::Exception you can write std::exception, since the former is derived from the latter. Then, obviously, to make it all work and do not worry about the object destruction, try not to use IplImage*, CvMat* and plain pointers in general. Use cv::Mat, std::vector<>, cv::Ptr etc. 10.9 Threading and Reenterability OpenCV uses OpenMP to run some time-consuming operations in parallel. Threading can be ex- plicitly controlled by setNumThreads function. Also, functions and ”const” methods of the classes are generally re-enterable, that is, they can be called from different threads asynchronously. 476 CHAPTER 10. INTRODUCTION Chapter 11 core. The Core Functionality 11.1 Basic Structures DataType Template ”traits” class for other OpenCV primitive data types template class DataType { // value_type is always a synonym for _Tp. typedef _Tp value_type; // intermediate type used for operations on _Tp. // it is int for uchar, signed char, unsigned short, signed short and int, // float for float, double for double, ... typedef <...> work_type; // in the case of multi-channel data it is the data type of each channel typedef <...> channel_type; enum { // CV_8U ... CV_64F depth = DataDepth::value, // 1 ... channels = <...>, // ’1u’, ’4i’, ’3f’, ’2d’ etc. fmt=<...>, // CV_8UC3, CV_32FC2 ... type = CV_MAKETYPE(depth, channels) }; }; 477 478 CHAPTER 11. CORE. THE CORE FUNCTIONALITY The template class DataType is descriptive class for OpenCV primitive data types and other types that comply with the following definition. A primitive OpenCV data type is one of unsigned char, bool, signed char, unsigned short, signed short, int, float, double or a tuple of values of one of these types, where all the values in the tuple have the same type. If you are familiar with OpenCV CvMat ’s type notation, CV 8U ... CV 32FC3, CV 64FC2 etc., then a primitive type can be defined as a type for which you can give a unique identifier in a form CV U|S|FC. A universal OpenCV structure able to store a single instance of such primitive data type is Vec . Multiple instances of such a type can be stored to a std::vector, Mat, Mat , SparseMat, SparseMat or any other container that is able to store Vec instances. The class DataType is basically used to provide some description of such primitive data types without adding any fields or methods to the corresponding classes (and it is actually impossible to add anything to primitive C/C++ data types). This technique is known in C++ as class traits. It’s not DataType itself that is used, but its specialized versions, such as: template<> class DataType { typedef uchar value_type; typedef int work_type; typedef uchar channel_type; enum { channel_type = CV_8U, channels = 1, fmt=’u’, type = CV_8U }; }; ... template DataType > { typedef std::complex<_Tp> value_type; typedef std::complex<_Tp> work_type; typedef _Tp channel_type; // DataDepth is another helper trait class enum { depth = DataDepth<_Tp>::value, channels=2, fmt=(channels-1)*256+DataDepth<_Tp>::fmt, type=CV_MAKETYPE(depth, channels) }; }; ... The main purpose of the classes is to convert compile-time type information to OpenCV- compatible data type identifier, for example: // allocates 30x40 floating-point matrix Mat A(30, 40, DataType::type); Mat B = Mat_ >(3, 3); // the statement below will print 6, 2 /* i.e. depth == CV_64F, channels == 2 */ cout << B.depth() << ", " << B.channels() << endl; 11.1. BASIC STRUCTURES 479 that is, such traits are used to tell OpenCV which data type you are working with, even if such a type is not native to OpenCV (the matrix B intialization above compiles because OpenCV defines the proper specialized template class DataType >). Also, this mechanism is useful (and used in OpenCV this way) for generic algorithms implementations. Point Template class for 2D points template class Point_ { public: typedef _Tp value_type; Point_(); Point_(_Tp _x, _Tp _y); Point_(const Point_& pt); Point_(const CvPoint& pt); Point_(const CvPoint2D32f& pt); Point_(const Size_<_Tp>& sz); Point_(const Vec<_Tp, 2>& v); Point_& operator = (const Point_& pt); template operator Point_<_Tp2>() const; operator CvPoint() const; operator CvPoint2D32f() const; operator Vec<_Tp, 2>() const; // computes dot-product (this->x*pt.x + this->y*pt.y) _Tp dot(const Point_& pt) const; // computes dot-product using double-precision arithmetics double ddot(const Point_& pt) const; // returns true if the point is inside the rectangle "r". bool inside(const Rect_<_Tp>& r) const; _Tp x, y; }; The class represents a 2D point, specified by its coordinates x and y. Instance of the class is interchangeable with C structures CvPoint and CvPoint2D32f. There is also cast operator to convert point coordinates to the specified type. The conversion from floating-point coordinates to integer coordinates is done by rounding; in general case the conversion uses saturate cast operation on each of the coordinates. Besides the class members listed in the declaration above, the following operations on points are implemented: pt1 = pt2 + pt3; 480 CHAPTER 11. CORE. THE CORE FUNCTIONALITY pt1 = pt2 - pt3; pt1 = pt2 * a; pt1 = a * pt2; pt1 += pt2; pt1 -= pt2; pt1 *= a; double value = norm(pt); // L2 norm pt1 == pt2; pt1 != pt2; For user convenience, the following type aliases are defined: typedef Point_ Point2i; typedef Point2i Point; typedef Point_ Point2f; typedef Point_ Point2d; Here is a short example: Point2f a(0.3f, 0.f), b(0.f, 0.4f); Point pt = (a + b)*10.f; cout << pt.x << ", " << pt.y << endl; Point3 Template class for 3D points template class Point3_ { public: typedef _Tp value_type; Point3_(); Point3_(_Tp _x, _Tp _y, _Tp _z); Point3_(const Point3_& pt); explicit Point3_(const Point_<_Tp>& pt); Point3_(const CvPoint3D32f& pt); Point3_(const Vec<_Tp, 3>& v); Point3_& operator = (const Point3_& pt); template operator Point3_<_Tp2>() const; operator CvPoint3D32f() const; operator Vec<_Tp, 3>() const; _Tp dot(const Point3_& pt) const; double ddot(const Point3_& pt) const; 11.1. BASIC STRUCTURES 481 _Tp x, y, z; }; The class represents a 3D point, specified by its coordinates x, y and z. Instance of the class is interchangeable with C structure CvPoint2D32f. Similarly to Point , the 3D points’ coordinates can be converted to another type, and the vector arithmetic and comparison operations are also supported. The following type aliases are available: typedef Point3_ Point3i; typedef Point3_ Point3f; typedef Point3_ Point3d; Size Template class for specfying image or rectangle size. template class Size_ { public: typedef _Tp value_type; Size_(); Size_(_Tp _width, _Tp _height); Size_(const Size_& sz); Size_(const CvSize& sz); Size_(const CvSize2D32f& sz); Size_(const Point_<_Tp>& pt); Size_& operator = (const Size_& sz); _Tp area() const; operator Size_() const; operator Size_() const; operator Size_() const; operator CvSize() const; operator CvSize2D32f() const; _Tp width, height; }; The class Size is similar to Point , except that the two members are called width and height instead of x and y. The structure can be converted to and from the old OpenCV structures CvSize and CvSize2D32f . The same set of arithmetic and comparison operations as for Point is available. 482 CHAPTER 11. CORE. THE CORE FUNCTIONALITY OpenCV defines the following type aliases: typedef Size_ Size2i; typedef Size2i Size; typedef Size_ Size2f; Rect Template class for 2D rectangles template class Rect_ { public: typedef _Tp value_type; Rect_(); Rect_(_Tp _x, _Tp _y, _Tp _width, _Tp _height); Rect_(const Rect_& r); Rect_(const CvRect& r); // (x, y) <- org, (width, height) <- sz Rect_(const Point_<_Tp>& org, const Size_<_Tp>& sz); // (x, y) <- min(pt1, pt2), (width, height) <- max(pt1, pt2) - (x, y) Rect_(const Point_<_Tp>& pt1, const Point_<_Tp>& pt2); Rect_& operator = ( const Rect_& r ); // returns Point_<_Tp>(x, y) Point_<_Tp> tl() const; // returns Point_<_Tp>(x+width, y+height) Point_<_Tp> br() const; // returns Size_<_Tp>(width, height) Size_<_Tp> size() const; // returns width*height _Tp area() const; operator Rect_() const; operator Rect_() const; operator Rect_() const; operator CvRect() const; // x <= pt.x && pt.x < x + width && // y <= pt.y && pt.y < y + height ? true : false bool contains(const Point_<_Tp>& pt) const; _Tp x, y, width, height; }; 11.1. BASIC STRUCTURES 483 The rectangle is described by the coordinates of the top-left corner (which is the default inter- pretation of Rect ::x and Rect ::y in OpenCV; though, in your algorithms you may count x and y from the bottom-left corner), the rectangle width and height. Another assumption OpenCV usually makes is that the top and left boundary of the rect- angle are inclusive, while the right and bottom boundaries are not, for example, the method Rect ::contains returns true if x ≤ pt.x < x + width, y ≤ pt.y < y + height And virtually every loop over an image ROI in OpenCV (where ROI is specified by Rect ) is implemented as: for(int y = roi.y; y < roi.y + rect.height; y++) for(int x = roi.x; x < roi.x + rect.width; x++) { // ... } In addition to the class members, the following operations on rectangles are implemented: • rect = rect ± point (shifting rectangle by a certain offset) • rect = rect ± size (expanding or shrinking rectangle by a certain amount) • rect += point, rect -= point, rect += size, rect -= size (augmenting op- erations) • rect = rect1 & rect2 (rectangle intersection) • rect = rect1 | rect2 (minimum area rectangle containing rect2 and rect3) • rect &= rect1, rect |= rect1 (and the corresponding augmenting operations) • rect == rect1, rect != rect1 (rectangle comparison) Example. Here is how the partial ordering on rectangles can be established (rect1 ⊆ rect2): template inline bool operator <= (const Rect_<_Tp>& r1, const Rect_<_Tp>& r2) { return (r1 & r2) == r1; } For user convenience, the following type alias is available: typedef Rect_ Rect; 484 CHAPTER 11. CORE. THE CORE FUNCTIONALITY RotatedRect Possibly rotated rectangle class RotatedRect { public: // constructors RotatedRect(); RotatedRect(const Point2f& _center, const Size2f& _size, float _angle); RotatedRect(const CvBox2D& box); // returns minimal up-right rectangle that contains the rotated rectangle Rect boundingRect() const; // backward conversion to CvBox2D operator CvBox2D() const; // mass center of the rectangle Point2f center; // size Size2f size; // rotation angle in degrees float angle; }; The class RotatedRect replaces the old CvBox2D and fully compatible with it. TermCriteria Termination criteria for iterative algorithms class TermCriteria { public: enum { COUNT=1, MAX_ITER=COUNT, EPS=2 }; // constructors TermCriteria(); // type can be MAX_ITER, EPS or MAX_ITER+EPS. // type = MAX_ITER means that only the number of iterations does matter; // type = EPS means that only the required precision (epsilon) does matter // (though, most algorithms put some limit on the number of iterations anyway) // type = MAX_ITER + EPS means that algorithm stops when // either the specified number of iterations is made, // or when the specified accuracy is achieved - whatever happens first. 11.1. BASIC STRUCTURES 485 TermCriteria(int _type, int _maxCount, double _epsilon); TermCriteria(const CvTermCriteria& criteria); operator CvTermCriteria() const; int type; int maxCount; double epsilon; }; The class TermCriteria replaces the old CvTermCriteria and fully compatible with it. Matx Template class for small matrices template class Matx { public: typedef T value_type; enum { depth = DataDepth::value, channels = m*n, type = CV_MAKETYPE(depth, channels) }; // various methods ... Tp val[m*n]; }; typedef Matx Matx12f; typedef Matx Matx12d; ... typedef Matx Matx16f; typedef Matx Matx16d; typedef Matx Matx21f; typedef Matx Matx21d; ... typedef Matx Matx61f; typedef Matx Matx61d; typedef Matx Matx22f; typedef Matx Matx22d; ... typedef Matx Matx66f; typedef Matx Matx66d; 486 CHAPTER 11. CORE. THE CORE FUNCTIONALITY The class represents small matrices, which type and size are known at compile time. If you need more flexible type, use Mat . The elements of a matrix M are accessible using M(i,j) notation, and most of the common matrix operations (see also MatrixExpressions ) are available. If you need to do some operation on Matx that is not implemented, it is easy to convert the matrix to Mat and backwards. Matx33f m(1, 2, 3, 4, 5, 6, 7, 8, 9); cout << sum(Mat(m*m.t())) << endl; Vec Template class for short numerical vectors template class Vec : public Matx { public: typedef T value_type; enum { depth = DataDepth::value, channels = cn, type = CV_MAKETYPE(depth, channels) }; // various methods ... }; typedef Vec Vec2b; typedef Vec Vec3b; typedef Vec Vec4b; typedef Vec Vec2s; typedef Vec Vec3s; typedef Vec Vec4s; typedef Vec Vec2i; typedef Vec Vec3i; typedef Vec Vec4i; typedef Vec Vec2f; typedef Vec Vec3f; typedef Vec Vec4f; typedef Vec Vec6f; typedef Vec Vec2d; typedef Vec Vec3d; 11.1. BASIC STRUCTURES 487 typedef Vec Vec4d; typedef Vec Vec6d; Vec is a partial case of Matx. It is possible to convert Vec to/from Point , Vec to/from Point3 , and Vec to CvScalar or Scalar . The elements of Vec are accessed using operator[]. All the expected vector operations are implemented too: • v1 = v2±v3, v1 = v2∗α, v1 = α∗v2 (plus the corresponding augmenting operations; note that these operations apply saturate cast.3C.3E to the each computed vector component) • v1 == v2, v1 != v2 • norm(v1) (L2-norm) The class Vec is commonly used to describe pixel types of multi-channel arrays, see Mat description. Scalar 4-element vector template class Scalar_ : public Vec<_Tp, 4> { public: Scalar_(); Scalar_(_Tp v0, _Tp v1, _Tp v2=0, _Tp v3=0); Scalar_(const CvScalar& s); Scalar_(_Tp v0); static Scalar_<_Tp> all(_Tp v0); operator CvScalar() const; template operator Scalar_() const; Scalar_<_Tp> mul(const Scalar_<_Tp>& t, double scale=1 ) const; template void convertTo(T2* buf, int channels, int unroll_to=0) const; }; typedef Scalar_ Scalar; The template class Scalar and it’s double-precision instantiation Scalar represent 4-element vector. Being derived from Vec< Tp, 4>, they can be used as typical 4-element vectors, but in addition they can be converted to/from CvScalar. The type Scalar is widely used in OpenCV for passing pixel values and it is a drop-in replacement for CvScalar that was used for the same purpose in the earlier versions of OpenCV. 488 CHAPTER 11. CORE. THE CORE FUNCTIONALITY Range Specifies a continuous subsequence (a.k.a. slice) of a sequence. class Range { public: Range(); Range(int _start, int _end); Range(const CvSlice& slice); int size() const; bool empty() const; static Range all(); operator CvSlice() const; int start, end; }; The class is used to specify a row or column span in a matrix ( Mat ), and for many other purposes. Range(a,b) is basically the same as a:b in Matlab or a..b in Python. As in Python, start is inclusive left boundary of the range, and end is exclusive right boundary of the range. Such a half-opened interval is usually denoted as [start, end). The static method Range::all() returns some special variable that means ”the whole se- quence” or ”the whole range”, just like ”:” in Matlab or ”...” in Python. All the methods and functions in OpenCV that take Range support this special Range::all() value, but of course, in the case of your own custom processing you will probably have to check and handle it explicitly: void my_function(..., const Range& r, ....) { if(r == Range::all()) { // process all the data } else { // process [r.start, r.end) } } Ptr A template class for smart reference-counting pointers template class Ptr { public: 11.1. BASIC STRUCTURES 489 // default constructor Ptr(); // constructor that wraps the object pointer Ptr(_Tp*_obj); // destructor: calls release() ˜Ptr(); // copy constructor; increments ptr’s reference counter Ptr(const Ptr& ptr); // assignment operator; decrements own reference counter // (with release()) and increments ptr’s reference counter Ptr& operator = (const Ptr& ptr); // increments reference counter void addref(); // decrements reference counter; when it becomes 0, // delete_obj() is called void release(); // user-specified custom object deletion operation. // by default, "delete obj;" is called void delete_obj(); // returns true if obj == 0; bool empty() const; // provide access to the object fields and methods _Tp* operator -> (); const _Tp* operator -> () const; // return the underlying object pointer; // thanks to the methods, the Ptr<_Tp> can be // used instead of _Tp* operator _Tp*(); operator const _Tp*() const; protected: // the encapsulated object pointer _Tp* obj; // the associated reference counter int* refcount; }; The class Ptr< Tp> is a template class that wraps pointers of the corresponding type. It is similar to shared ptr that is a part of Boost library (http://www.boost.org/doc/libs/1_ 40_0/libs/smart_ptr/shared_ptr.htm) and also a part of the C++0x standard. By using this class you can get the following capabilities: • default constructor, copy constructor and assignment operator for an arbitrary C++ class or a C structure. For some objects, like files, windows, mutexes, sockets etc, copy constructor 490 CHAPTER 11. CORE. THE CORE FUNCTIONALITY or assignment operator are difficult to define. For some other objects, like complex classi- fiers in OpenCV, copy constructors are absent and not easy to implement. Finally, some of complex OpenCV and your own data structures may have been written in C. However, copy constructors and default constructors can simplify programming a lot; besides, they are often required (e.g. by STL containers). By wrapping a pointer to such a complex object TObj to Ptr you will automatically get all of the necessary constructors and the assignment operator. • all the above-mentioned operations running very fast, regardless of the data size, i.e. as ”O(1)” operations. Indeed, while some structures, like std::vector provide a copy con- structor and an assignment operator, the operations may take considerable time if the data structures are big. But if the structures are put into Ptr<>, the overhead becomes small and independent of the data size. • automatic destruction, even for C structures. See the example below with FILE*. • heterogeneous collections of objects. The standard STL and most other C++ and OpenCV containers can only store objects of the same type and the same size. The classical solution to store objects of different types in the same container is to store pointers to the base class base class t* instead, but when you loose the automatic memory management. Again, by using Ptr() instead of the raw pointers, you can solve the problem. The class Ptr treats the wrapped object as a black box, the reference counter is allocated and managed separately. The only thing the pointer class needs to know about the object is how to deallocate it. This knowledge is incapsulated in Ptr::delete obj() method, which is called when the reference counter becomes 0. If the object is a C++ class instance, no additional coding is needed, because the default implementation of this method calls delete obj;. However, if the object is deallocated in a different way, then the specialized method should be created. For example, if you want to wrap FILE, the delete obj may be implemented as following: template<> inline void Ptr::delete_obj() { fclose(obj); // no need to clear the pointer afterwards, // it is done externally. } ... // now use it: Ptr f(fopen("myfile.txt", "r")); if(f.empty()) throw ...; fprintf(f, ....); ... // the file will be closed automatically by the Ptr destructor. 11.1. BASIC STRUCTURES 491 Note: The reference increment/decrement operations are implemented as atomic operations, and therefore it is normally safe to use the classes in multi-threaded applications. The same is true for Mat and other C++ OpenCV classes that operate on the reference counters. Mat OpenCV C++ n-dimensional dense array class. class CV_EXPORTS Mat { public: // ... a lot of methods ... ... /*! includes several bit-fields: - the magic signature - continuity flag - depth - number of channels */ int flags; //! the array dimensionality, >= 2 int dims; //! the number of rows and columns or (-1, -1) when the array has more than 2 dimensions int rows, cols; //! pointer to the data uchar* data; //! pointer to the reference counter; // when array points to user-allocated data, the pointer is NULL int* refcount; // other members ... }; The class Mat represents an n-dimensional dense numerical single-channel or multi-channel array. It can be used to store real or complex-valued vectors and matrices, grayscale or color im- ages, voxel volumes, vector fields, point clouds, tensors, histograms (though, very high-dimensional histograms may be better stored in a SparseMat). The data layout of array M is defined by the array M.step[], so that the address of element (i0, ..., iM.dims−1), where 0 ≤ ik < M.size[k] is computed as: addr(Mi0,...,iM.dims−1 ) = M.data+M.step[0]∗i0 +M.step[1]∗i1 +...+M.step[M.dims−1]∗iM.dims−1 492 CHAPTER 11. CORE. THE CORE FUNCTIONALITY In the case of 2-dimensional array the above formula is reduced to: addr(Mi,j) = M.data + M.step[0] ∗ i + M.step[1] ∗ j Note that M.step[i] >= M.step[i+1] (in fact, M.step[i] >= M.step[i+1]*M.size[i+1]), that is, 2-dimensional matrices are stored row-by-row, 3-dimensional matrices are stored plane-by- plane etc. M.step[M.dims-1] is minimal and always equal to the element size M.elemSize(). That is, the data layout in Mat is fully compatible with CvMat, IplImage and CvMatND types from OpenCV 1.x, as well as with majority of dense array types from the standard toolkits and SDKs, such as Numpy (ndarray), Win32 (independent device bitmaps) etc, i.e. any other array that uses ”steps”, a.k.a. ”strides”, to compute position of a pixel. Because of such compatibility, it is possible to make a Mat header for user-allocated data and process it in-place using OpenCV functions. There are many different ways to create Mat object. Here are the some popular ones: • using create(nrows, ncols, type) method or the similar constructor Mat(nrows, ncols, type[, fillValue]) constructor. A new array of the specified size and specifed type will be allocated. type has the same meaning as in cv::cvCreateMat method, e.g. CV 8UC1 means 8-bit single-channel array, CV 32FC2 means 2-channel (i.e. complex) floating- point array etc: // make 7x7 complex matrix filled with 1+3j. cv::Mat M(7,7,CV_32FC2,Scalar(1,3)); // and now turn M to 100x60 15-channel 8-bit matrix. // The old content will be deallocated M.create(100,60,CV_8UC(15)); As noted in the introduction of this chapter, create() will only allocate a new array when the current array shape or type are different from the specified. • similarly to above, you can create a multi-dimensional array: // create 100x100x100 8-bit array int sz[] = {100, 100, 100}; cv::Mat bigCube(3, sz, CV_8U, Scalar::all(0)); note that it is pass number of dimensions =1 to the Mat constructor, but the created array will be 2-dimensional, with the number of columns set to 1. That’s why Mat::dims is always ¿= 2 (can also be 0 when the array is empty) • by using a copy constructor or assignment operator, where on the right side it can be a array or expression, see below. Again, as noted in the introduction, array assignment is O(1) operation because it only copies the header and increases the reference counter. Mat::clone() method can be used to get a full (a.k.a. deep) copy of the array when you need it. 11.1. BASIC STRUCTURES 493 • by constructing a header for a part of another array. It can be a single row, single column, several rows, several columns, rectangular region in the array (called a minor in algebra) or a diagonal. Such operations are also O(1), because the new header will reference the same data. You can actually modify a part of the array using this feature, e.g. // add 5-th row, multiplied by 3 to the 3rd row M.row(3) = M.row(3) + M.row(5)*3; // now copy 7-th column to the 1-st column // M.col(1) = M.col(7); // this will not work Mat M1 = M.col(1); M.col(7).copyTo(M1); // create new 320x240 image cv::Mat img(Size(320,240),CV_8UC3); // select a roi cv::Mat roi(img, Rect(10,10,100,100)); // fill the ROI with (0,255,0) (which is green in RGB space); // the original 320x240 image will be modified roi = Scalar(0,255,0); Thanks to the additional datastart and dataend members, it is possible to compute the relative sub-array position in the main ”container” array using locateROI(): Mat A = Mat::eye(10, 10, CV_32S); // extracts A columns, 1 (inclusive) to 3 (exclusive). Mat B = A(Range::all(), Range(1, 3)); // extracts B rows, 5 (inclusive) to 9 (exclusive). // that is, C ˜ A(Range(5, 9), Range(1, 3)) Mat C = B(Range(5, 9), Range::all()); Size size; Point ofs; C.locateROI(size, ofs); // size will be (width=10,height=10) and the ofs will be (x=1, y=5) As in the case of whole matrices, if you need a deep copy, use clone() method of the extracted sub-matrices. • by making a header for user-allocated-data. It can be useful for 1. processing ”foreign” data using OpenCV (e.g. when you implement a DirectShow filter or a processing module for gstreamer etc.), e.g. void process_video_frame(const unsigned char* pixels, int width, int height, int step) { cv::Mat img(height, width, CV_8UC3, pixels, step); 494 CHAPTER 11. CORE. THE CORE FUNCTIONALITY cv::GaussianBlur(img, img, cv::Size(7,7), 1.5, 1.5); } 2. for quick initialization of small matrices and/or super-fast element access double m[3][3] = {{a, b, c}, {d, e, f}, {g, h, i}}; cv::Mat M = cv::Mat(3, 3, CV_64F, m).inv(); partial yet very common cases of this ”user-allocated data” case are conversions from Cv- Mat and IplImage to Mat. For this purpose there are special constructors taking pointers to CvMat or IplImage and the optional flag indicating whether to copy the data or not. Backward conversion from Mat to CvMat or IplImage is provided via cast operators Mat::operator CvMat() const an Mat::operator IplImage(). The operators do not copy the data. IplImage* img = cvLoadImage("greatwave.jpg", 1); Mat mtx(img); // convert IplImage*-> cv::Mat CvMat oldmat = mtx; // convert cv::Mat -> CvMat CV_Assert(oldmat.cols == img->width && oldmat.rows == img->height && oldmat.data.ptr == (uchar*)img->imageData && oldmat.step == img->widthStep); • by using MATLAB-style array initializers, zeros(), ones(), eye(), e.g.: // create a double-precision identity martix and add it to M. M += Mat::eye(M.rows, M.cols, CV_64F); • by using comma-separated initializer: // create 3x3 double-precision identity matrix Mat M = (Mat_(3,3) << 1, 0, 0, 0, 1, 0, 0, 0, 1); here we first call constructor of Mat class (that we describe further) with the proper param- eters, and then we just put << operator followed by comma-separated values that can be constants, variables, expressions etc. Also, note the extra parentheses that are needed to avoid compiler errors. Once array is created, it will be automatically managed by using reference-counting mecha- nism (unless the array header is built on top of user-allocated data, in which case you should handle the data by yourself). The array data will be deallocated when no one points to it; if you want to release the data pointed by a array header before the array destructor is called, use Mat::release(). The next important thing to learn about the array class is element access. Earlier it was shown how to compute address of each array element. Normally, it’s not needed to use the formula directly in your code. If you know the array element type (which can be retrieved using the method Mat::type()), you can access element Mij of 2-dimensional array as: 11.1. BASIC STRUCTURES 495 M.at(i,j) += 1.f; assuming that M is double-precision floating-point array. There are several variants of the method at for different number of dimensions. If you need to process a whole row of a 2d array, the most efficient way is to get the pointer to the row first, and then just use plain C operator []: // compute sum of positive matrix elements // (assuming that M is double-precision matrix) double sum=0; for(int i = 0; i < M.rows; i++) { const double* Mi = M.ptr(i); for(int j = 0; j < M.cols; j++) sum += std::max(Mi[j], 0.); } Some operations, like the above one, do not actually depend on the array shape, they just process elements of an array one by one (or elements from multiple arrays that have the same coordinates, e.g. array addition). Such operations are called element-wise and it makes sense to check whether all the input/output arrays are continuous, i.e. have no gaps in the end of each row, and if yes, process them as a single long row: // compute sum of positive matrix elements, optimized variant double sum=0; int cols = M.cols, rows = M.rows; if(M.isContinuous()) { cols *= rows; rows = 1; } for(int i = 0; i < rows; i++) { const double* Mi = M.ptr(i); for(int j = 0; j < cols; j++) sum += std::max(Mi[j], 0.); } in the case of continuous matrix the outer loop body will be executed just once, so the overhead will be smaller, which will be especially noticeable in the case of small matrices. Finally, there are STL-style iterators that are smart enough to skip gaps between successive rows: // compute sum of positive matrix elements, iterator-based variant double sum=0; MatConstIterator_ it = M.begin(), it_end = M.end(); 496 CHAPTER 11. CORE. THE CORE FUNCTIONALITY for(; it != it_end; ++it) sum += std::max(*it, 0.); The matrix iterators are random-access iterators, so they can be passed to any STL algorithm, including std::sort(). Matrix Expressions This is a list of implemented matrix operations that can be combined in arbitrary complex expres- sions (here A,B stand for matrices (Mat), s for a scalar (Scalar), α for a real-valued scalar (double)): • addition, subtraction, negation: A ± B,A ± s, s ± A, −A • scaling: A ∗ α,A ∗ α • per-element multiplication and division: A.mul(B), A/B, α/A • matrix multiplication: A ∗ B • transposition: A.t() ∼ At • matrix inversion and pseudo-inversion, solving linear systems and least-squares problems: A.inv([method]) ∼ A−1, A.inv([method]) ∗ B ∼ X: AX = B • comparison: ATB,A 6= B,AT α, A 6= α. The result of comparison is 8-bit single channel mask, which elements are set to 255 (if the particular element or pair of elements satisfy the condition) and 0 otherwise. • bitwise logical operations: A & B, A & s, A | B, A | s, A ˆ B, A ˆ s, ˜A • element-wise minimum and maximum: min(A, B), min(A, α), max(A, B), max(A, α) • element-wise absolute value: abs(A) • cross-product, dot-product: A.cross(B), A.dot(B) • any function of matrix or matrices and scalars that returns a matrix or a scalar, such as cv::norm, cv::mean, cv::sum, cv::countNonZero, cv::trace, cv::determinant, cv::repeat etc. • matrix initializers (eye(), zeros(), ones()), matrix comma-separated initializers, ma- trix constructors and operators that extract sub-matrices (see Mat description). • Mat_() constructors to cast the result to the proper type. 11.1. BASIC STRUCTURES 497 Note, however, that comma-separated initializers and probably some other operations may require additional explicit Mat() or Mat_() constuctor calls to resolve possible ambiguity. Below is the formal description of the Mat methods. cv::Mat::Mat (view/add comments) Various array constructors (1) Mat::Mat(); (2) Mat::Mat(int rows, int cols, int type); (3) Mat::Mat(Size size, int type); (4) Mat::Mat(int rows, int cols, int type, const Scalar& s); (5) Mat::Mat(Size size, int type, const Scalar& s); (6) Mat::Mat(const Mat& m); (7) Mat::Mat(int rows, int cols, int type, void* data, size t step=AUTO STEP); (8) Mat::Mat(Size size, int type, void* data, size t step=AUTO STEP); (9) Mat::Mat(const Mat& m, const Range& rowRange, const Range& colRange); (10) Mat::Mat(const Mat& m, const Rect& roi); (11) Mat::Mat(const CvMat* m, bool copyData=false); (12) Mat::Mat(const IplImage* img, bool copyData=false); (13) template explicit Mat::Mat(const Vec& vec, bool copyData=true); (14) template explicit Mat::Mat(const Matx& vec, bool copyData=true); (15) template explicit Mat::Mat(const vector& vec, bool copyData=false); (16) Mat::Mat(const MatExpr& expr); (17) Mat::Mat(int ndims, const int* sizes, int type); (18) Mat::Mat(int ndims, const int* sizes, int type, const Scalar& s); (19) Mat::Mat(int ndims, const int* sizes, int type, void* data, const size t* steps=0); (20) Mat::Mat(const Mat& m, const Range* ranges); ndims The array dimensionality rows The number of rows in 2D array 498 CHAPTER 11. CORE. THE CORE FUNCTIONALITY cols The number of columns in 2D array size The 2D array size: Size(cols, rows). Note that in the Size() constructor the number of rows and the number of columns go in the reverse order. sizes The array of integers, specifying the n-dimensional array shape type The array type, use CV 8UC1, ..., CV 64FC4 to create 1-4 channel matrices, or CV 8UC(n), ..., CV 64FC(n) to create multi-channel (up to CV MAX CN channels) matrices s The optional value to initialize each matrix element with. To set all the matrix elements to the par- ticular value after the construction, use the assignment operator Mat::operator=(const Scalar& value). data Pointer to the user data. Matrix constructors that take data and step parameters do not allocate matrix data. Instead, they just initialize the matrix header that points to the specified data, i.e. no data is copied. This operation is very efficient and can be used to process external data using OpenCV functions. The external data is not automatically deallocated, user should take care of it. step The data buddy. This optional parameter specifies the number of bytes that each matrix row occupies. The value should include the padding bytes in the end of each row, if any. If the parameter is missing (set to cv::AUTO STEP), no padding is assumed and the actual step is calculated as cols*elemSize(), see Mat::elemSize (). steps The array of ndims-1 steps in the case of multi-dimensional array (the last step is always set to the element size). If not specified, the matrix is assumed to be continuous. m The array that (in whole, a partly) is assigned to the constructed matrix. No data is copied by these constructors. Instead, the header pointing to m data, or its sub-array, is constructed and the associated with it reference counter, if any, is incremented. That is, when you modify the matrix formed using such a constructor, you will also modify the corresponding elements of m. If you want to have an independent copy of the sub-array, use Mat::clone(). img Pointer to the old-style IplImage image structure. By default, the data is shared between the original image and the new matrix, but when copyData is set, the full copy of the image data is created. vec STL vector, which elements will form the matrix. The matrix will have a single column and the number of rows equal to the number of vector elements. Type of the matrix will match the type of vector elements. The constructor can handle arbitrary types, for which there is properly declared DataType , i.e. the vector elements must be primitive numbers or uni-type numerical tuples of numbers. Mixed-type structures are not supported, of course. Note that 11.1. BASIC STRUCTURES 499 the corresponding constructor is explicit, meaning that STL vectors are not automatically converted to Mat instances, you should write Mat(vec) explicitly. Another obvious note: unless you copied the data into the matrix (copyData=true), no new elements should be added to the vector, because it can potentially yield vector data reallocation, and thus the matrix data pointer will become invalid. copyData Specifies, whether the underlying data of the STL vector, or the old-style CvMat or IplImage should be copied to (true) or shared with (false) the newly constructed matrix. When the data is copied, the allocated buffer will be managed using Mat’s reference counting mechanism. While when the data is shared, the reference counter will be NULL, and you should not deallocate the data until the matrix is not destructed. rowRange The range of the m’s rows to take. As usual, the range start is inclusive and the range end is exclusive. Use Range::all() to take all the rows. colRange The range of the m’s columns to take. Use Range::all() to take all the columns. ranges The array of selected ranges of m along each dimensionality . expr Matrix expression. See Matrix Expressions. These are various constructors that form a matrix. As noticed in theoften the default construc- tor is enough, and the proper matrix will be allocated by an OpenCV function. The constructed matrix can further be assigned to another matrix or matrix expression, in which case the old con- tent is dereferenced, or be allocated with Mat::create. cv::Mat::Mat (view/add comments) Matrix destructor Mat::˜Mat(); The matrix destructor calls Mat::release. cv::Mat::operator = (view/add comments) Matrix assignment operators 500 CHAPTER 11. CORE. THE CORE FUNCTIONALITY Mat& Mat::operator = (const Mat& m); Mat& Mat::operator = (const MatExpr Base& expr); Mat& operator = (const Scalar& s); m The assigned, right-hand-side matrix. Matrix assignment is O(1) operation, that is, no data is copied. Instead, the data is shared and the reference counter, if any, is incremented. Before assigning new data, the old data is dereferenced via Mat::release. expr The assigned matrix expression object. As opposite to the first form of assignment opera- tion, the second form can reuse already allocated matrix if it has the right size and type to fit the matrix expression result. It is automatically handled by the real function that the matrix expressions is expanded to. For example, C=A+B is expanded to cv::add(A, B, C), and cv::add will take care of automatic C reallocation. s The scalar, assigned to each matrix element. The matrix size or type is not changed. These are the available assignment operators, and they all are very different, so, please, look at the operator parameters description. cv::Mat::operator MatExpr (view/add comments) Mat-to-MatExpr cast operator Mat::operator MatExpr () const; The cast operator should not be called explicitly. It is used internally by the Matrix Expressions engine. cv::Mat::row (view/add comments) Makes a matrix header for the specified matrix row Mat Mat::row(int i) const; 11.1. BASIC STRUCTURES 501 i the 0-based row index The method makes a new header for the specified matrix row and returns it. This is O(1) operation, regardless of the matrix size. The underlying data of the new matrix will be shared with the original matrix. Here is the example of one of the classical basic matrix processing operations, axpy, used by LU and many other algorithms: inline void matrix_axpy(Mat& A, int i, int j, double alpha) { A.row(i) += A.row(j)*alpha; } Important note. In the current implementation the following code will not work as expected: Mat A; ... A.row(i) = A.row(j); // will not work This is because A.row(i) forms a temporary header, which is further assigned another header. Remember, each of these operations is O(1), i.e. no data is copied. Thus, the above assignment will have absolutely no effect, while you may have expected j-th row being copied to i-th row. To achieve that, you should either turn this simple assignment into an expression, or use Mat::copyTo method: Mat A; ... // works, but looks a bit obscure. A.row(i) = A.row(j) + 0; // this is a bit longer, but the recommended method. Mat Ai = A.row(i); M.row(j).copyTo(Ai); cv::Mat::col (view/add comments) Makes a matrix header for the specified matrix column Mat Mat::col(int j) const; j the 0-based column index The method makes a new header for the specified matrix column and returns it. This is O(1) operation, regardless of the matrix size. The underlying data of the new matrix will be shared with the original matrix. See also Mat::row description. 502 CHAPTER 11. CORE. THE CORE FUNCTIONALITY cv::Mat::rowRange (view/add comments) Makes a matrix header for the specified row span Mat Mat::rowRange(int startrow, int endrow) const; Mat Mat::rowRange(const Range& r) const; startrow the 0-based start index of the row span endrow the 0-based ending index of the row span r The cv::Range structure containing both the start and the end indices The method makes a new header for the specified row span of the matrix. Similarly to cv::Mat::row and cv::Mat::col, this is O(1) operation. cv::Mat::colRange (view/add comments) Makes a matrix header for the specified row span Mat Mat::colRange(int startcol, int endcol) const; Mat Mat::colRange(const Range& r) const; startcol the 0-based start index of the column span endcol the 0-based ending index of the column span r The cv::Range structure containing both the start and the end indices The method makes a new header for the specified column span of the matrix. Similarly to cv::Mat::row and cv::Mat::col, this is O(1) operation. cv::Mat::diag (view/add comments) Extracts diagonal from a matrix, or creates a diagonal matrix. 11.1. BASIC STRUCTURES 503 Mat Mat::diag(int d) const; static Mat Mat::diag(const Mat& matD); d index of the diagonal, with the following meaning: d=0 the main diagonal d>0 a diagonal from the lower half, e.g. d=1 means the diagonal immediately below the main one d<0 a diagonal from the upper half, e.g. d=1 means the diagonal immediately above the main one matD single-column matrix that will form the diagonal matrix. The method makes a new header for the specified matrix diagonal. The new matrix will be represented as a single-column matrix. Similarly to cv::Mat::row and cv::Mat::col, this is O(1) operation. cv::Mat::clone (view/add comments) Creates full copy of the array and the underlying data. Mat Mat::clone() const; The method creates full copy of the array. The original step[] are not taken into the account. That is, the array copy will be a continuous array occupying total()*elemSize() bytes. cv::Mat::copyTo (view/add comments) Copies the matrix to another one. void Mat::copyTo( Mat& m ) const; void Mat::copyTo( Mat& m, const Mat& mask ) const; 504 CHAPTER 11. CORE. THE CORE FUNCTIONALITY m The destination matrix. If it does not have a proper size or type before the operation, it will be reallocated mask The operation mask. Its non-zero elements indicate, which matrix elements need to be copied The method copies the matrix data to another matrix. Before copying the data, the method invokes m.create(this->size(), this->type); so that the destination matrix is reallocated if needed. While m.copyTo(m); will work as expected, i.e. will have no effect, the function does not handle the case of a partial overlap between the source and the destination matrices. When the operation mask is specified, and the Mat::create call shown above reallocated the matrix, the newly allocated matrix is initialized with all 0’s before copying the data. cv::Mat::convertTo (view/add comments) Converts array to another datatype with optional scaling. void Mat::convertTo( Mat& m, int rtype, double alpha=1, double beta=0 ) const; m The destination matrix. If it does not have a proper size or type before the operation, it will be reallocated rtype The desired destination matrix type, or rather, the depth (since the number of channels will be the same with the source one). If rtype is negative, the destination matrix will have the same type as the source. alpha The optional scale factor beta The optional delta, added to the scaled values. The method converts source pixel values to the target datatype. saturate cast<> is applied in the end to avoid possible overflows: m(x, y) = saturate cast < rT ype > (α(∗this)(x, y) + β) 11.1. BASIC STRUCTURES 505 cv::Mat::assignTo (view/add comments) Functional form of convertTo void Mat::assignTo( Mat& m, int type=-1 ) const; m The destination array type The desired destination array depth (or -1 if it should be the same as the source one). This is internal-use method called by the Matrix Expressions engine. cv::Mat::setTo (view/add comments) Sets all or some of the array elements to the specified value. Mat& Mat::setTo(const Scalar& s, const Mat& mask=Mat()); s Assigned scalar, which is converted to the actual array type mask The operation mask of the same size as *this This is the advanced variant of Mat::operator=(const Scalar& s) operator. cv::Mat::reshape (view/add comments) Changes the 2D matrix’s shape and/or the number of channels without copying the data. Mat Mat::reshape(int cn, int rows=0) const; cn The new number of channels. If the parameter is 0, the number of channels remains the same. rows The new number of rows. If the parameter is 0, the number of rows remains the same. 506 CHAPTER 11. CORE. THE CORE FUNCTIONALITY The method makes a new matrix header for *this elements. The new matrix may have different size and/or different number of channels. Any combination is possible, as long as: 1. No extra elements is included into the new matrix and no elements are excluded. Conse- quently, the product rows*cols*channels() must stay the same after the transformation. 2. No data is copied, i.e. this is O(1) operation. Consequently, if you change the number of rows, or the operation changes elements’ row indices in some other way, the matrix must be continuous. See cv::Mat::isContinuous. Here is some small example. Assuming, there is a set of 3D points that are stored as STL vector, and you want to represent the points as 3xN matrix. Here is how it can be done: std::vector vec; ... Mat pointMat = Mat(vec). // convert vector to Mat, O(1) operation reshape(1). // make Nx3 1-channel matrix out of Nx1 3-channel. // Also, an O(1) operation t(); // finally, transpose the Nx3 matrix. // This involves copying of all the elements cv::Mat::t (view/add comments) Transposes the matrix MatExpr Mat::t() const; The method performs matrix transposition by means of matrix expressions. It does not perform the actual transposition, but returns a temporary ”matrix transposition” object that can be further used as a part of more complex matrix expression or be assigned to a matrix: Mat A1 = A + Mat::eye(A.size(), A.type)*lambda; Mat C = A1.t()*A1; // compute (A + lambda*I)ˆt *(A + lamda*I) cv::Mat::inv (view/add comments) Inverses the matrix 11.1. BASIC STRUCTURES 507 MatExpr Mat::inv(int method=DECOMP LU) const; method The matrix inversion method, one of DECOMP LU LU decomposition. The matrix must be non-singular DECOMP CHOLESKY Cholesky LLT decomposition, for symmetrical positively defined matri- ces only. About twice faster than LU on big matrices. DECOMP SVD SVD decomposition. The matrix can be a singular or even non-square, then the pseudo-inverse is computed The method performs matrix inversion by means of matrix expressions, i.e. a temporary ”matrix inversion” object is returned by the method, and can further be used as a part of more complex matrix expression or be assigned to a matrix. cv::Mat::mul (view/add comments) Performs element-wise multiplication or division of the two matrices MatExpr Mat::mul(const Mat& m, double scale=1) const; MatExpr Mat::mul(const MatExpr& m, double scale=1) const; m Another matrix, of the same type and the same size as *this, or a matrix expression scale The optional scale factor The method returns a temporary object encoding per-element array multiplication, with optional scale. Note that this is not a matrix multiplication, which corresponds to a simpler ”*” operator. Here is a example: Mat C = A.mul(5/B); // equivalent to divide(A, B, C, 5) 508 CHAPTER 11. CORE. THE CORE FUNCTIONALITY cv::Mat::cross (view/add comments) Computes cross-product of two 3-element vectors Mat Mat::cross(const Mat& m) const; m Another cross-product operand The method computes cross-product of the two 3-element vectors. The vectors must be 3- elements floating-point vectors of the same shape and the same size. The result will be another 3-element vector of the same shape and the same type as operands. cv::Mat::dot (view/add comments) Computes dot-product of two vectors double Mat::dot(const Mat& m) const; m Another dot-product operand. The method computes dot-product of the two matrices. If the matrices are not single-column or single-row vectors, the top-to-bottom left-to-right scan ordering is used to treat them as 1D vectors. The vectors must have the same size and the same type. If the matrices have more than one channel, the dot products from all the channels are summed together. cv::Mat::zeros (view/add comments) Returns zero array of the specified size and type static MatExpr Mat::zeros(int rows, int cols, int type); static MatExpr Mat::zeros(Size size, int type); static MatExpr Mat::zeros(int ndims, const int* sizes, int type); 11.1. BASIC STRUCTURES 509 ndims The array dimensionality rows The number of rows cols The number of columns size Alternative matrix size specification: Size(cols, rows) sizes The array of integers, specifying the array shape type The created matrix type The method returns Matlab-style zero array initializer. It can be used to quickly form a constant array and use it as a function parameter, as a part of matrix expression, or as a matrix initializer. Mat A; A = Mat::zeros(3, 3, CV_32F); Note that in the above sample a new matrix will be allocated only if A is not 3x3 floating-point matrix, otherwise the existing matrix A will be filled with 0’s. cv::Mat::ones (view/add comments) Returns array of all 1’s of the specified size and type static MatExpr Mat::ones(int rows, int cols, int type); static MatExpr Mat::ones(Size size, int type); static MatExpr Mat::ones(int ndims, const int* sizes, int type); ndims The array dimensionality rows The number of rows cols The number of columns size Alternative matrix size specification: Size(cols, rows) sizes The array of integers, specifying the array shape type The created matrix type The method returns Matlab-style ones’ array initializer, similarly to cv::Mat::zeros. Note that using this method you can initialize an array with arbitrary value, using the following Matlab idiom: 510 CHAPTER 11. CORE. THE CORE FUNCTIONALITY Mat A = Mat::ones(100, 100, CV_8U)*3; // make 100x100 matrix filled with 3. The above operation will not form 100x100 matrix of ones and then multiply it by 3. Instead, it will just remember the scale factor (3 in this case) and use it when actually invoking the matrix initializer. cv::Mat::eye (view/add comments) Returns identity matrix of the specified size and type static MatExpr Mat::eye(int rows, int cols, int type); static MatExpr Mat::eye(Size size, int type); rows The number of rows cols The number of columns size Alternative matrix size specification: Size(cols, rows) type The created matrix type The method returns Matlab-style identity matrix initializer, similarly to cv::Mat::zeros. Similarly to Mat::ones, you can use a scale operation to create a scaled identity matrix efficiently: // make a 4x4 diagonal matrix with 0.1’s on the diagonal. Mat A = Mat::eye(4, 4, CV_32F)*0.1; cv::Mat::create (view/add comments) Allocates new array data if needed. void Mat::create(int rows, int cols, int type); void Mat::create(Size size, int type); void Mat::create(int ndims, const int* sizes, int type); ndims The new array dimensionality 11.1. BASIC STRUCTURES 511 rows The new number of rows cols The new number of columns size Alternative new matrix size specification: Size(cols, rows) sizes The array of integers, specifying the new array shape type The new matrix type This is one of the key Mat methods. Most new-style OpenCV functions and methods that produce arrays call this method for each output array. The method uses the following algorithm: 1. if the current array shape and the type match the new ones, return immediately. 2. otherwise, dereference the previous data by calling cv::Mat::release 3. initialize the new header 4. allocate the new data of total()*elemSize() bytes 5. allocate the new, associated with the data, reference counter and set it to 1. Such a scheme makes the memory management robust and efficient at the same time, and also saves quite a bit of typing for the user, i.e. usually there is no need to explicitly allocate output arrays. That is, instead of writing: Mat color; ... Mat gray(color.rows, color.cols, color.depth()); cvtColor(color, gray, CV_BGR2GRAY); you can simply write: Mat color; ... Mat gray; cvtColor(color, gray, CV_BGR2GRAY); because cvtColor, as well as most of OpenCV functions, calls Mat::create() for the output array internally. cv::Mat::addref (view/add comments) Increments the reference counter 512 CHAPTER 11. CORE. THE CORE FUNCTIONALITY void Mat::addref(); The method increments the reference counter, associated with the matrix data. If the matrix header points to an external data (see cv::Mat::Mat), the reference counter is NULL, and the method has no effect in this case. Normally, the method should not be called explicitly, to avoid memory leaks. It is called implicitly by the matrix assignment operator. The reference counter increment is the atomic operation on the platforms that support it, thus it is safe to operate on the same matrices asynchronously in different threads. cv::Mat::release (view/add comments) Decrements the reference counter and deallocates the matrix if needed void Mat::release(); The method decrements the reference counter, associated with the matrix data. When the reference counter reaches 0, the matrix data is deallocated and the data and the reference counter pointers are set to NULL’s. If the matrix header points to an external data (see cv::Mat::Mat), the reference counter is NULL, and the method has no effect in this case. This method can be called manually to force the matrix data deallocation. But since this method is automatically called in the destructor, or by any other method that changes the data pointer, it is usually not needed. The reference counter decrement and check for 0 is the atomic operation on the platforms that support it, thus it is safe to operate on the same matrices asynchronously in different threads. cv::Mat::resize (view/add comments) Changes the number of matrix rows void Mat::resize( size t sz ) const; sz The new number of rows 11.1. BASIC STRUCTURES 513 The method changes the number of matrix rows. If the matrix is reallocated, the first min(Mat::rows, sz) rows are preserved. The method emulates the corresponding method of STL vector class. Mat::push back (view/add comments) Adds elements to the bottom of the matrix template void Mat::push back(const T& elem); template void Mat::push back(const Mat & elem); elem The added element(s). The methods add one or more elements to the bottom of the matrix. They emulate the cor- responding method of STL vector class. When elem is Mat, its type and the number of columns must be the same as in the container matrix. Mat::pop back (view/add comments) Removes elements from the bottom of the matrix. template void Mat::pop back(size t nelems=1); nelems The number of rows removed. If it is greater than the total number of rows, an exception is thrown. The method removes one or more rows from the bottom of the matrix. cv::Mat::locateROI (view/add comments) Locates matrix header within a parent matrix void Mat::locateROI( Size& wholeSize, Point& ofs ) const; 514 CHAPTER 11. CORE. THE CORE FUNCTIONALITY wholeSize The output parameter that will contain size of the whole matrix, which *this is a part of. ofs The output parameter that will contain offset of *this inside the whole matrix After you extracted a submatrix from a matrix using cv::Mat::row, cv::Mat::col, cv::Mat::rowRange, cv::Mat::colRange etc., the result submatrix will point just to the part of the original big matrix. However, each submatrix contains some information (represented by datastart and dataend fields), using which it is possible to reconstruct the original matrix size and the position of the extracted submatrix within the original matrix. The method locateROI does exactly that. cv::Mat::adjustROI (view/add comments) Adjust submatrix size and position within the parent matrix Mat& Mat::adjustROI( int dtop, int dbottom, int dleft, int dright ); dtop The shift of the top submatrix boundary upwards dbottom The shift of the bottom submatrix boundary downwards dleft The shift of the left submatrix boundary to the left dright The shift of the right submatrix boundary to the right The method is complimentary to the cv::Mat::locateROI. Indeed, the typical use of these func- tions is to determine the submatrix position within the parent matrix and then shift the position somehow. Typically it can be needed for filtering operations, when pixels outside of the ROI should be taken into account. When all the method’s parameters are positive, it means that the ROI needs to grow in all directions by the specified amount, i.e. A.adjustROI(2, 2, 2, 2); increases the matrix size by 4 elements in each direction and shifts it by 2 elements to the left and 2 elements up, which brings in all the necessary pixels for the filtering with 5x5 kernel. It’s user responsibility to make sure that adjustROI does not cross the parent matrix boundary. If it does, the function will signal an error. The function is used internally by the OpenCV filtering functions, like cv::filter2D, morphologi- cal operations etc. See also cv::copyMakeBorder. 11.1. BASIC STRUCTURES 515 cv::Mat::operator() (view/add comments) Extracts a rectangular submatrix Mat Mat::operator()( Range rowRange, Range colRange ) const; Mat Mat::operator()( const Rect& roi ) const; Mat Mat::operator()( const Ranges* ranges ) const; rowRange The start and the end row of the extracted submatrix. The upper boundary is not included. To select all the rows, use Range::all() colRange The start and the end column of the extracted submatrix. The upper boundary is not included. To select all the columns, use Range::all() roi The extracted submatrix specified as a rectangle ranges The array of selected ranges along each array dimension The operators make a new header for the specified sub-array of *this. They are the most generalized forms of cv::Mat::row, cv::Mat::col, cv::Mat::rowRange and cv::Mat::colRange. For example, A(Range(0, 10), Range::all()) is equivalent to A.rowRange(0, 10). Simi- larly to all of the above, the operators are O(1) operations, i.e. no matrix data is copied. cv::Mat::operator CvMat (view/add comments) Creates CvMat header for the matrix Mat::operator CvMat() const; The operator makes CvMat header for the matrix without copying the underlying data. The reference counter is not taken into account by this operation, thus you should make sure than the original matrix is not deallocated while the CvMat header is used. The operator is useful for intermixing the new and the old OpenCV API’s, e.g: Mat img(Size(320, 240), CV_8UC3); ... 516 CHAPTER 11. CORE. THE CORE FUNCTIONALITY CvMat cvimg = img; mycvOldFunc( &cvimg, ...); where mycvOldFunc is some function written to work with OpenCV 1.x data structures. cv::Mat::operator IplImage (view/add comments) Creates IplImage header for the matrix Mat::operator IplImage() const; The operator makes IplImage header for the matrix without copying the underlying data. You should make sure than the original matrix is not deallocated while the IplImage header is used. Similarly to Mat::operator CvMat, the operator is useful for intermixing the new and the old OpenCV API’s. cv::Mat::total (view/add comments) Returns the total number of array elements. size t Mat::total() const; The method returns the number of array elements (e.g. number of pixels if the array represents an image). cv::Mat::isContinuous (view/add comments) Reports whether the matrix is continuous or not bool Mat::isContinuous() const; 11.1. BASIC STRUCTURES 517 The method returns true if the matrix elements are stored continuously, i.e. without gaps in the end of each row, and false otherwise. Obviously, 1x1 or 1xN matrices are always continuous. Matrices created with cv::Mat::create are always continuous, but if you extract a part of the matrix using cv::Mat::col, cv::Mat::diag etc. or constructed a matrix header for externally allocated data, such matrices may no longer have this property. The continuity flag is stored as a bit in Mat::flags field, and is computed automatically when you construct a matrix header, thus the continuity check is very fast operation, though it could be, in theory, done as following: // alternative implementation of Mat::isContinuous() bool myCheckMatContinuity(const Mat& m) { //return (m.flags & Mat::CONTINUOUS_FLAG) != 0; return m.rows == 1 || m.step == m.cols*m.elemSize(); } The method is used in a quite a few of OpenCV functions, and you are welcome to use it as well. The point is that element-wise operations (such as arithmetic and logical operations, math functions, alpha blending, color space transformations etc.) do not depend on the image geometry, and thus, if all the input and all the output arrays are continuous, the functions can process them as very long single-row vectors. Here is the example of how alpha-blending function can be implemented. template void alphaBlendRGBA(const Mat& src1, const Mat& src2, Mat& dst) { const float alpha_scale = (float)std::numeric_limits::max(), inv_scale = 1.f/alpha_scale; CV_Assert( src1.type() == src2.type() && src1.type() == CV_MAKETYPE(DataType::depth, 4) && src1.size() == src2.size()); Size size = src1.size(); dst.create(size, src1.type()); // here is the idiom: check the arrays for continuity and, // if this is the case, // treat the arrays as 1D vectors if( src1.isContinuous() && src2.isContinuous() && dst.isContinuous() ) { size.width *= size.height; size.height = 1; } size.width *= 4; 518 CHAPTER 11. CORE. THE CORE FUNCTIONALITY for( int i = 0; i < size.height; i++ ) { // when the arrays are continuous, // the outer loop is executed only once const T* ptr1 = src1.ptr(i); const T* ptr2 = src2.ptr(i); T* dptr = dst.ptr(i); for( int j = 0; j < size.width; j += 4 ) { float alpha = ptr1[j+3]*inv_scale, beta = ptr2[j+3]*inv_scale; dptr[j] = saturate_cast(ptr1[j]*alpha + ptr2[j]*beta); dptr[j+1] = saturate_cast(ptr1[j+1]*alpha + ptr2[j+1]*beta); dptr[j+2] = saturate_cast(ptr1[j+2]*alpha + ptr2[j+2]*beta); dptr[j+3] = saturate_cast((1 - (1-alpha)*(1-beta))*alpha_scale); } } } This trick, while being very simple, can boost performance of a simple element-operation by 10-20 percents, especially if the image is rather small and the operation is quite simple. Also, note that we use another OpenCV idiom in this function - we call cv::Mat::create for the destination array instead of checking that it already has the proper size and type. And while the newly allocated arrays are always continuous, we still check the destination array, because cv::create does not always allocate a new matrix. cv::Mat::elemSize (view/add comments) Returns matrix element size in bytes size t Mat::elemSize() const; The method returns the matrix element size in bytes. For example, if the matrix type is CV 16SC3, the method will return 3*sizeof(short) or 6. cv::Mat::elemSize1 (view/add comments) Returns size of each matrix element channel in bytes 11.1. BASIC STRUCTURES 519 size t Mat::elemSize1() const; The method returns the matrix element channel size in bytes, that is, it ignores the number of channels. For example, if the matrix type is CV 16SC3, the method will return sizeof(short) or 2. cv::Mat::type (view/add comments) Returns matrix element type int Mat::type() const; The method returns the matrix element type, an id, compatible with the CvMat type system, like CV 16SC3 or 16-bit signed 3-channel array etc. cv::Mat::depth (view/add comments) Returns matrix element depth int Mat::depth() const; The method returns the matrix element depth id, i.e. the type of each individual channel. For example, for 16-bit signed 3-channel array the method will return CV 16S. The complete list of matrix types: • CV 8U - 8-bit unsigned integers (0..255) • CV 8S - 8-bit signed integers (-128..127) • CV 16U - 16-bit unsigned integers (0..65535) • CV 16S - 16-bit signed integers (-32768..32767) • CV 32S - 32-bit signed integers (-2147483648..2147483647) 520 CHAPTER 11. CORE. THE CORE FUNCTIONALITY • CV 32F - 32-bit floating-point numbers (-FLT MAX..FLT MAX, INF, NAN) • CV 64F - 64-bit floating-point numbers (-DBL MAX..DBL MAX, INF, NAN) cv::Mat::channels (view/add comments) Returns matrix element depth int Mat::channels() const; The method returns the number of matrix channels. cv::Mat::step1 (view/add comments) Returns normalized step size t Mat::step1() const; The method returns the matrix step, divided by cv::Mat::elemSize1(). It can be useful for fast access to arbitrary matrix element. cv::Mat::size (view/add comments) Returns the matrix size Size Mat::size() const; The method returns the matrix size: Size(cols, rows). 11.1. BASIC STRUCTURES 521 cv::Mat::empty (view/add comments) Returns true if the array has no elemens bool Mat::empty() const; The method returns true if Mat::total() is 0 or if Mat::data is NULL. Because of pop back() and resize() methods M.total() == 0 does not imply that M.data == NULL. cv::Mat::ptr (view/add comments) Return pointer to the specified matrix row uchar* Mat::ptr(int i=0); const uchar* Mat::ptr(int i=0) const; template Tp* Mat::ptr(int i=0); template const Tp* Mat::ptr(int i=0) const; i The 0-based row index The methods return uchar* or typed pointer to the specified matrix row. See the sample in cv::Mat::isContinuous() on how to use these methods. cv::Mat::at (view/add comments) Return reference to the specified array element template T& Mat::at(int i) const; template const T& Mat::at(int i) const; template T& Mat::at(int i, int j); template const T& Mat::at(int i, int j) const; 522 CHAPTER 11. CORE. THE CORE FUNCTIONALITY template T& Mat::at(Point pt); template const T& Mat::at(Point pt) const; template T& Mat::at(int i, int j, int k); template const T& Mat::at(int i, int j, int k) const; template T& Mat::at(const int* idx); template const T& Mat::at(const int* idx) const; i, j, k Indices along the dimensions 0, 1 and 2, respectively pt The element position specified as Point(j,i) idx The array of Mat::dims indices The template methods return reference to the specified array element. For the sake of higher performance the index range checks are only performed in Debug configuration. Note that the variants with a single index (i) can be used to access elements of single-row or single-column 2-dimensional arrays. That is, if, for example, A is 1 x N floating-point matrix and B is M x 1 integer matrix, you can simply write A.at(k+4) and B.at(2*i+1) instead of A.at(0,k+4) and B.at(2*i+1,0), respectively. Here is an example of initialization of a Hilbert matrix: Mat H(100, 100, CV_64F); for(int i = 0; i < H.rows; i++) for(int j = 0; j < H.cols; j++) H.at(i,j)=1./(i+j+1); cv::Mat::begin (view/add comments) Return the matrix iterator, set to the first matrix element template MatIterator < Tp> Mat::begin(); template MatConstIterator < Tp> Mat::begin() const; The methods return the matrix read-only or read-write iterators. The use of matrix iterators is very similar to the use of bi-directional STL iterators. Here is the alpha blending function rewritten using the matrix iterators: 11.1. BASIC STRUCTURES 523 template void alphaBlendRGBA(const Mat& src1, const Mat& src2, Mat& dst) { typedef Vec VT; const float alpha_scale = (float)std::numeric_limits::max(), inv_scale = 1.f/alpha_scale; CV_Assert( src1.type() == src2.type() && src1.type() == DataType::type && src1.size() == src2.size()); Size size = src1.size(); dst.create(size, src1.type()); MatConstIterator_ it1 = src1.begin(), it1_end = src1.end(); MatConstIterator_ it2 = src2.begin(); MatIterator_ dst_it = dst.begin(); for( ; it1 != it1_end; ++it1, ++it2, ++dst_it ) { VT pix1 = *it1, pix2 = *it2; float alpha = pix1[3]*inv_scale, beta = pix2[3]*inv_scale; *dst_it = VT(saturate_cast(pix1[0]*alpha + pix2[0]*beta), saturate_cast(pix1[1]*alpha + pix2[1]*beta), saturate_cast(pix1[2]*alpha + pix2[2]*beta), saturate_cast((1 - (1-alpha)*(1-beta))*alpha_scale)); } } cv::Mat::end (view/add comments) Return the matrix iterator, set to the after-last matrix element template MatIterator < Tp> Mat::end(); template MatConstIterator < Tp> Mat::end() const; The methods return the matrix read-only or read-write iterators, set to the point following the last matrix element. 524 CHAPTER 11. CORE. THE CORE FUNCTIONALITY Mat Template matrix class derived from Mat template class Mat_ : public Mat { public: // ... some specific methods // and // no new extra fields }; The class Mat < Tp> is a ”thin” template wrapper on top of Mat class. It does not have any extra data fields, nor it or Mat have any virtual methods and thus references or pointers to these two classes can be freely converted one to another. But do it with care, e.g.: // create 100x100 8-bit matrix Mat M(100,100,CV_8U); // this will compile fine. no any data conversion will be done. Mat_& M1 = (Mat_&)M; // the program will likely crash at the statement below M1(99,99) = 1.f; While Mat is sufficient in most cases, Mat can be more convenient if you use a lot of element access operations and if you know matrix type at compile time. Note that Mat::at< Tp>(int y, int x) and Mat < Tp>::operator ()(int y, int x) do absolutely the same and run at the same speed, but the latter is certainly shorter: Mat_ M(20,20); for(int i = 0; i < M.rows; i++) for(int j = 0; j < M.cols; j++) M(i,j) = 1./(i+j+1); Mat E, V; eigen(M,E,V); cout << E.at(0,0)/E.at(M.rows-1,0); How to use Mat for multi-channel images/matrices? This is simple - just pass Vec as Mat parameter: // allocate 320x240 color image and fill it with green (in RGB space) Mat_ img(240, 320, Vec3b(0,255,0)); // now draw a diagonal white line for(int i = 0; i < 100; i++) img(i,i)=Vec3b(255,255,255); // and now scramble the 2nd (red) channel of each pixel for(int i = 0; i < img.rows; i++) for(int j = 0; j < img.cols; j++) img(i,j)[2] ˆ= (uchar)(i ˆ j); 11.1. BASIC STRUCTURES 525 NAryMatIterator n-ary multi-dimensional array iterator class CV_EXPORTS NAryMatIterator { public: //! the default constructor NAryMatIterator(); //! the full constructor taking arbitrary number of n-dim matrices NAryMatIterator(const Mat** arrays, Mat* planes, int narrays=-1); //! the separate iterator initialization method void init(const Mat** arrays, Mat* planes, int narrays=-1); //! proceeds to the next plane of every iterated matrix NAryMatIterator& operator ++(); //! proceeds to the next plane of every iterated matrix (postfix increment operator) NAryMatIterator operator ++(int); ... int nplanes; // the total number of planes }; The class is used for implementation of unary, binary and, generally, n-ary element-wise oper- ations on multi-dimensional arrays. Some of the arguments of n-ary function may be continuous arrays, some may be not. It is possible to use conventional MatIterator ’s for each array, but it can be a big overhead to increment all of the iterators after each small operations. That’s where NAryMatIterator can be used. Using it, you can iterate though several matrices simultane- ously as long as they have the same geometry (dimensionality and all the dimension sizes are the same). On each iteration it.planes[0], it.planes[1], ... will be the slices of the corre- sponding matrices. Here is an example of how you can compute a normalized and thresholded 3D color histogram: void computeNormalizedColorHist(const Mat& image, Mat& hist, int N, double minProb) { const int histSize[] = {N, N, N}; // make sure that the histogram has proper size and type hist.create(3, histSize, CV_32F); // and clear it hist = Scalar(0); // the loop below assumes that the image // is 8-bit 3-channel, so let’s check it. 526 CHAPTER 11. CORE. THE CORE FUNCTIONALITY CV_Assert(image.type() == CV_8UC3); MatConstIterator_ it = image.begin(), it_end = image.end(); for( ; it != it_end; ++it ) { const Vec3b& pix = *it; hist.at(pix[0]*N/256, pix[1]*N/256, pix[2]*N/256) += 1.f; } minProb *= image.rows*image.cols; Mat plane; NAryMatIterator it(&hist, &plane, 1); double s = 0; // iterate through the matrix. on each iteration // it.planes[*] (of type Mat) will be set to the current plane. for(int p = 0; p < it.nplanes; p++, ++it) { threshold(it.planes[0], it.planes[0], minProb, 0, THRESH_TOZERO); s += sum(it.planes[0])[0]; } s = 1./s; it = NAryMatIterator(&hist, &plane, 1); for(int p = 0; p < it.nplanes; p++, ++it) it.planes[0] *= s; } SparseMat Sparse n-dimensional array. class SparseMat { public: typedef SparseMatIterator iterator; typedef SparseMatConstIterator const_iterator; // internal structure - sparse matrix header struct Hdr { ... }; // sparse matrix node - element of a hash table 11.1. BASIC STRUCTURES 527 struct Node { size_t hashval; size_t next; int idx[CV_MAX_DIM]; }; ////////// constructors and destructor ////////// // default constructor SparseMat(); // creates matrix of the specified size and type SparseMat(int dims, const int*_sizes, int _type); // copy constructor SparseMat(const SparseMat& m); // converts dense array to the sparse form, // if try1d is true and matrix is a single-column matrix (Nx1), // then the sparse matrix will be 1-dimensional. SparseMat(const Mat& m, bool try1d=false); // converts old-style sparse matrix to the new-style. // all the data is copied, so that "m" can be safely // deleted after the conversion SparseMat(const CvSparseMat* m); // destructor ˜SparseMat(); ///////// assignment operations /////////// // this is O(1) operation; no data is copied SparseMat& operator = (const SparseMat& m); // (equivalent to the corresponding constructor with try1d=false) SparseMat& operator = (const Mat& m); // creates full copy of the matrix SparseMat clone() const; // copy all the data to the destination matrix. // the destination will be reallocated if needed. void copyTo( SparseMat& m ) const; // converts 1D or 2D sparse matrix to dense 2D matrix. // If the sparse matrix is 1D, then the result will // be a single-column matrix. void copyTo( Mat& m ) const; // converts arbitrary sparse matrix to dense matrix. // multiplies all the matrix elements by the specified scalar void convertTo( SparseMat& m, int rtype, double alpha=1 ) const; 528 CHAPTER 11. CORE. THE CORE FUNCTIONALITY // converts sparse matrix to dense matrix with optional type conversion and scaling. // When rtype=-1, the destination element type will be the same // as the sparse matrix element type. // Otherwise rtype will specify the depth and // the number of channels will remain the same is in the sparse matrix void convertTo( Mat& m, int rtype, double alpha=1, double beta=0 ) const; // not used now void assignTo( SparseMat& m, int type=-1 ) const; // reallocates sparse matrix. If it was already of the proper size and type, // it is simply cleared with clear(), otherwise, // the old matrix is released (using release()) and the new one is allocated. void create(int dims, const int*_sizes, int _type); // sets all the matrix elements to 0, which means clearing the hash table. void clear(); // manually increases reference counter to the header. void addref(); // decreses the header reference counter, when it reaches 0, // the header and all the underlying data are deallocated. void release(); // converts sparse matrix to the old-style representation. // all the elements are copied. operator CvSparseMat*() const; // size of each element in bytes // (the matrix nodes will be bigger because of // element indices and other SparseMat::Node elements). size_t elemSize() const; // elemSize()/channels() size_t elemSize1() const; // the same is in Mat int type() const; int depth() const; int channels() const; // returns the array of sizes and 0 if the matrix is not allocated const int* size() const; // returns i-th size (or 0) int size(int i) const; // returns the matrix dimensionality int dims() const; // returns the number of non-zero elements size_t nzcount() const; 11.1. BASIC STRUCTURES 529 // compute element hash value from the element indices: // 1D case size_t hash(int i0) const; // 2D case size_t hash(int i0, int i1) const; // 3D case size_t hash(int i0, int i1, int i2) const; // n-D case size_t hash(const int* idx) const; // low-level element-acccess functions, // special variants for 1D, 2D, 3D cases and the generic one for n-D case. // // return pointer to the matrix element. // if the element is there (it’s non-zero), the pointer to it is returned // if it’s not there and createMissing=false, NULL pointer is returned // if it’s not there and createMissing=true, then the new element // is created and initialized with 0. Pointer to it is returned // If the optional hashval pointer is not NULL, the element hash value is // not computed, but *hashval is taken instead. uchar* ptr(int i0, bool createMissing, size_t* hashval=0); uchar* ptr(int i0, int i1, bool createMissing, size_t* hashval=0); uchar* ptr(int i0, int i1, int i2, bool createMissing, size_t* hashval=0); uchar* ptr(const int* idx, bool createMissing, size_t* hashval=0); // higher-level element access functions: // ref<_Tp>(i0,...[,hashval]) - equivalent to *(_Tp*)ptr(i0,...true[,hashval]). // always return valid reference to the element. // If it’s did not exist, it is created. // find<_Tp>(i0,...[,hashval]) - equivalent to (_const Tp*)ptr(i0,...false[,hashval]). // return pointer to the element or NULL pointer if the element is not there. // value<_Tp>(i0,...[,hashval]) - equivalent to // { const _Tp* p = find<_Tp>(i0,...[,hashval]); return p ? *p : _Tp(); } // that is, 0 is returned when the element is not there. // note that _Tp must match the actual matrix type - // the functions do not do any on-fly type conversion // 1D case template _Tp& ref(int i0, size_t* hashval=0); template _Tp value(int i0, size_t* hashval=0) const; template const _Tp* find(int i0, size_t* hashval=0) const; // 2D case template _Tp& ref(int i0, int i1, size_t* hashval=0); 530 CHAPTER 11. CORE. THE CORE FUNCTIONALITY template _Tp value(int i0, int i1, size_t* hashval=0) const; template const _Tp* find(int i0, int i1, size_t* hashval=0) const; // 3D case template _Tp& ref(int i0, int i1, int i2, size_t* hashval=0); template _Tp value(int i0, int i1, int i2, size_t* hashval=0) const; template const _Tp* find(int i0, int i1, int i2, size_t* hashval=0) const; // n-D case template _Tp& ref(const int* idx, size_t* hashval=0); template _Tp value(const int* idx, size_t* hashval=0) const; template const _Tp* find(const int* idx, size_t* hashval=0) const; // erase the specified matrix element. // When there is no such element, the methods do nothing void erase(int i0, int i1, size_t* hashval=0); void erase(int i0, int i1, int i2, size_t* hashval=0); void erase(const int* idx, size_t* hashval=0); // return the matrix iterators, // pointing to the first sparse matrix element, SparseMatIterator begin(); SparseMatConstIterator begin() const; // ... or to the point after the last sparse matrix element SparseMatIterator end(); SparseMatConstIterator end() const; // and the template forms of the above methods. // _Tp must match the actual matrix type. template SparseMatIterator_<_Tp> begin(); template SparseMatConstIterator_<_Tp> begin() const; template SparseMatIterator_<_Tp> end(); template SparseMatConstIterator_<_Tp> end() const; // return value stored in the sparse martix node template _Tp& value(Node* n); template const _Tp& value(const Node* n) const; ////////////// some internal-use methods /////////////// ... // pointer to the sparse matrix header Hdr* hdr; }; 11.1. BASIC STRUCTURES 531 The class SparseMat represents multi-dimensional sparse numerical arrays. Such a sparse array can store elements of any type that Mat can store. ”Sparse” means that only non-zero elements are stored (though, as a result of operations on a sparse matrix, some of its stored elements can actually become 0. It’s up to the user to detect such elements and delete them using SparseMat::erase). The non-zero elements are stored in a hash table that grows when it’s filled enough, so that the search time is O(1) in average (regardless of whether element is there or not). Elements can be accessed using the following methods: 1. query operations (SparseMat::ptr and the higher-level SparseMat::ref, SparseMat::value and SparseMat::find), e.g.: const int dims = 5; int size[] = {10, 10, 10, 10, 10}; SparseMat sparse_mat(dims, size, CV_32F); for(int i = 0; i < 1000; i++) { int idx[dims]; for(int k = 0; k < dims; k++) idx[k] = rand()%sparse_mat.size(k); sparse_mat.ref(idx) += 1.f; } 2. sparse matrix iterators. Like Mat iterators and unlike MatND iterators, the sparse matrix iterators are STL-style, that is, the iteration loop is familiar to C++ users: // prints elements of a sparse floating-point matrix // and the sum of elements. SparseMatConstIterator_ it = sparse_mat.begin(), it_end = sparse_mat.end(); double s = 0; int dims = sparse_mat.dims(); for(; it != it_end; ++it) { // print element indices and the element value const Node* n = it.node(); printf("(") for(int i = 0; i < dims; i++) printf("%3d%c", n->idx[i], i < dims-1 ? ’,’ : ’)’); printf(": %f\n", *it); s += *it; } printf("Element sum is %g\n", s); 532 CHAPTER 11. CORE. THE CORE FUNCTIONALITY If you run this loop, you will notice that elements are enumerated in no any logical order (lexicographical etc.), they come in the same order as they stored in the hash table, i.e. semi- randomly. You may collect pointers to the nodes and sort them to get the proper ordering. Note, however, that pointers to the nodes may become invalid when you add more elements to the matrix; this is because of possible buffer reallocation. 3. a combination of the above 2 methods when you need to process 2 or more sparse matrices simultaneously, e.g. this is how you can compute unnormalized cross-correlation of the 2 floating-point sparse matrices: double cross_corr(const SparseMat& a, const SparseMat& b) { const SparseMat *_a = &a, *_b = &b; // if b contains less elements than a, // it’s faster to iterate through b if(_a->nzcount() > _b->nzcount()) std::swap(_a, _b); SparseMatConstIterator_ it = _a->begin(), it_end = _a->end(); double ccorr = 0; for(; it != it_end; ++it) { // take the next element from the first matrix float avalue = *it; const Node* anode = it.node(); // and try to find element with the same index in the second matrix. // since the hash value depends only on the element index, // we reuse hashvalue stored in the node float bvalue = _b->value(anode->idx,&anode->hashval); ccorr += avalue*bvalue; } return ccorr; } SparseMat Template sparse n-dimensional array class derived from SparseMat template class SparseMat_ : public SparseMat { public: typedef SparseMatIterator_<_Tp> iterator; typedef SparseMatConstIterator_<_Tp> const_iterator; 11.1. BASIC STRUCTURES 533 // constructors; // the created matrix will have data type = DataType<_Tp>::type SparseMat_(); SparseMat_(int dims, const int*_sizes); SparseMat_(const SparseMat& m); SparseMat_(const SparseMat_& m); SparseMat_(const Mat& m); SparseMat_(const CvSparseMat* m); // assignment operators; data type conversion is done when necessary SparseMat_& operator = (const SparseMat& m); SparseMat_& operator = (const SparseMat_& m); SparseMat_& operator = (const Mat& m); SparseMat_& operator = (const MatND& m); // equivalent to the correspoding parent class methods SparseMat_ clone() const; void create(int dims, const int*_sizes); operator CvSparseMat*() const; // overriden methods that do extra checks for the data type int type() const; int depth() const; int channels() const; // more convenient element access operations. // ref() is retained (but <_Tp> specification is not need anymore); // operator () is equivalent to SparseMat::value<_Tp> _Tp& ref(int i0, size_t* hashval=0); _Tp operator()(int i0, size_t* hashval=0) const; _Tp& ref(int i0, int i1, size_t* hashval=0); _Tp operator()(int i0, int i1, size_t* hashval=0) const; _Tp& ref(int i0, int i1, int i2, size_t* hashval=0); _Tp operator()(int i0, int i1, int i2, size_t* hashval=0) const; _Tp& ref(const int* idx, size_t* hashval=0); _Tp operator()(const int* idx, size_t* hashval=0) const; // iterators SparseMatIterator_<_Tp> begin(); SparseMatConstIterator_<_Tp> begin() const; SparseMatIterator_<_Tp> end(); SparseMatConstIterator_<_Tp> end() const; }; SparseMat is a thin wrapper on top of SparseMat , made in the same way as Mat . It simplifies notation of some operations, and that’s it. 534 CHAPTER 11. CORE. THE CORE FUNCTIONALITY int sz[] = {10, 20, 30}; SparseMat_ M(3, sz); ... M.ref(1, 2, 3) = M(4, 5, 6) + M(7, 8, 9); 11.2 Operations on Arrays cv::abs (view/add comments) Computes absolute value of each matrix element MatExpr<...> abs(const Mat& src); MatExpr<...> abs(const MatExpr<...>& src); src matrix or matrix expression abs is a meta-function that is expanded to one of cv::absdiff forms: • C = abs(A-B) is equivalent to absdiff(A, B, C) and • C = abs(A) is equivalent to absdiff(A, Scalar::all(0), C). • C = Mat >(abs(A*alpha + beta)) is equivalent to convertScaleAbs(A, C, alpha, beta) The output matrix will have the same size and the same type as the input one (except for the last case, where C will be depth=CV 8U). See also: Matrix Expressions, cv::absdiff, saturate cast cv::absdiff (view/add comments) Computes per-element absolute difference between 2 arrays or between array and a scalar. void absdiff(const Mat& src1, const Mat& src2, Mat& dst); void absdiff(const Mat& src1, const Scalar& sc, Mat& dst); void absdiff(const MatND& src1, const MatND& src2, MatND& dst); void absdiff(const MatND& src1, const Scalar& sc, MatND& dst); 11.2. OPERATIONS ON ARRAYS 535 src1 The first input array src2 The second input array; Must be the same size and same type as src1 sc Scalar; the second input parameter dst The destination array; it will have the same size and same type as src1; see Mat::create The functions absdiff compute: • absolute difference between two arrays dst(I) = saturate(|src1(I) − src2(I)|) • or absolute difference between array and a scalar: dst(I) = saturate(|src1(I) − sc|) where I is multi-dimensional index of array elements. in the case of multi-channel arrays each channel is processed independently. See also: cv::abs, saturate cast cv::add (view/add comments) Computes the per-element sum of two arrays or an array and a scalar. void add(const Mat& src1, const Mat& src2, Mat& dst); void add(const Mat& src1, const Mat& src2, Mat& dst, const Mat& mask); void add(const Mat& src1, const Scalar& sc, Mat& dst, const Mat& mask=Mat()); void add(const MatND& src1, const MatND& src2, MatND& dst); void add(const MatND& src1, const MatND& src2, MatND& dst, const MatND& mask); void add(const MatND& src1, const Scalar& sc, MatND& dst, const MatND& mask=MatND()); src1 The first source array src2 The second source array. It must have the same size and same type as src1 536 CHAPTER 11. CORE. THE CORE FUNCTIONALITY sc Scalar; the second input parameter dst The destination array; it will have the same size and same type as src1; see Mat::create mask The optional operation mask, 8-bit single channel array; specifies elements of the destina- tion array to be changed The functions add compute: • the sum of two arrays: dst(I) = saturate(src1(I) + src2(I)) if mask(I) 6= 0 • or the sum of array and a scalar: dst(I) = saturate(src1(I) + sc) if mask(I) 6= 0 where I is multi-dimensional index of array elements. The first function in the above list can be replaced with matrix expressions: dst = src1 + src2; dst += src1; // equivalent to add(dst, src1, dst); in the case of multi-channel arrays each channel is processed independently. See also: cv::subtract, cv::addWeighted, cv::scaleAdd, cv::convertScale, Matrix Expres- sions, saturate cast. cv::addWeighted (view/add comments) Computes the weighted sum of two arrays. void addWeighted(const Mat& src1, double alpha, const Mat& src2, double beta, double gamma, Mat& dst); void addWeighted(const MatND& src1, double alpha, const MatND& src2, double beta, double gamma, MatND& dst); src1 The first source array alpha Weight for the first array elements src2 The second source array; must have the same size and same type as src1 11.2. OPERATIONS ON ARRAYS 537 beta Weight for the second array elements dst The destination array; it will have the same size and same type as src1 gamma Scalar, added to each sum The functions addWeighted calculate the weighted sum of two arrays as follows: dst(I) = saturate(src1(I) ∗ alpha + src2(I) ∗ beta + gamma) where I is multi-dimensional index of array elements. The first function can be replaced with a matrix expression: dst = src1*alpha + src2*beta + gamma; In the case of multi-channel arrays each channel is processed independently. See also: cv::add, cv::subtract, cv::scaleAdd, cv::convertScale, Matrix Expressions, saturate cast. bitwise and (view/add comments) Calculates per-element bit-wise conjunction of two arrays and an array and a scalar. void bitwise and(const Mat& src1, const Mat& src2, Mat& dst, const Mat& mask=Mat()); void bitwise and(const Mat& src1, const Scalar& sc, Mat& dst, const Mat& mask=Mat()); void bitwise and(const MatND& src1, const MatND& src2, MatND& dst, const MatND& mask=MatND()); void bitwise and(const MatND& src1, const Scalar& sc, MatND& dst, const MatND& mask=MatND()); src1 The first source array src2 The second source array. It must have the same size and same type as src1 sc Scalar; the second input parameter dst The destination array; it will have the same size and same type as src1; see Mat::create mask The optional operation mask, 8-bit single channel array; specifies elements of the destina- tion array to be changed 538 CHAPTER 11. CORE. THE CORE FUNCTIONALITY The functions bitwise and compute per-element bit-wise logical conjunction: • of two arrays dst(I) = src1(I) ∧ src2(I) if mask(I) 6= 0 • or array and a scalar: dst(I) = src1(I) ∧ sc if mask(I) 6= 0 In the case of floating-point arrays their machine-specific bit representations (usually IEEE754- compliant) are used for the operation, and in the case of multi-channel arrays each channel is processed independently. See also: bitwise and, bitwise not, bitwise xor bitwise not (view/add comments) Inverts every bit of array void bitwise not(const Mat& src, Mat& dst); void bitwise not(const MatND& src, MatND& dst); src1 The source array dst The destination array; it is reallocated to be of the same size and the same type as src; see Mat::create mask The optional operation mask, 8-bit single channel array; specifies elements of the destina- tion array to be changed The functions bitwise not compute per-element bit-wise inversion of the source array: dst(I) = ¬src(I) In the case of floating-point source array its machine-specific bit representation (usually IEEE754- compliant) is used for the operation. in the case of multi-channel arrays each channel is processed independently. See also: bitwise and, bitwise or, bitwise xor 11.2. OPERATIONS ON ARRAYS 539 bitwise or (view/add comments) Calculates per-element bit-wise disjunction of two arrays and an array and a scalar. void bitwise or(const Mat& src1, const Mat& src2, Mat& dst, const Mat& mask=Mat()); void bitwise or(const Mat& src1, const Scalar& sc, Mat& dst, const Mat& mask=Mat()); void bitwise or(const MatND& src1, const MatND& src2, MatND& dst, const MatND& mask=MatND()); void bitwise or(const MatND& src1, const Scalar& sc, MatND& dst, const MatND& mask=MatND()); src1 The first source array src2 The second source array. It must have the same size and same type as src1 sc Scalar; the second input parameter dst The destination array; it is reallocated to be of the same size and the same type as src1; see Mat::create mask The optional operation mask, 8-bit single channel array; specifies elements of the destina- tion array to be changed The functions bitwise or compute per-element bit-wise logical disjunction • of two arrays dst(I) = src1(I) ∨ src2(I) if mask(I) 6= 0 • or array and a scalar: dst(I) = src1(I) ∨ sc if mask(I) 6= 0 In the case of floating-point arrays their machine-specific bit representations (usually IEEE754- compliant) are used for the operation. in the case of multi-channel arrays each channel is pro- cessed independently. See also: bitwise and, bitwise not, bitwise or 540 CHAPTER 11. CORE. THE CORE FUNCTIONALITY bitwise xor (view/add comments) Calculates per-element bit-wise ”exclusive or” operation on two arrays and an array and a scalar. void bitwise xor(const Mat& src1, const Mat& src2, Mat& dst, const Mat& mask=Mat()); void bitwise xor(const Mat& src1, const Scalar& sc, Mat& dst, const Mat& mask=Mat()); void bitwise xor(const MatND& src1, const MatND& src2, MatND& dst, const MatND& mask=MatND()); void bitwise xor(const MatND& src1, const Scalar& sc, MatND& dst, const MatND& mask=MatND()); src1 The first source array src2 The second source array. It must have the same size and same type as src1 sc Scalar; the second input parameter dst The destination array; it is reallocated to be of the same size and the same type as src1; see Mat::create mask The optional operation mask, 8-bit single channel array; specifies elements of the destina- tion array to be changed The functions bitwise xor compute per-element bit-wise logical ”exclusive or” operation • on two arrays dst(I) = src1(I) ⊕ src2(I) if mask(I) 6= 0 • or array and a scalar: dst(I) = src1(I) ⊕ sc if mask(I) 6= 0 In the case of floating-point arrays their machine-specific bit representations (usually IEEE754- compliant) are used for the operation. in the case of multi-channel arrays each channel is pro- cessed independently. See also: bitwise and, bitwise not, bitwise or 11.2. OPERATIONS ON ARRAYS 541 cv::calcCovarMatrix (view/add comments) Calculates covariation matrix of a set of vectors void calcCovarMatrix( const Mat* samples, int nsamples, Mat& covar, Mat& mean, int flags, int ctype=CV 64F); void calcCovarMatrix( const Mat& samples, Mat& covar, Mat& mean, int flags, int ctype=CV 64F); samples The samples, stored as separate matrices, or as rows or columns of a single matrix nsamples The number of samples when they are stored separately covar The output covariance matrix; it will have type=ctype and square size mean The input or output (depending on the flags) array - the mean (average) vector of the input vectors flags The operation flags, a combination of the following values CV COVAR SCRAMBLED The output covariance matrix is calculated as: scale·[vects[0]−mean, vects[1]−mean, ...]T·[vects[0]−mean, vects[1]−mean, ...] , that is, the covariance matrix will be nsamples × nsamples. Such an unusual co- variance matrix is used for fast PCA of a set of very large vectors (see, for example, the EigenFaces technique for face recognition). Eigenvalues of this ”scrambled” matrix will match the eigenvalues of the true covariance matrix and the ”true” eigenvectors can be easily calculated from the eigenvectors of the ”scrambled” covariance matrix. CV COVAR NORMAL The output covariance matrix is calculated as: scale·[vects[0]−mean, vects[1]−mean, ...]·[vects[0]−mean, vects[1]−mean, ...]T , that is, covar will be a square matrix of the same size as the total number of elements in each input vector. One and only one of CV COVAR SCRAMBLED and CV COVAR NORMAL must be specified 542 CHAPTER 11. CORE. THE CORE FUNCTIONALITY CV COVAR USE AVG If the flag is specified, the function does not calculate mean from the input vectors, but, instead, uses the passed mean vector. This is useful if mean has been pre-computed or known a-priori, or if the covariance matrix is calculated by parts - in this case, mean is not a mean vector of the input sub-set of vectors, but rather the mean vector of the whole set. CV COVAR SCALE If the flag is specified, the covariance matrix is scaled. In the ”normal” mode scale is 1./nsamples; in the ”scrambled” mode scale is the reciprocal of the total number of elements in each input vector. By default (if the flag is not specified) the covariance matrix is not scaled (i.e. scale=1). CV COVAR ROWS [Only useful in the second variant of the function] The flag means that all the input vectors are stored as rows of the samples matrix. mean should be a single- row vector in this case. CV COVAR COLS [Only useful in the second variant of the function] The flag means that all the input vectors are stored as columns of the samples matrix. mean should be a single-column vector in this case. The functions calcCovarMatrix calculate the covariance matrix and, optionally, the mean vector of the set of input vectors. See also: cv::PCA, cv::mulTransposed, cv::Mahalanobis cv::cartToPolar (view/add comments) Calculates the magnitude and angle of 2d vectors. void cartToPolar(const Mat& x, const Mat& y, Mat& magnitude, Mat& angle, bool angleInDegrees=false); x The array of x-coordinates; must be single-precision or double-precision floating-point array y The array of y-coordinates; it must have the same size and same type as x magnitude The destination array of magnitudes of the same size and same type as x angle The destination array of angles of the same size and same type as x. The angles are measured in radians (0 to 2π) or in degrees (0 to 360 degrees). 11.2. OPERATIONS ON ARRAYS 543 angleInDegrees The flag indicating whether the angles are measured in radians, which is de- fault mode, or in degrees The function cartToPolar calculates either the magnitude, angle, or both of every 2d vector (x(I),y(I)): magnitude(I) = px(I)2 + y(I)2, angle(I) = atan2(y(I), x(I))[·180/π] The angles are calculated with ∼ 0.3◦ accuracy. For the (0,0) point, the angle is set to 0. cv::checkRange (view/add comments) Checks every element of an input array for invalid values. bool checkRange(const Mat& src, bool quiet=true, Point* pos=0, double minVal=-DBL MAX, double maxVal=DBL MAX); bool checkRange(const MatND& src, bool quiet=true, int* pos=0, double minVal=-DBL MAX, double maxVal=DBL MAX); src The array to check quiet The flag indicating whether the functions quietly return false when the array elements are out of range, or they throw an exception. pos The optional output parameter, where the position of the first outlier is stored. In the second function pos, when not NULL, must be a pointer to array of src.dims elements minVal The inclusive lower boundary of valid values range maxVal The exclusive upper boundary of valid values range The functions checkRange check that every array element is neither NaN nor ±∞. When minVal < -DBL MAX and maxVal < DBL MAX, then the functions also check that each value is between minVal and maxVal. in the case of multi-channel arrays each channel is processed independently. If some values are out of range, position of the first outlier is stored in pos (when pos 6= 0), and then the functions either return false (when quiet=true) or throw an exception. 544 CHAPTER 11. CORE. THE CORE FUNCTIONALITY cv::compare (view/add comments) Performs per-element comparison of two arrays or an array and scalar value. void compare(const Mat& src1, const Mat& src2, Mat& dst, int cmpop); void compare(const Mat& src1, double value, Mat& dst, int cmpop); void compare(const MatND& src1, const MatND& src2, MatND& dst, int cmpop); void compare(const MatND& src1, double value, MatND& dst, int cmpop); src1 The first source array src2 The second source array; must have the same size and same type as src1 value The scalar value to compare each array element with dst The destination array; will have the same size as src1 and type=CV 8UC1 cmpop The flag specifying the relation between the elements to be checked CMP EQ src1(I) = src2(I) or src1(I) = value CMP GT src1(I) > src2(I) or src1(I) > value CMP GE src1(I) ≥ src2(I) or src1(I) ≥ value CMP LT src1(I) < src2(I) or src1(I) < value CMP LE src1(I) ≤ src2(I) or src1(I) ≤ value CMP NE src1(I) 6= src2(I) or src1(I) 6= value The functions compare compare each element of src1 with the corresponding element of src2 or with real scalar value. When the comparison result is true, the corresponding element of destination array is set to 255, otherwise it is set to 0: • dst(I) = src1(I) cmpop src2(I) ? 255 : 0 • dst(I) = src1(I) cmpop value ? 255 : 0 The comparison operations can be replaced with the equivalent matrix expressions: 11.2. OPERATIONS ON ARRAYS 545 Mat dst1 = src1 >= src2; Mat dst2 = src1 < 8; ... See also: cv::checkRange, cv::min, cv::max, cv::threshold, Matrix Expressions cv::completeSymm (view/add comments) Copies the lower or the upper half of a square matrix to another half. void completeSymm(Mat& mtx, bool lowerToUpper=false); mtx Input-output floating-point square matrix lowerToUpper If true, the lower half is copied to the upper half, otherwise the upper half is copied to the lower half The function completeSymm copies the lower half of a square matrix to its another half; the matrix diagonal remains unchanged: • mtxij = mtxji for i > j if lowerToUpper=false • mtxij = mtxji for i < j if lowerToUpper=true See also: cv::flip, cv::transpose cv::convertScaleAbs (view/add comments) Scales, computes absolute values and converts the result to 8-bit. void convertScaleAbs(const Mat& src, Mat& dst, double alpha=1, double beta=0); src The source array dst The destination array 546 CHAPTER 11. CORE. THE CORE FUNCTIONALITY alpha The optional scale factor beta The optional delta added to the scaled values On each element of the input array the function convertScaleAbs performs 3 operations sequentially: scaling, taking absolute value, conversion to unsigned 8-bit type: dst(I) = saturate cast(|src(I) ∗ alpha + beta|) in the case of multi-channel arrays the function processes each channel independently. When the output is not 8-bit, the operation can be emulated by calling Mat::convertTo method (or by using matrix expressions) and then by computing absolute value of the result, for example: Mat_ A(30,30); randu(A, Scalar(-100), Scalar(100)); Mat_ B = A*5 + 3; B = abs(B); // Mat_ B = abs(A*5+3) will also do the job, // but it will allocate a temporary matrix See also: cv::Mat::convertTo, cv::abs cv::countNonZero (view/add comments) Counts non-zero array elements. int countNonZero( const Mat& mtx ); int countNonZero( const MatND& mtx ); mtx Single-channel array The function cvCountNonZero returns the number of non-zero elements in mtx: X I: mtx(I)6=0 1 See also: cv::mean, cv::meanStdDev, cv::norm, cv::minMaxLoc, cv::calcCovarMatrix 11.2. OPERATIONS ON ARRAYS 547 cv::cubeRoot (view/add comments) Computes cube root of the argument float cubeRoot(float val); val The function argument The function cubeRoot computes 3√val. Negative arguments are handled correctly, NaN and ±∞ are not handled. The accuracy approaches the maximum possible accuracy for single- precision data. cv::cvarrToMat (view/add comments) Converts CvMat, IplImage or CvMatND to cv::Mat. Mat cvarrToMat(const CvArr* src, bool copyData=false, bool allowND=true, int coiMode=0); src The source CvMat, IplImage or CvMatND copyData When it is false (default value), no data is copied, only the new header is created. In this case the original array should not be deallocated while the new matrix header is used. The the parameter is true, all the data is copied, then user may deallocate the original array right after the conversion allowND When it is true (default value), then CvMatND is converted to Mat if it’s possible (e.g. then the data is contiguous). If it’s not possible, or when the parameter is false, the function will report an error coiMode The parameter specifies how the IplImage COI (when set) is handled. • If coiMode=0, the function will report an error if COI is set. • If coiMode=1, the function will never report an error; instead it returns the header to the whole original image and user will have to check and process COI manually, see cv::extractImageCOI. 548 CHAPTER 11. CORE. THE CORE FUNCTIONALITY The function cvarrToMat converts CvMat, IplImage or CvMatND header to cv::Mat header, and optionally duplicates the underlying data. The constructed header is returned by the function. When copyData=false, the conversion is done really fast (in O(1) time) and the newly cre- ated matrix header will have refcount=0, which means that no reference counting is done for the matrix data, and user has to preserve the data until the new header is destructed. Other- wise, when copyData=true, the new buffer will be allocated and managed as if you created a new matrix from scratch and copy the data there. That is, cvarrToMat(src, true) ∼ cvarrToMat(src, false).clone() (assuming that COI is not set). The function provides uniform way of supporting CvArr paradigm in the code that is migrated to use new-style data structures internally. The reverse transformation, from cv::Mat to CvMat or IplImage can be done by simple assignment: CvMat* A = cvCreateMat(10, 10, CV_32F); cvSetIdentity(A); IplImage A1; cvGetImage(A, &A1); Mat B = cvarrToMat(A); Mat B1 = cvarrToMat(&A1); IplImage C = B; CvMat C1 = B1; // now A, A1, B, B1, C and C1 are different headers // for the same 10x10 floating-point array. // note, that you will need to use "&" // to pass C & C1 to OpenCV functions, e.g: printf("%g", cvDet(&C1)); Normally, the function is used to convert an old-style 2D array ( CvMat or IplImage ) to Mat, however, the function can also take CvMatND on input and create cv::Mat for it, if it’s possible. And for CvMatND A it is possible if and only if A.dim[i].size*A.dim.step[i] == A.dim.step[i-1] for all or for all but one i, 0 < i < A.dims. That is, the matrix data should be continuous or it should be representable as a sequence of continuous matrices. By using this function in this way, you can process CvMatND using arbitrary element-wise function. But for more complex operations, such as filtering functions, it will not work, and you need to convert CvMatND to cv::MatND using the corresponding constructor of the latter. The last parameter, coiMode, specifies how to react on an image with COI set: by default it’s 0, and then the function reports an error when an image with COI comes in. And coiMode=1 means that no error is signaled - user has to check COI presence and handle it manually. The modern structures, such as cv::Mat and cv::MatND do not support COI natively. To process individual channel of an new-style array, you will need either to organize loop over the array (e.g. using matrix iterators) where the channel of interest will be processed, or extract the COI using cv::mixChannels (for new-style arrays) or cv::extractImageCOI (for old-style arrays), process this individual channel and insert it back to the destination array if need (using cv::mixChannel or 11.2. OPERATIONS ON ARRAYS 549 cv::insertImageCOI, respectively). See also: cv::cvGetImage, cv::cvGetMat, cv::cvGetMatND, cv::extractImageCOI, cv::insertImageCOI, cv::mixChannels cv::dct (view/add comments) Performs a forward or inverse discrete cosine transform of 1D or 2D array void dct(const Mat& src, Mat& dst, int flags=0); src The source floating-point array dst The destination array; will have the same size and same type as src flags Transformation flags, a combination of the following values DCT INVERSE do an inverse 1D or 2D transform instead of the default forward transform. DCT ROWS do a forward or inverse transform of every individual row of the input matrix. This flag allows user to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself), to do 3D and higher-dimensional transforms and so forth. The function dct performs a forward or inverse discrete cosine transform (DCT) of a 1D or 2D floating-point array: Forward Cosine transform of 1D vector of N elements: Y = C(N)·X where C(N) jk = qαj/N cos π(2k + 1)j 2N  and α0 = 1, αj = 2 for j > 0. Inverse Cosine transform of 1D vector of N elements: X = C(N)−1 ·Y = C(N)T ·Y (since C(N) is orthogonal matrix, C(N)· C(N)T = I) 550 CHAPTER 11. CORE. THE CORE FUNCTIONALITY Forward Cosine transform of 2D M × N matrix: Y = C(N)·X· C(N)T Inverse Cosine transform of 2D vector of M × N elements: X = C(N)T ·X·C(N) The function chooses the mode of operation by looking at the flags and size of the input array: • if (flags & DCT INVERSE) == 0, the function does forward 1D or 2D transform, other- wise it is inverse 1D or 2D transform. • if (flags & DCT ROWS) 6= 0, the function performs 1D transform of each row. • otherwise, if the array is a single column or a single row, the function performs 1D transform • otherwise it performs 2D transform. Important note: currently cv::dct supports even-size arrays (2, 4, 6 ...). For data analysis and approximation you can pad the array when necessary. Also, the function’s performance depends very much, and not monotonically, on the array size, see cv::getOptimalDFTSize. In the current implementation DCT of a vector of size N is computed via DFT of a vector of size N/2, thus the optimal DCT size N∗ ≥ N can be computed as: size_t getOptimalDCTSize(size_t N) { return 2*getOptimalDFTSize((N+1)/2); } See also: cv::dft, cv::getOptimalDFTSize, cv::idct cv::dft (view/add comments) Performs a forward or inverse Discrete Fourier transform of 1D or 2D floating-point array. void dft(const Mat& src, Mat& dst, int flags=0, int nonzeroRows=0); src The source array, real or complex dst The destination array, which size and type depends on the flags flags Transformation flags, a combination of the following values 11.2. OPERATIONS ON ARRAYS 551 DFT INVERSE do an inverse 1D or 2D transform instead of the default forward transform. DFT SCALE scale the result: divide it by the number of array elements. Normally, it is com- bined with DFT INVERSE . DFT ROWS do a forward or inverse transform of every individual row of the input matrix. This flag allows the user to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself), to do 3D and higher-dimensional transforms and so forth. DFT COMPLEX OUTPUT then the function performs forward transformation of 1D or 2D real array, the result, though being a complex array, has complex-conjugate symmetry (CCS), see the description below. Such an array can be packed into real array of the same size as input, which is the fastest option and which is what the function does by default. However, you may wish to get the full complex array (for simpler spectrum analysis etc.). Pass the flag to tell the function to produce full-size complex output array. DFT REAL OUTPUT then the function performs inverse transformation of 1D or 2D complex array, the result is normally a complex array of the same size. However, if the source array has conjugate-complex symmetry (for example, it is a result of forward transforma- tion with DFT COMPLEX OUTPUT flag), then the output is real array. While the function itself does not check whether the input is symmetrical or not, you can pass the flag and then the function will assume the symmetry and produce the real output array. Note that when the input is packed real array and inverse transformation is executed, the function treats the input as packed complex-conjugate symmetrical array, so the output will also be real array nonzeroRows When the parameter 6= 0, the function assumes that only the first nonzeroRows rows of the input array (DFT INVERSE is not set) or only the first nonzeroRows of the output array (DFT INVERSE is set) contain non-zeros, thus the function can handle the rest of the rows more efficiently and thus save some time. This technique is very useful for computing array cross-correlation or convolution using DFT Forward Fourier transform of 1D vector of N elements: Y = F(N)·X, where F(N) jk = exp(−2πijk/N) and i = √−1 Inverse Fourier transform of 1D vector of N elements: X0 = F(N)−1 ·Y = F(N)∗ · y X = (1/N)·X, where F ∗ = Re(F(N)) − Im(F(N))T 552 CHAPTER 11. CORE. THE CORE FUNCTIONALITY Forward Fourier transform of 2D vector of M × N elements: Y = F(M)·X·F(N) Inverse Fourier transform of 2D vector of M × N elements: X0 = F(M)∗ ·Y· F(N)∗ X = 1 M·N·X0 In the case of real (single-channel) data, the packed format called CCS (complex-conjugate- symmetrical) that was borrowed from IPL and used to represent the result of a forward Fourier transform or input for an inverse Fourier transform:   ReY0,0 ReY0,1 ImY0,1 ReY0,2 ImY0,2 ··· ReY0,N/2−1 ImY0,N/2−1 ReY0,N/2 ReY1,0 ReY1,1 ImY1,1 ReY1,2 ImY1,2 ··· ReY1,N/2−1 ImY1,N/2−1 ReY1,N/2 ImY1,0 ReY2,1 ImY2,1 ReY2,2 ImY2,2 ··· ReY2,N/2−1 ImY2,N/2−1 ImY1,N/2 .......................................................................................................... ReYM/2−1,0 ReYM−3,1 ImYM−3,1 .................... ReYM−3,N/2−1 ImYM−3,N/2−1 ReYM/2−1,N/2 ImYM/2−1,0 ReYM−2,1 ImYM−2,1 .................... ReYM−2,N/2−1 ImYM−2,N/2−1 ImYM/2−1,N/2 ReYM/2,0 ReYM−1,1 ImYM−1,1 .................... ReYM−1,N/2−1 ImYM−1,N/2−1 ReYM/2,N/2   in the case of 1D transform of real vector, the output will look as the first row of the above matrix. So, the function chooses the operation mode depending on the flags and size of the input array: • if DFT ROWS is set or the input array has single row or single column then the function per- forms 1D forward or inverse transform (of each row of a matrix when DFT ROWS is set, oth- erwise it will be 2D transform. • if input array is real and DFT INVERSE is not set, the function does forward 1D or 2D trans- form: – when DFT COMPLEX OUTPUT is set then the output will be complex matrix of the same size as input. – otherwise the output will be a real matrix of the same size as input. in the case of 2D transform it will use the packed format as shown above; in the case of single 1D transform it will look as the first row of the above matrix; in the case of multiple 1D transforms (when using DCT ROWS flag) each row of the output matrix will look like the first row of the above matrix. 11.2. OPERATIONS ON ARRAYS 553 • otherwise, if the input array is complex and either DFT INVERSE or DFT REAL OUTPUT are not set then the output will be a complex array of the same size as input and the function will perform the forward or inverse 1D or 2D transform of the whole input array or each row of the input array independently, depending on the flags DFT INVERSE and DFT ROWS. • otherwise, i.e. when DFT INVERSE is set, the input array is real, or it is complex but DFT REAL OUTPUT is set, the output will be a real array of the same size as input, and the function will perform 1D or 2D inverse transformation of the whole input array or each individual row, depending on the flags DFT INVERSE and DFT ROWS. The scaling is done after the transformation if DFT SCALE is set. Unlike cv::dct, the function supports arrays of arbitrary size, but only those arrays are pro- cessed efficiently, which sizes can be factorized in a product of small prime numbers (2, 3 and 5 in the current implementation). Such an efficient DFT size can be computed using cv::getOptimalDFTSize method. Here is the sample on how to compute DFT-based convolution of two 2D real arrays: void convolveDFT(const Mat& A, const Mat& B, Mat& C) { // reallocate the output array if needed C.create(abs(A.rows - B.rows)+1, abs(A.cols - B.cols)+1, A.type()); Size dftSize; // compute the size of DFT transform dftSize.width = getOptimalDFTSize(A.cols + B.cols - 1); dftSize.height = getOptimalDFTSize(A.rows + B.rows - 1); // allocate temporary buffers and initialize them with 0’s Mat tempA(dftSize, A.type(), Scalar::all(0)); Mat tempB(dftSize, B.type(), Scalar::all(0)); // copy A and B to the top-left corners of tempA and tempB, respectively Mat roiA(tempA, Rect(0,0,A.cols,A.rows)); A.copyTo(roiA); Mat roiB(tempB, Rect(0,0,B.cols,B.rows)); B.copyTo(roiB); // now transform the padded A & B in-place; // use "nonzeroRows" hint for faster processing dft(tempA, tempA, 0, A.rows); dft(tempB, tempB, 0, B.rows); // multiply the spectrums; // the function handles packed spectrum representations well mulSpectrums(tempA, tempB, tempA); 554 CHAPTER 11. CORE. THE CORE FUNCTIONALITY // transform the product back from the frequency domain. // Even though all the result rows will be non-zero, // we need only the first C.rows of them, and thus we // pass nonzeroRows == C.rows dft(tempA, tempA, DFT_INVERSE + DFT_SCALE, C.rows); // now copy the result back to C. tempA(Rect(0, 0, C.cols, C.rows)).copyTo(C); // all the temporary buffers will be deallocated automatically } What can be optimized in the above sample? • since we passed nonzeroRows 6= 0 to the forward transform calls and since we copied A/B to the top-left corners of tempA/tempB, respectively, it’s not necessary to clear the whole tempA and tempB; it is only necessary to clear the tempA.cols - A.cols (tempB.cols - B.cols) rightmost columns of the matrices. • this DFT-based convolution does not have to be applied to the whole big arrays, especially if B is significantly smaller than A or vice versa. Instead, we can compute convolution by parts. For that we need to split the destination array C into multiple tiles and for each tile estimate, which parts of A and B are required to compute convolution in this tile. If the tiles in C are too small, the speed will decrease a lot, because of repeated work - in the ultimate case, when each tile in C is a single pixel, the algorithm becomes equivalent to the naive convolution algorithm. If the tiles are too big, the temporary arrays tempA and tempB become too big and there is also slowdown because of bad cache locality. So there is optimal tile size somewhere in the middle. • if the convolution is done by parts, since different tiles in C can be computed in parallel, the loop can be threaded. All of the above improvements have been implemented in cv::matchTemplate and cv::filter2D, therefore, by using them, you can get even better performance than with the above theoretically optimal implementation (though, those two functions actually compute cross-correlation, not con- volution, so you will need to ”flip” the kernel or the image around the center using cv::flip). See also: cv::dct, cv::getOptimalDFTSize, cv::mulSpectrums, cv::filter2D, cv::matchTemplate, cv::flip, cv::cartToPolar, cv::magnitude, cv::phase cv::divide (view/add comments) Performs per-element division of two arrays or a scalar by an array. 11.2. OPERATIONS ON ARRAYS 555 void divide(const Mat& src1, const Mat& src2, Mat& dst, double scale=1); void divide(double scale, const Mat& src2, Mat& dst); void divide(const MatND& src1, const MatND& src2, MatND& dst, double scale=1); void divide(double scale, const MatND& src2, MatND& dst); src1 The first source array src2 The second source array; should have the same size and same type as src1 scale Scale factor dst The destination array; will have the same size and same type as src2 The functions divide divide one array by another: dst(I) = saturate(src1(I)*scale/src2(I)) or a scalar by array, when there is no src1: dst(I) = saturate(scale/src2(I)) The result will have the same type as src1. When src2(I)=0, dst(I)=0 too. See also: cv::multiply, cv::add, cv::subtract, Matrix Expressions cv::determinant (view/add comments) Returns determinant of a square floating-point matrix. double determinant(const Mat& mtx); mtx The input matrix; must have CV 32FC1 or CV 64FC1 type and square size The function determinant computes and returns determinant of the specified matrix. For small matrices (mtx.cols=mtx.rows<=3) the direct method is used; for larger matrices the function uses LU factorization. For symmetric positive-determined matrices, it is also possible to compute cv::SVD: mtx = U·W·VT and then calculate the determinant as a product of the diagonal elements of W. See also: cv::SVD, cv::trace, cv::invert, cv::solve, Matrix Expressions 556 CHAPTER 11. CORE. THE CORE FUNCTIONALITY cv::eigen (view/add comments) Computes eigenvalues and eigenvectors of a symmetric matrix. bool eigen(const Mat& src, Mat& eigenvalues, int lowindex=-1, int highindex=-1); bool eigen(const Mat& src, Mat& eigenvalues, Mat& eigenvectors, int lowindex=-1, int highindex=-1); src The input matrix; must have CV 32FC1 or CV 64FC1 type, square size and be symmetric: srcT = src eigenvalues The output vector of eigenvalues of the same type as src; The eigenvalues are stored in the descending order. eigenvectors The output matrix of eigenvectors; It will have the same size and the same type as src; The eigenvectors are stored as subsequent matrix rows, in the same order as the corresponding eigenvalues lowindex Optional index of largest eigenvalue/-vector to calculate. (See below.) highindex Optional index of smallest eigenvalue/-vector to calculate. (See below.) The functions eigen compute just eigenvalues, or eigenvalues and eigenvectors of symmetric matrix src: src*eigenvectors(i,:)’ = eigenvalues(i)*eigenvectors(i,:)’ (in MATLAB notation) If either low- or highindex is supplied the other is required, too. Indexing is 0-based. Example: To calculate the largest eigenvector/-value set lowindex = highindex = 0. For legacy reasons this function always returns a square matrix the same size as the source matrix with eigenvectors and a vector the length of the source matrix with eigenvalues. The selected eigenvectors/-values are always in the first highindex - lowindex + 1 rows. See also: cv::SVD, cv::completeSymm, cv::PCA cv::exp (view/add comments) Calculates the exponent of every array element. 11.2. OPERATIONS ON ARRAYS 557 void exp(const Mat& src, Mat& dst); void exp(const MatND& src, MatND& dst); src The source array dst The destination array; will have the same size and same type as src The function exp calculates the exponent of every element of the input array: dst[I] = esrc(I) The maximum relative error is about 7×10−6 for single-precision and less than 10−10 for double- precision. Currently, the function converts denormalized values to zeros on output. Special values (NaN, ±∞) are not handled. See also: cv::log, cv::cartToPolar, cv::polarToCart, cv::phase, cv::pow, cv::sqrt, cv::magnitude cv::extractImageCOI (view/add comments) Extract the selected image channel void extractImageCOI(const CvArr* src, Mat& dst, int coi=-1); src The source array. It should be a pointer to CvMat or IplImage dst The destination array; will have single-channel, and the same size and the same depth as src coi If the parameter is >=0, it specifies the channel to extract; If it is <0, src must be a pointer to IplImage with valid COI set - then the selected COI is extracted. The function extractImageCOI is used to extract image COI from an old-style array and put the result to the new-style C++ matrix. As usual, the destination matrix is reallocated using Mat::create if needed. To extract a channel from a new-style matrix, use cv::mixChannels or cv::split See also: cv::mixChannels, cv::split, cv::merge, cv::cvarrToMat, cv::cvSetImageCOI, cv::cvGetImageCOI 558 CHAPTER 11. CORE. THE CORE FUNCTIONALITY cv::fastAtan2 (view/add comments) Calculates the angle of a 2D vector in degrees float fastAtan2(float y, float x); x x-coordinate of the vector y y-coordinate of the vector The function fastAtan2 calculates the full-range angle of an input 2D vector. The angle is measured in degrees and varies from 0◦ to 360◦. The accuracy is about 0.3◦. cv::flip (view/add comments) Flips a 2D array around vertical, horizontal or both axes. void flip(const Mat& src, Mat& dst, int flipCode); src The source array dst The destination array; will have the same size and same type as src flipCode Specifies how to flip the array: 0 means flipping around the x-axis, positive (e.g., 1) means flipping around y-axis, and negative (e.g., -1) means flipping around both axes. See also the discussion below for the formulas. The function flip flips the array in one of three different ways (row and column indices are 0-based): dstij =    srcsrc.rows−i−1,j if flipCode = 0 srci,src.cols−j−1 if flipCode ¿ 0 srcsrc.rows−i−1,src.cols−j−1 if flipCode ¡ 0 The example scenarios of function use are: 11.2. OPERATIONS ON ARRAYS 559 • vertical flipping of the image (flipCode = 0) to switch between top-left and bottom-left image origin, which is a typical operation in video processing in Windows. • horizontal flipping of the image with subsequent horizontal shift and absolute difference cal- culation to check for a vertical-axis symmetry (flipCode > 0) • simultaneous horizontal and vertical flipping of the image with subsequent shift and absolute difference calculation to check for a central symmetry (flipCode < 0) • reversing the order of 1d point arrays (flipCode > 0 or flipCode = 0) See also: cv::transpose, cv::repeat, cv::completeSymm cv::gemm (view/add comments) Performs generalized matrix multiplication. void gemm(const Mat& src1, const Mat& src2, double alpha, const Mat& src3, double beta, Mat& dst, int flags=0); src1 The first multiplied input matrix; should have CV 32FC1, CV 64FC1, CV 32FC2 or CV 64FC2 type src2 The second multiplied input matrix; should have the same type as src1 alpha The weight of the matrix product src3 The third optional delta matrix added to the matrix product; should have the same type as src1 and src2 beta The weight of src3 dst The destination matrix; It will have the proper size and the same type as input matrices flags Operation flags: GEMM 1 T transpose src1 GEMM 2 T transpose src2 GEMM 3 T transpose src3 560 CHAPTER 11. CORE. THE CORE FUNCTIONALITY The function performs generalized matrix multiplication and similar to the corresponding func- tions *gemm in BLAS level 3. For example, gemm(src1, src2, alpha, src3, beta, dst, GEMM 1 T + GEMM 3 T) corresponds to dst = alpha · src1T· src2 + beta · src3T The function can be replaced with a matrix expression, e.g. the above call can be replaced with: dst = alpha*src1.t()*src2 + beta*src3.t(); See also: cv::mulTransposed, cv::transform, Matrix Expressions cv::getConvertElem (view/add comments) Returns conversion function for a single pixel ConvertData getConvertElem(int fromType, int toType); ConvertScaleData getConvertScaleElem(int fromType, int toType); typedef void (*ConvertData)(const void* from, void* to, int cn); typedef void (*ConvertScaleData)(const void* from, void* to, int cn, double alpha, double beta); fromType The source pixel type toType The destination pixel type from Callback parameter: pointer to the input pixel to Callback parameter: pointer to the output pixel cn Callback parameter: the number of channels; can be arbitrary, 1, 100, 100000, ... alpha ConvertScaleData callback optional parameter: the scale factor beta ConvertScaleData callback optional parameter: the delta or offset The functions getConvertElem and getConvertScaleElem return pointers to the func- tions for converting individual pixels from one type to another. While the main function purpose is to convert single pixels (actually, for converting sparse matrices from one type to another), you can use them to convert the whole row of a dense matrix or the whole matrix at once, by setting cn = matrix.cols*matrix.rows*matrix.channels() if the matrix data is continuous. See also: cv::Mat::convertTo, cv::MatND::convertTo, cv::SparseMat::convertTo 11.2. OPERATIONS ON ARRAYS 561 cv::getOptimalDFTSize (view/add comments) Returns optimal DFT size for a given vector size. int getOptimalDFTSize(int vecsize); vecsize Vector size DFT performance is not a monotonic function of a vector size, therefore, when you compute convolution of two arrays or do a spectral analysis of array, it usually makes sense to pad the input data with zeros to get a bit larger array that can be transformed much faster than the original one. Arrays, which size is a power-of-two (2, 4, 8, 16, 32, ...) are the fastest to process, though, the arrays, which size is a product of 2’s, 3’s and 5’s (e.g. 300 = 5*5*3*2*2), are also processed quite efficiently. The function getOptimalDFTSize returns the minimum number N that is greater than or equal to vecsize, such that the DFT of a vector of size N can be computed efficiently. In the current implementation N = 2p × 3q × 5r, for some p, q, r. The function returns a negative number if vecsize is too large (very close to INT MAX). While the function cannot be used directly to estimate the optimal vector size for DCT transform (since the current DCT implementation supports only even-size vectors), it can be easily computed as getOptimalDFTSize((vecsize+1)/2)*2. See also: cv::dft, cv::dct, cv::idft, cv::idct, cv::mulSpectrums cv::idct (view/add comments) Computes inverse Discrete Cosine Transform of a 1D or 2D array void idct(const Mat& src, Mat& dst, int flags=0); src The source floating-point single-channel array dst The destination array. Will have the same size and same type as src flags The operation flags. 562 CHAPTER 11. CORE. THE CORE FUNCTIONALITY idct(src, dst, flags) is equivalent to dct(src, dst, flags | DCT INVERSE). See cv::dct for details. See also: cv::dct, cv::dft, cv::idft, cv::getOptimalDFTSize cv::idft (view/add comments) Computes inverse Discrete Fourier Transform of a 1D or 2D array void idft(const Mat& src, Mat& dst, int flags=0, int outputRows=0); src The source floating-point real or complex array dst The destination array, which size and type depends on the flags flags The operation flags. See cv::dft nonzeroRows The number of dst rows to compute. The rest of the rows will have undefined content. See the convolution sample in cv::dft description idft(src, dst, flags) is equivalent to dct(src, dst, flags | DFT INVERSE). See cv::dft for details. Note, that none of dft and idft scale the result by default. Thus, you should pass DFT SCALE to one of dft or idft explicitly to make these transforms mutually inverse. See also: cv::dft, cv::dct, cv::idct, cv::mulSpectrums, cv::getOptimalDFTSize cv::inRange (view/add comments) Checks if array elements lie between the elements of two other arrays. void inRange(const Mat& src, const Mat& lowerb, const Mat& upperb, Mat& dst); void inRange(const Mat& src, const Scalar& lowerb, const Scalar& upperb, Mat& dst); void inRange(const MatND& src, const MatND& lowerb, const MatND& upperb, MatND& dst); void inRange(const MatND& src, const Scalar& lowerb, const Scalar& upperb, MatND& dst); 11.2. OPERATIONS ON ARRAYS 563 src The first source array lowerb The inclusive lower boundary array of the same size and type as src upperb The exclusive upper boundary array of the same size and type as src dst The destination array, will have the same size as src and CV 8U type The functions inRange do the range check for every element of the input array: dst(I) = lowerb(I)0 ≤ src(I)0 < upperb(I)0 for single-channel arrays, dst(I) = lowerb(I)0 ≤ src(I)0 < upperb(I)0 ∧ lowerb(I)1 ≤ src(I)1 < upperb(I)1 for two-channel arrays and so forth. dst(I) is set to 255 (all 1-bits) if src(I) is within the specified range and 0 otherwise. cv::invert (view/add comments) Finds the inverse or pseudo-inverse of a matrix double invert(const Mat& src, Mat& dst, int method=DECOMP LU); src The source floating-point M × N matrix dst The destination matrix; will have N × M size and the same type as src flags The inversion method : DECOMP LU Gaussian elimination with optimal pivot element chosen DECOMP SVD Singular value decomposition (SVD) method DECOMP CHOLESKY Cholesky decomposion. The matrix must be symmetrical and positively defined 564 CHAPTER 11. CORE. THE CORE FUNCTIONALITY The function invert inverts matrix src and stores the result in dst. When the matrix src is singular or non-square, the function computes the pseudo-inverse matrix, i.e. the matrix dst, such that ksrc · dst − Ik is minimal. In the case of DECOMP LU method, the function returns the src determinant (src must be square). If it is 0, the matrix is not inverted and dst is filled with zeros. In the case of DECOMP SVD method, the function returns the inversed condition number of src (the ratio of the smallest singular value to the largest singular value) and 0 if src is singular. The SVD method calculates a pseudo-inverse matrix if src is singular. Similarly to DECOMP LU, the method DECOMP CHOLESKY works only with non-singular square matrices. In this case the function stores the inverted matrix in dst and returns non-zero, other- wise it returns 0. See also: cv::solve, cv::SVD cv::log (view/add comments) Calculates the natural logarithm of every array element. void log(const Mat& src, Mat& dst); void log(const MatND& src, MatND& dst); src The source array dst The destination array; will have the same size and same type as src The function log calculates the natural logarithm of the absolute value of every element of the input array: dst(I) =  log |src(I)| if src(I) 6= 0 C otherwise Where C is a large negative number (about -700 in the current implementation). The maximum relative error is about 7 × 10−6 for single-precision input and less than 10−10 for double-precision input. Special values (NaN, ±∞) are not handled. See also: cv::exp, cv::cartToPolar, cv::polarToCart, cv::phase, cv::pow, cv::sqrt, cv::magnitude cv::LUT (view/add comments) Performs a look-up table transform of an array. 11.2. OPERATIONS ON ARRAYS 565 void LUT(const Mat& src, const Mat& lut, Mat& dst); src Source array of 8-bit elements lut Look-up table of 256 elements. In the case of multi-channel source array, the table should either have a single channel (in this case the same table is used for all channels) or the same number of channels as in the source array dst Destination array; will have the same size and the same number of channels as src, and the same depth as lut The function LUT fills the destination array with values from the look-up table. Indices of the entries are taken from the source array. That is, the function processes each element of src as follows: dst(I) ← lut(src(I) + d) where d =  0 if src has depth CV 8U 128 if src has depth CV 8S See also: cv::convertScaleAbs, Mat::convertTo cv::magnitude (view/add comments) Calculates magnitude of 2D vectors. void magnitude(const Mat& x, const Mat& y, Mat& magnitude); x The floating-point array of x-coordinates of the vectors y The floating-point array of y-coordinates of the vectors; must have the same size as x dst The destination array; will have the same size and same type as x 566 CHAPTER 11. CORE. THE CORE FUNCTIONALITY The function magnitude calculates magnitude of 2D vectors formed from the corresponding elements of x and y arrays: dst(I) = px(I)2 + y(I)2 See also: cv::cartToPolar, cv::polarToCart, cv::phase, cv::sqrt cv::Mahalanobis (view/add comments) Calculates the Mahalanobis distance between two vectors. double Mahalanobis(const Mat& vec1, const Mat& vec2, const Mat& icovar); vec1 The first 1D source vector vec2 The second 1D source vector icovar The inverse covariance matrix The function cvMahalonobis calculates and returns the weighted distance between two vec- tors: d(vec1, vec2) = sX i,j icovar(i,j) ·(vec1(I) − vec2(I)) ·(vec1(j) − vec2(j)) The covariance matrix may be calculated using the cv::calcCovarMatrix function and then inverted using the cv::invert function (preferably using DECOMP SVD method, as the most accu- rate). cv::max (view/add comments) Calculates per-element maximum of two arrays or array and a scalar 11.2. OPERATIONS ON ARRAYS 567 Mat Expr<...> max(const Mat& src1, const Mat& src2); Mat Expr<...> max(const Mat& src1, double value); Mat Expr<...> max(double value, const Mat& src1); void max(const Mat& src1, const Mat& src2, Mat& dst); void max(const Mat& src1, double value, Mat& dst); void max(const MatND& src1, const MatND& src2, MatND& dst); void max(const MatND& src1, double value, MatND& dst); src1 The first source array src2 The second source array of the same size and type as src1 value The real scalar value dst The destination array; will have the same size and type as src1 The functions max compute per-element maximum of two arrays: dst(I) = max(src1(I), src2(I)) or array and a scalar: dst(I) = max(src1(I), value) In the second variant, when the source array is multi-channel, each channel is compared with value independently. The first 3 variants of the function listed above are actually a part of Matrix Expressions , they return the expression object that can be further transformed, or assigned to a matrix, or passed to a function etc. See also: cv::min, cv::compare, cv::inRange, cv::minMaxLoc, Matrix Expressions cv::mean (view/add comments) Calculates average (mean) of array elements Scalar mean(const Mat& mtx); Scalar mean(const Mat& mtx, const Mat& mask); Scalar mean(const MatND& mtx); Scalar mean(const MatND& mtx, const MatND& mask); 568 CHAPTER 11. CORE. THE CORE FUNCTIONALITY mtx The source array; it should have 1 to 4 channels (so that the result can be stored in cv::Scalar) mask The optional operation mask The functions mean compute mean value M of array elements, independently for each channel, and return it: N = P I: mask(I)6=0 1 Mc = P I: mask(I)6=0 mtx(I)c  /N When all the mask elements are 0’s, the functions return Scalar::all(0). See also: cv::countNonZero, cv::meanStdDev, cv::norm, cv::minMaxLoc cv::meanStdDev (view/add comments) Calculates mean and standard deviation of array elements void meanStdDev(const Mat& mtx, Scalar& mean, Scalar& stddev, const Mat& mask=Mat()); void meanStdDev(const MatND& mtx, Scalar& mean, Scalar& stddev, const MatND& mask=MatND()); mtx The source array; it should have 1 to 4 channels (so that the results can be stored in cv::Scalar’s) mean The output parameter: computed mean value stddev The output parameter: computed standard deviation mask The optional operation mask The functions meanStdDev compute the mean and the standard deviation M of array elements, independently for each channel, and return it via the output parameters: N = P I,mask(I)6=0 1 meanc = P I: mask(I)6=0 src(I)c N stddevc = qP I: mask(I)6=0 (src(I)c − meanc)2 11.2. OPERATIONS ON ARRAYS 569 When all the mask elements are 0’s, the functions return mean=stddev=Scalar::all(0). Note that the computed standard deviation is only the diagonal of the complete normalized covari- ance matrix. If the full matrix is needed, you can reshape the multi-channel array M × N to the single-channel array M ∗N ×mtx.channels() (only possible when the matrix is continuous) and then pass the matrix to cv::calcCovarMatrix. See also: cv::countNonZero, cv::mean, cv::norm, cv::minMaxLoc, cv::calcCovarMatrix cv::merge (view/add comments) Composes a multi-channel array from several single-channel arrays. void merge(const Mat* mv, size t count, Mat& dst); void merge(const vector& mv, Mat& dst); void merge(const MatND* mv, size t count, MatND& dst); void merge(const vector& mv, MatND& dst); mv The source array or vector of the single-channel matrices to be merged. All the matrices in mv must have the same size and the same type count The number of source matrices when mv is a plain C array; must be greater than zero dst The destination array; will have the same size and the same depth as mv[0], the number of channels will match the number of source matrices The functions merge merge several single-channel arrays (or rather interleave their elements) to make a single multi-channel array. dst(I)c = mv[c](I) The function cv::split does the reverse operation and if you need to merge several multi- channel images or shuffle channels in some other advanced way, use cv::mixChannels See also: cv::mixChannels, cv::split, cv::reshape cv::min (view/add comments) Calculates per-element minimum of two arrays or array and a scalar 570 CHAPTER 11. CORE. THE CORE FUNCTIONALITY Mat Expr<...> min(const Mat& src1, const Mat& src2); Mat Expr<...> min(const Mat& src1, double value); Mat Expr<...> min(double value, const Mat& src1); void min(const Mat& src1, const Mat& src2, Mat& dst); void min(const Mat& src1, double value, Mat& dst); void min(const MatND& src1, const MatND& src2, MatND& dst); void min(const MatND& src1, double value, MatND& dst); src1 The first source array src2 The second source array of the same size and type as src1 value The real scalar value dst The destination array; will have the same size and type as src1 The functions min compute per-element minimum of two arrays: dst(I) = min(src1(I), src2(I)) or array and a scalar: dst(I) = min(src1(I), value) In the second variant, when the source array is multi-channel, each channel is compared with value independently. The first 3 variants of the function listed above are actually a part of Matrix Expressions , they return the expression object that can be further transformed, or assigned to a matrix, or passed to a function etc. See also: cv::max, cv::compare, cv::inRange, cv::minMaxLoc, Matrix Expressions cv::minMaxLoc (view/add comments) Finds global minimum and maximum in a whole array or sub-array void minMaxLoc(const Mat& src, double* minVal, double* maxVal=0, Point* minLoc=0, 11.2. OPERATIONS ON ARRAYS 571 Point* maxLoc=0, const Mat& mask=Mat()); void minMaxLoc(const MatND& src, double* minVal, double* maxVal, int* minIdx=0, int* maxIdx=0, const MatND& mask=MatND()); void minMaxLoc(const SparseMat& src, double* minVal, double* maxVal, int* minIdx=0, int* maxIdx=0); src The source single-channel array minVal Pointer to returned minimum value; NULL if not required maxVal Pointer to returned maximum value; NULL if not required minLoc Pointer to returned minimum location (in 2D case); NULL if not required maxLoc Pointer to returned maximum location (in 2D case); NULL if not required minIdx Pointer to returned minimum location (in nD case); NULL if not required, otherwise must point to an array of src.dims elements and the coordinates of minimum element in each dimensions will be stored sequentially there. maxIdx Pointer to returned maximum location (in nD case); NULL if not required mask The optional mask used to select a sub-array The functions ninMaxLoc find minimum and maximum element values and their positions. The extremums are searched across the whole array, or, if mask is not an empty array, in the specified array region. The functions do not work with multi-channel arrays. If you need to find minimum or maximum elements across all the channels, use cv::reshape first to reinterpret the array as single-channel. Or you may extract the particular channel using cv::extractImageCOI or cv::mixChannels or cv::split. in the case of a sparse matrix the minimum is found among non-zero elements only. See also: cv::max, cv::min, cv::compare, cv::inRange, cv::extractImageCOI, cv::mixChannels, cv::split, cv::reshape. cv::mixChannels (view/add comments) Copies specified channels from input arrays to the specified channels of output arrays 572 CHAPTER 11. CORE. THE CORE FUNCTIONALITY void mixChannels(const Mat* srcv, int nsrc, Mat* dstv, int ndst, const int* fromTo, size t npairs); void mixChannels(const MatND* srcv, int nsrc, MatND* dstv, int ndst, const int* fromTo, size t npairs); void mixChannels(const vector& srcv, vector& dstv, const int* fromTo, int npairs); void mixChannels(const vector& srcv, vector& dstv, const int* fromTo, int npairs); srcv The input array or vector of matrices. All the matrices must have the same size and the same depth nsrc The number of elements in srcv dstv The output array or vector of matrices. All the matrices must be allocated, their size and depth must be the same as in srcv[0] ndst The number of elements in dstv fromTo The array of index pairs, specifying which channels are copied and where. fromTo[k*2] is the 0-based index of the input channel in srcv and fromTo[k*2+1] is the index of the output channel in dstv. Here the continuous channel numbering is used, that is, the first input image channels are indexed from 0 to srcv[0].channels()-1, the second input image channels are indexed from srcv[0].channels() to srcv[0].channels() + srcv[1].channels()-1 etc., and the same scheme is used for the output image chan- nels. As a special case, when fromTo[k*2] is negative, the corresponding output channel is filled with zero. npairsThe number of pairs. In the latter case the parameter is not passed explicitly, but computed as srcv.size() (=dstv.size()) The functions mixChannels provide an advanced mechanism for shuffling image channels. cv::split and cv::merge and some forms of cv::cvtColor are partial cases of mixChannels. As an example, this code splits a 4-channel RGBA image into a 3-channel BGR (i.e. with R and B channels swapped) and separate alpha channel image: Mat rgba( 100, 100, CV_8UC4, Scalar(1,2,3,4) ); Mat bgr( rgba.rows, rgba.cols, CV_8UC3 ); Mat alpha( rgba.rows, rgba.cols, CV_8UC1 ); // forming array of matrices is quite efficient operations, 11.2. OPERATIONS ON ARRAYS 573 // because the matrix data is not copied, only the headers Mat out[] = { bgr, alpha }; // rgba[0] -> bgr[2], rgba[1] -> bgr[1], // rgba[2] -> bgr[0], rgba[3] -> alpha[0] int from_to[] = { 0,2, 1,1, 2,0, 3,3 }; mixChannels( &rgba, 1, out, 2, from_to, 4 ); Note that, unlike many other new-style C++ functions in OpenCV (see the introduction section and cv::Mat::create), mixChannels requires the destination arrays be pre-allocated before calling the function. See also: cv::split, cv::merge, cv::cvtColor cv::mulSpectrums (view/add comments) Performs per-element multiplication of two Fourier spectrums. void mulSpectrums(const Mat& src1, const Mat& src2, Mat& dst, int flags, bool conj=false); src1 The first source array src2 The second source array; must have the same size and the same type as src1 dst The destination array; will have the same size and the same type as src1 flags The same flags as passed to cv::dft; only the flag DFT ROWS is checked for conj The optional flag that conjugate the second source array before the multiplication (true) or not (false) The function mulSpectrums performs per-element multiplication of the two CCS-packed or complex matrices that are results of a real or complex Fourier transform. The function, together with cv::dft and cv::idft, may be used to calculate convolution (pass conj=false) or correlation (pass conj=false) of two arrays rapidly. When the arrays are complex, they are simply multiplied (per-element) with optional conjugation of the second array elements. When the arrays are real, they assumed to be CCS-packed (see cv::dft for details). 574 CHAPTER 11. CORE. THE CORE FUNCTIONALITY cv::multiply (view/add comments) Calculates the per-element scaled product of two arrays void multiply(const Mat& src1, const Mat& src2, Mat& dst, double scale=1); void multiply(const MatND& src1, const MatND& src2, MatND& dst, double scale=1); src1 The first source array src2 The second source array of the same size and the same type as src1 dst The destination array; will have the same size and the same type as src1 scale The optional scale factor The function multiply calculates the per-element product of two arrays: dst(I) = saturate(scale · src1(I)· src2(I)) There is also Matrix Expressions -friendly variant of the first function, see cv::Mat::mul. If you are looking for a matrix product, not per-element product, see cv::gemm. See also: cv::add, cv::substract, cv::divide, Matrix Expressions, cv::scaleAdd, cv::addWeighted, cv::accumulate, cv::accumulateProduct, cv::accumulateSquare, cv::Mat::convertTo cv::mulTransposed (view/add comments) Calculates the product of a matrix and its transposition. void mulTransposed( const Mat& src, Mat& dst, bool aTa, const Mat& delta=Mat(), double scale=1, int rtype=-1 ); src The source matrix 11.2. OPERATIONS ON ARRAYS 575 dst The destination square matrix aTa Specifies the multiplication ordering; see the description below delta The optional delta matrix, subtracted from src before the multiplication. When the matrix is empty (delta=Mat()), it’s assumed to be zero, i.e. nothing is subtracted, otherwise if it has the same size as src, then it’s simply subtracted, otherwise it is ”repeated” (see cv::repeat) to cover the full src and then subtracted. Type of the delta matrix, when it’s not empty, must be the same as the type of created destination matrix, see the rtype description scale The optional scale factor for the matrix product rtype When it’s negative, the destination matrix will have the same type as src. Otherwise, it will have type=CV MAT DEPTH(rtype), which should be either CV 32F or CV 64F The function mulTransposed calculates the product of src and its transposition: dst = scale(src − delta)T(src − delta) if aTa=true, and dst = scale(src − delta)(src − delta)T otherwise. The function is used to compute covariance matrix and with zero delta can be used as a faster substitute for general matrix product A ∗ B when B = AT. See also: cv::calcCovarMatrix, cv::gemm, cv::repeat, cv::reduce cv::norm (view/add comments) Calculates absolute array norm, absolute difference norm, or relative difference norm. double norm(const Mat& src1, int normType=NORM L2); double norm(const Mat& src1, const Mat& src2, int normType=NORM L2); double norm(const Mat& src1, int normType, const Mat& mask); double norm(const Mat& src1, const Mat& src2, int normType, const Mat& mask); double norm(const MatND& src1, int normType=NORM L2, const MatND& mask=MatND()); double norm(const MatND& src1, const MatND& src2, int normType=NORM L2, const MatND& mask=MatND()); double norm( const SparseMat& src, int normType ); 576 CHAPTER 11. CORE. THE CORE FUNCTIONALITY src1 The first source array src2 The second source array of the same size and the same type as src1 normType Type of the norm; see the discussion below mask The optional operation mask The functions norm calculate the absolute norm of src1 (when there is no src2): norm =    ksrc1kL∞ = maxI |src1(I)| if normType = NORM INF ksrc1kL1 = P I |src1(I)| if normType = NORM L1 ksrc1kL2 = pP I src1(I)2 if normType = NORM L2 or an absolute or relative difference norm if src2 is there: norm =    ksrc1 − src2kL∞ = maxI |src1(I) − src2(I)| if normType = NORM INF ksrc1 − src2kL1 = P I |src1(I) − src2(I)| if normType = NORM L1 ksrc1 − src2kL2 = pP I(src1(I) − src2(I))2 if normType = NORM L2 or norm =    ksrc1−src2kL∞ ksrc2kL∞ if normType = NORM RELATIVE INF ksrc1−src2kL1 ksrc2kL1 if normType = NORM RELATIVE L1 ksrc1−src2kL2 ksrc2kL2 if normType = NORM RELATIVE L2 The functions norm return the calculated norm. When there is mask parameter, and it is not empty (then it should have type CV 8U and the same size as src1), the norm is computed only over the specified by the mask region. A multiple-channel source arrays are treated as a single-channel, that is, the results for all channels are combined. cv::normalize (view/add comments) Normalizes array’s norm or the range void normalize( const Mat& src, Mat& dst, double alpha=1, double beta=0, int normType=NORM L2, int rtype=-1, 11.2. OPERATIONS ON ARRAYS 577 const Mat& mask=Mat()); void normalize( const MatND& src, MatND& dst, double alpha=1, double beta=0, int normType=NORM L2, int rtype=-1, const MatND& mask=MatND()); void normalize( const SparseMat& src, SparseMat& dst, double alpha, int normType ); src The source array dst The destination array; will have the same size as src alpha The norm value to normalize to or the lower range boundary in the case of range normal- ization beta The upper range boundary in the case of range normalization; not used for norm normal- ization normType The normalization type, see the discussion rtype When the parameter is negative, the destination array will have the same type as src, oth- erwise it will have the same number of channels as src and the depth=CV MAT DEPTH(rtype) mask The optional operation mask The functions normalize scale and shift the source array elements, so that kdstkLp = alpha (where p = ∞, 1 or 2) when normType=NORM INF, NORM L1 or NORM L2, or so that min I dst(I) = alpha, max I dst(I) = beta when normType=NORM MINMAX (for dense arrays only). The optional mask specifies the sub-array to be normalize, that is, the norm or min-n-max are computed over the sub-array and then this sub-array is modified to be normalized. If you want to only use the mask to compute the norm or min-max, but modify the whole array, you can use cv::norm and cv::Mat::convertScale/ cv::MatND::convertScale/crossSparseMat::convertScale sep- arately. in the case of sparse matrices, only the non-zero values are analyzed and transformed. Be- cause of this, the range transformation for sparse matrices is not allowed, since it can shift the zero level. See also: cv::norm, cv::Mat::convertScale, cv::MatND::convertScale, cv::SparseMat::convertScale 578 CHAPTER 11. CORE. THE CORE FUNCTIONALITY cv::PCA (view/add comments) Class for Principal Component Analysis class PCA { public: // default constructor PCA(); // computes PCA for a set of vectors stored as data rows or columns. PCA(const Mat& data, const Mat& mean, int flags, int maxComponents=0); // computes PCA for a set of vectors stored as data rows or columns PCA& operator()(const Mat& data, const Mat& mean, int flags, int maxComponents=0); // projects vector into the principal components space Mat project(const Mat& vec) const; void project(const Mat& vec, Mat& result) const; // reconstructs the vector from its PC projection Mat backProject(const Mat& vec) const; void backProject(const Mat& vec, Mat& result) const; // eigenvectors of the PC space, stored as the matrix rows Mat eigenvectors; // the corresponding eigenvalues; not used for PCA compression/decompression Mat eigenvalues; // mean vector, subtracted from the projected vector // or added to the reconstructed vector Mat mean; }; The class PCA is used to compute the special basis for a set of vectors. The basis will consist of eigenvectors of the covariance matrix computed from the input set of vectors. And also the class PCA can transform vectors to/from the new coordinate space, defined by the basis. Usually, in this new coordinate system each vector from the original set (and any linear combination of such vectors) can be quite accurately approximated by taking just the first few its components, corre- sponding to the eigenvectors of the largest eigenvalues of the covariance matrix. Geometrically it means that we compute projection of the vector to a subspace formed by a few eigenvectors cor- responding to the dominant eigenvalues of the covariation matrix. And usually such a projection is very close to the original vector. That is, we can represent the original vector from a high- dimensional space with a much shorter vector consisting of the projected vector’s coordinates in the subspace. Such a transformation is also known as Karhunen-Loeve Transform, or KLT. See http://en.wikipedia.org/wiki/Principal_component_analysis The following sample is the function that takes two matrices. The first one stores the set of vectors (a row per vector) that is used to compute PCA, the second one stores another ”test” set of vectors (a row per vector) that are first compressed with PCA, then reconstructed back and then 11.2. OPERATIONS ON ARRAYS 579 the reconstruction error norm is computed and printed for each vector. PCA compressPCA(const Mat& pcaset, int maxComponents, const Mat& testset, Mat& compressed) { PCA pca(pcaset, // pass the data Mat(), // we do not have a pre-computed mean vector, // so let the PCA engine to compute it CV_PCA_DATA_AS_ROW, // indicate that the vectors // are stored as matrix rows // (use CV_PCA_DATA_AS_COL if the vectors are // the matrix columns) maxComponents // specify, how many principal components to retain ); // if there is no test data, just return the computed basis, ready-to-use if( !testset.data ) return pca; CV_Assert( testset.cols == pcaset.cols ); compressed.create(testset.rows, maxComponents, testset.type()); Mat reconstructed; for( int i = 0; i < testset.rows; i++ ) { Mat vec = testset.row(i), coeffs = compressed.row(i); // compress the vector, the result will be stored // in the i-th row of the output matrix pca.project(vec, coeffs); // and then reconstruct it pca.backProject(coeffs, reconstructed); // and measure the error printf("%d. diff = %g\n", i, norm(vec, reconstructed, NORM_L2)); } return pca; } See also: cv::calcCovarMatrix, cv::mulTransposed, cv::SVD, cv::dft, cv::dct cv::PCA::PCA (view/add comments) PCA constructors 580 CHAPTER 11. CORE. THE CORE FUNCTIONALITY PCA::PCA(); PCA::PCA(const Mat& data, const Mat& mean, int flags, int maxComponents=0); data the input samples, stored as the matrix rows or as the matrix columns mean the optional mean value. If the matrix is empty (Mat()), the mean is computed from the data. flags operation flags. Currently the parameter is only used to specify the data layout. CV PCA DATA AS ROWS Indicates that the input samples are stored as matrix rows. CV PCA DATA AS COLS Indicates that the input samples are stored as matrix columns. maxComponents The maximum number of components that PCA should retain. By default, all the components are retained. The default constructor initializes empty PCA structure. The second constructor initializes the structure and calls cv::PCA::operator (). cv::PCA::operator () (view/add comments) Performs Principal Component Analysis of the supplied dataset. PCA& PCA::operator()(const Mat& data, const Mat& mean, int flags, int maxComponents=0); data the input samples, stored as the matrix rows or as the matrix columns mean the optional mean value. If the matrix is empty (Mat()), the mean is computed from the data. flags operation flags. Currently the parameter is only used to specify the data layout. CV PCA DATA AS ROWS Indicates that the input samples are stored as matrix rows. CV PCA DATA AS COLS Indicates that the input samples are stored as matrix columns. 11.2. OPERATIONS ON ARRAYS 581 maxComponents The maximum number of components that PCA should retain. By default, all the components are retained. The operator performs PCA of the supplied dataset. It is safe to reuse the same PCA structure for multiple dataset. That is, if the structure has been previously used with another dataset, the existing internal data is reclaimed and the new eigenvalues, eigenvectors and mean are allocated and computed. The computed eigenvalues are sorted from the largest to the smallest and the corresponding eigenvectors are stored as PCA::eigenvectors rows. cv::PCA::project (view/add comments) Project vector(s) to the principal component subspace Mat PCA::project(const Mat& vec) const; void PCA::project(const Mat& vec, Mat& result) const; vec the input vector(s). They have to have the same dimensionality and the same layout as the input data used at PCA phase. That is, if CV PCA DATA AS ROWS had been specified, then vec.cols==data.cols (that’s vectors’ dimensionality) and vec.rows is the number of vectors to project; and similarly for the CV PCA DATA AS COLS case. result the output vectors. Let’s now consider CV PCA DATA AS COLS case. In this case the out- put matrix will have as many columns as the number of input vectors, i.e. result.cols==vec.cols and the number of rows will match the number of principal components (e.g. maxComponents parameter passed to the constructor). The methods project one or more vectors to the principal component subspace, where each vector projection is represented by coefficients in the principal component basis. The first form of the method returns the matrix that the second form writes to the result. So the first form can be used as a part of expression, while the second form can be more efficient in a processing loop. cv::PCA::backProject (view/add comments) Reconstruct vectors from their PC projections. 582 CHAPTER 11. CORE. THE CORE FUNCTIONALITY Mat PCA::backProject(const Mat& vec) const; void PCA::backProject(const Mat& vec, Mat& result) const; vec Coordinates of the vectors in the principal component subspace. The layout and size are the same as of PCA::project output vectors. result The reconstructed vectors. The layout and size are the same as of PCA::project input vectors. The methods are inverse operations to cv::PCA::project. They take PC coordinates of pro- jected vectors and reconstruct the original vectors. Of course, unless all the principal components have been retained, the reconstructed vectors will be different from the originals, but typically the difference will be small is if the number of components is large enough (but still much smaller than the original vector dimensionality) - that’s why PCA is used after all. cv::perspectiveTransform (view/add comments) Performs perspective matrix transformation of vectors. void perspectiveTransform(const Mat& src, Mat& dst, const Mat& mtx ); src The source two-channel or three-channel floating-point array; each element is 2D/3D vector to be transformed dst The destination array; it will have the same size and same type as src mtx 3 × 3 or 4 × 4 transformation matrix The function perspectiveTransform transforms every element of src, by treating it as 2D or 3D vector, in the following way (here 3D vector transformation is shown; in the case of 2D vector transformation the z component is omitted): (x, y, z) → (x0/w, y0/w, z0/w) where 11.2. OPERATIONS ON ARRAYS 583 (x0, y0, z0, w0) = mat · x y z 1 and w =  w0 if w0 6= 0 ∞ otherwise Note that the function transforms a sparse set of 2D or 3D vectors. If you want to transform an image using perspective transformation, use cv::warpPerspective. If you have an inverse task, i.e. want to compute the most probable perspective transformation out of several pairs of corresponding points, you can use cv::getPerspectiveTransform or cv::findHomography. See also: cv::transform, cv::warpPerspective, cv::getPerspectiveTransform, cv::findHomography cv::phase (view/add comments) Calculates the rotation angle of 2d vectors void phase(const Mat& x, const Mat& y, Mat& angle, bool angleInDegrees=false); x The source floating-point array of x-coordinates of 2D vectors y The source array of y-coordinates of 2D vectors; must have the same size and the same type as x angle The destination array of vector angles; it will have the same size and same type as x angleInDegrees When it is true, the function will compute angle in degrees, otherwise they will be measured in radians The function phase computes the rotation angle of each 2D vector that is formed from the corresponding elements of x and y: angle(I) = atan2(y(I), x(I)) The angle estimation accuracy is ∼ 0.3◦, when x(I)=y(I)=0, the corresponding angle(I) is set to 0. See also: 584 CHAPTER 11. CORE. THE CORE FUNCTIONALITY cv::polarToCart (view/add comments) Computes x and y coordinates of 2D vectors from their magnitude and angle. void polarToCart(const Mat& magnitude, const Mat& angle, Mat& x, Mat& y, bool angleInDegrees=false); magnitude The source floating-point array of magnitudes of 2D vectors. It can be an empty matrix (=Mat()) - in this case the function assumes that all the magnitudes are =1. If it’s not empty, it must have the same size and same type as angle angle The source floating-point array of angles of the 2D vectors x The destination array of x-coordinates of 2D vectors; will have the same size and the same type as angle y The destination array of y-coordinates of 2D vectors; will have the same size and the same type as angle angleInDegrees When it is true, the input angles are measured in degrees, otherwise they are measured in radians The function polarToCart computes the cartesian coordinates of each 2D vector repre- sented by the corresponding elements of magnitude and angle: x(I) = magnitude(I) cos(angle(I)) y(I) = magnitude(I) sin(angle(I)) The relative accuracy of the estimated coordinates is ∼ 10−6. See also: cv::cartToPolar, cv::magnitude, cv::phase, cv::exp, cv::log, cv::pow, cv::sqrt cv::pow (view/add comments) Raises every array element to a power. void pow(const Mat& src, double p, Mat& dst); void pow(const MatND& src, double p, MatND& dst); 11.2. OPERATIONS ON ARRAYS 585 src The source array p The exponent of power dst The destination array; will have the same size and the same type as src The function pow raises every element of the input array to p: dst(I) =  src(I)p if p is integer |src(I)|p otherwise That is, for a non-integer power exponent the absolute values of input array elements are used. However, it is possible to get true values for negative values using some extra operations, as the following example, computing the 5th root of array src, shows: Mat mask = src < 0; pow(src, 1./5, dst); subtract(Scalar::all(0), dst, dst, mask); For some values of p, such as integer values, 0.5, and -0.5, specialized faster algorithms are used. See also: cv::sqrt, cv::exp, cv::log, cv::cartToPolar, cv::polarToCart RNG Random number generator class. class CV_EXPORTS RNG { public: enum { A=4164903690U, UNIFORM=0, NORMAL=1 }; // constructors RNG(); RNG(uint64 state); // returns 32-bit unsigned random number unsigned next(); // return random numbers of the specified type operator uchar(); operator schar(); operator ushort(); operator short(); operator unsigned(); // returns a random integer sampled uniformly from [0, N). 586 CHAPTER 11. CORE. THE CORE FUNCTIONALITY unsigned operator()(unsigned N); unsigned operator()(); operator int(); operator float(); operator double(); // returns a random number sampled uniformly from [a, b) range int uniform(int a, int b); float uniform(float a, float b); double uniform(double a, double b); // returns Gaussian random number with zero mean. double gaussian(double sigma); // fills array with random numbers sampled from the specified distribution void fill( Mat& mat, int distType, const Scalar& a, const Scalar& b ); void fill( MatND& mat, int distType, const Scalar& a, const Scalar& b ); // internal state of the RNG (could change in the future) uint64 state; }; The class RNG implements random number generator. It encapsulates the RNG state (cur- rently, a 64-bit integer) and has methods to return scalar random values and to fill arrays with random values. Currently it supports uniform and Gaussian (normal) distributions. The generator uses Multiply-With-Carry algorithm, introduced by G. Marsaglia (http://en.wikipedia.org/ wiki/Multiply-with-carry). Gaussian-distribution random numbers are generated using Ziggurat algorithm (http://en.wikipedia.org/wiki/Ziggurat_algorithm), introduced by G. Marsaglia and W. W. Tsang. cv::RNG::RNG (view/add comments) RNG constructors RNG::RNG(); RNG::RNG(uint64 state); state the 64-bit value used to initialize the RNG These are the RNG constructors. The first form sets the state to some pre-defined value, equal to 2**32-1 in the current implementation. The second form sets the state to the specified value. 11.2. OPERATIONS ON ARRAYS 587 If the user passed state=0, the constructor uses the above default value instead, to avoid the singular random number sequence, consisting of all zeros. cv::RNG::next (view/add comments) Returns the next random number unsigned RNG::next(); The method updates the state using MWC algorithm and returns the next 32-bit random num- ber. cv::RNG::operator T (view/add comments) Returns the next random number of the specified type RNG::operator uchar(); RNG::operator schar(); RNG::operator ushort(); RNG::operator short(); RNG::operator unsigned(); RNG::operator int(); RNG::operator float(); RNG::operator double(); Each of the methods updates the state using MWC algorithm and returns the next random number of the specified type. In the case of integer types the returned number is from the whole available value range for the specified type. In the case of floating-point types the returned value is from [0,1) range. cv::RNG::operator () (view/add comments) Returns the next random number unsigned RNG::operator ()(); unsigned RNG::operator ()(unsigned N); 588 CHAPTER 11. CORE. THE CORE FUNCTIONALITY N The upper non-inclusive boundary of the returned random number The methods transforms the state using MWC algorithm and returns the next random number. The first form is equivalent to cv::RNG::next, the second form returns the random number modulo N, i.e. the result will be in the range [0, N). cv::RNG::uniform (view/add comments) Returns the next random number sampled from the uniform distribution int RNG::uniform(int a, int b); float RNG::uniform(float a, float b); double RNG::uniform(double a, double b); a The lower inclusive boundary of the returned random numbers b The upper non-inclusive boundary of the returned random numbers The methods transforms the state using MWC algorithm and returns the next uniformly-distributed random number of the specified type, deduced from the input parameter type, from the range [a, b). There is one nuance, illustrated by the following sample: cv::RNG rng; // will always produce 0 double a = rng.uniform(0, 1); // will produce double from [0, 1) double a1 = rng.uniform((double)0, (double)1); // will produce float from [0, 1) double b = rng.uniform(0.f, 1.f); // will produce double from [0, 1) double c = rng.uniform(0., 1.); // will likely cause compiler error because of ambiguity: // RNG::uniform(0, (int)0.999999)? or RNG::uniform((double)0, 0.99999)? double d = rng.uniform(0, 0.999999); 11.2. OPERATIONS ON ARRAYS 589 That is, the compiler does not take into account type of the variable that you assign the result of RNG::uniform to, the only thing that matters to it is the type of a and b parameters. So if you want a floating-point random number, but the range boundaries are integer numbers, either put dots in the end, if they are constants, or use explicit type cast operators, as in a1 initialization above. cv::RNG::gaussian (view/add comments) Returns the next random number sampled from the Gaussian distribution double RNG::gaussian(double sigma); sigma The standard deviation of the distribution The methods transforms the state using MWC algorithm and returns the next random number from the Gaussian distribution N(0,sigma). That is, the mean value of the returned random numbers will be zero and the standard deviation will be the specified sigma. cv::RNG::fill (view/add comments) Fill arrays with random numbers void RNG::fill( Mat& mat, int distType, const Scalar& a, const Scalar& b ); void RNG::fill( MatND& mat, int distType, const Scalar& a, const Scalar& b ); mat 2D or N-dimensional matrix. Currently matrices with more than 4 channels are not supported by the methods. Use cv::reshape as a possible workaround. distType The distribution type, RNG::UNIFORM or RNG::NORMAL a The first distribution parameter. In the case of uniform distribution this is inclusive lower bound- ary. In the case of normal distribution this is mean value. 590 CHAPTER 11. CORE. THE CORE FUNCTIONALITY b The second distribution parameter. In the case of uniform distribution this is non-inclusive upper boundary. In the case of normal distribution this is standard deviation. Each of the methods fills the matrix with the random values from the specified distribution. As the new numbers are generated, the RNG state is updated accordingly. In the case of multiple- channel images every channel is filled independently, i.e. RNG can not generate samples from multi-dimensional Gaussian distribution with non-diagonal covariation matrix directly. To do that, first, generate matrix from the distribution N(0,In), i.e. Gaussian distribution with zero mean and identity covariation matrix, and then transform it using cv::transform and the specific covariation matrix. cv::randu (view/add comments) Generates a single uniformly-distributed random number or array of random numbers template Tp randu(); void randu(Mat& mtx, const Scalar& low, const Scalar& high); mtx The output array of random numbers. The array must be pre-allocated and have 1 to 4 channels low The inclusive lower boundary of the generated random numbers high The exclusive upper boundary of the generated random numbers The template functions randu generate and return the next uniformly-distributed random value of the specified type. randu() is equivalent to (int)theRNG(); etc. See cv::RNG description. The second non-template variant of the function fills the matrix mtx with uniformly-distributed random numbers from the specified range: lowc ≤ mtx(I)c < highc See also: cv::RNG, cv::randn, cv::theRNG. cv::randn (view/add comments) Fills array with normally distributed random numbers 11.2. OPERATIONS ON ARRAYS 591 void randn(Mat& mtx, const Scalar& mean, const Scalar& stddev); mtx The output array of random numbers. The array must be pre-allocated and have 1 to 4 channels mean The mean value (expectation) of the generated random numbers stddev The standard deviation of the generated random numbers The function randn fills the matrix mtx with normally distributed random numbers with the specified mean and standard deviation. saturate cast is applied to the generated numbers (i.e. the values are clipped) See also: cv::RNG, cv::randu cv::randShuffle (view/add comments) Shuffles the array elements randomly void randShuffle(Mat& mtx, double iterFactor=1., RNG* rng=0); mtx The input/output numerical 1D array iterFactor The scale factor that determines the number of random swap operations. See the discussion rng The optional random number generator used for shuffling. If it is zero, cv::theRNG() is used instead The function randShuffle shuffles the specified 1D array by randomly choosing pairs of ele- ments and swapping them. The number of such swap operations will be mtx.rows*mtx.cols*iterFactor See also: cv::RNG, cv::sort 592 CHAPTER 11. CORE. THE CORE FUNCTIONALITY cv::reduce (view/add comments) Reduces a matrix to a vector void reduce(const Mat& mtx, Mat& vec, int dim, int reduceOp, int dtype=-1); mtx The source 2D matrix vec The destination vector. Its size and type is defined by dim and dtype parameters dim The dimension index along which the matrix is reduced. 0 means that the matrix is reduced to a single row and 1 means that the matrix is reduced to a single column reduceOp The reduction operation, one of: CV REDUCE SUM The output is the sum of all of the matrix’s rows/columns. CV REDUCE AVG The output is the mean vector of all of the matrix’s rows/columns. CV REDUCE MAX The output is the maximum (column/row-wise) of all of the matrix’s rows/- columns. CV REDUCE MIN The output is the minimum (column/row-wise) of all of the matrix’s rows/- columns. dtype When it is negative, the destination vector will have the same type as the source matrix, otherwise, its type will be CV MAKE TYPE(CV MAT DEPTH(dtype), mtx.channels()) The function reduce reduces matrix to a vector by treating the matrix rows/columns as a set of 1D vectors and performing the specified operation on the vectors until a single row/column is obtained. For example, the function can be used to compute horizontal and vertical projections of an raster image. In the case of CV REDUCE SUM and CV REDUCE AVG the output may have a larger element bit-depth to preserve accuracy. And multi-channel arrays are also supported in these two reduction modes. See also: cv::repeat cv::repeat (view/add comments) Fill the destination array with repeated copies of the source array. 11.2. OPERATIONS ON ARRAYS 593 void repeat(const Mat& src, int ny, int nx, Mat& dst); Mat repeat(const Mat& src, int ny, int nx); src The source array to replicate dst The destination array; will have the same type as src ny How many times the src is repeated along the vertical axis nx How many times the src is repeated along the horizontal axis The functions cv::repeat duplicate the source array one or more times along each of the two axes: dstij = srci mod src.rows, j mod src.cols The second variant of the function is more convenient to use with Matrix Expressions See also: cv::reduce, Matrix Expressions saturate cast Template function for accurate conversion from one primitive type to another template inline Tp saturate cast(unsigned char v); template inline Tp saturate cast(signed char v); template inline Tp saturate cast(unsigned short v); template inline Tp saturate cast(signed short v); template inline Tp saturate cast(int v); template inline Tp saturate cast(unsigned int v); template inline Tp saturate cast(float v); template inline Tp saturate cast(double v); v The function parameter 594 CHAPTER 11. CORE. THE CORE FUNCTIONALITY The functions saturate cast resembles the standard C++ cast operations, such as static cast() etc. They perform an efficient and accurate conversion from one primitive type to another, see the introduction. ”saturate” in the name means that when the input value v is out of range of the target type, the result will not be formed just by taking low bits of the input, but instead the value will be clipped. For example: uchar a = saturate_cast(-100); // a = 0 (UCHAR_MIN) short b = saturate_cast(33333.33333); // b = 32767 (SHRT_MAX) Such clipping is done when the target type is unsigned char, signed char, unsigned short or signed short - for 32-bit integers no clipping is done. When the parameter is floating-point value and the target type is an integer (8-, 16- or 32-bit), the floating-point value is first rounded to the nearest integer and then clipped if needed (when the target type is 8- or 16-bit). This operation is used in most simple or complex image processing functions in OpenCV. See also: cv::add, cv::subtract, cv::multiply, cv::divide, cv::Mat::convertTo cv::scaleAdd (view/add comments) Calculates the sum of a scaled array and another array. void scaleAdd(const Mat& src1, double scale, const Mat& src2, Mat& dst); void scaleAdd(const MatND& src1, double scale, const MatND& src2, MatND& dst); src1 The first source array scale Scale factor for the first array src2 The second source array; must have the same size and the same type as src1 dst The destination array; will have the same size and the same type as src1 The function cvScaleAdd is one of the classical primitive linear algebra operations, known as DAXPY or SAXPY in BLAS. It calculates the sum of a scaled array and another array: dst(I) = scale · src1(I) + src2(I) The function can also be emulated with a matrix expression, for example: 11.2. OPERATIONS ON ARRAYS 595 Mat A(3, 3, CV_64F); ... A.row(0) = A.row(1)*2 + A.row(2); See also: cv::add, cv::addWeighted, cv::subtract, cv::Mat::dot, cv::Mat::convertTo, Matrix Expressions cv::setIdentity (view/add comments) Initializes a scaled identity matrix void setIdentity(Mat& dst, const Scalar& value=Scalar(1)); dst The matrix to initialize (not necessarily square) value The value to assign to the diagonal elements The function cv::setIdentity initializes a scaled identity matrix: dst(i, j) =  value if i = j 0 otherwise The function can also be emulated using the matrix initializers and the matrix expressions: Mat A = Mat::eye(4, 3, CV_32F)*5; // A will be set to [[5, 0, 0], [0, 5, 0], [0, 0, 5], [0, 0, 0]] See also: cv::Mat::zeros, cv::Mat::ones, Matrix Expressions, cv::Mat::setTo, cv::Mat::operator=, cv::solve (view/add comments) Solves one or more linear systems or least-squares problems. bool solve(const Mat& src1, const Mat& src2, Mat& dst, int flags=DECOMP LU); src1 The input matrix on the left-hand side of the system 596 CHAPTER 11. CORE. THE CORE FUNCTIONALITY src2 The input matrix on the right-hand side of the system dst The output solution flags The solution (matrix inversion) method DECOMP LU Gaussian elimination with optimal pivot element chosen DECOMP CHOLESKY Cholesky LLT factorization; the matrix src1 must be symmetrical and positively defined DECOMP EIG Eigenvalue decomposition; the matrix src1 must be symmetrical DECOMP SVD Singular value decomposition (SVD) method; the system can be over-defined and/or the matrix src1 can be singular DECOMP QR QR factorization; the system can be over-defined and/or the matrix src1 can be singular DECOMP NORMAL While all the previous flags are mutually exclusive, this flag can be used together with any of the previous. It means that the normal equations src1T· src1 · dst = src1T src2 are solved instead of the original system src1 · dst = src2 The function solve solves a linear system or least-squares problem (the latter is possible with SVD or QR methods, or by specifying the flag DECOMP NORMAL): dst = arg min X ksrc1 ·X − src2k If DECOMP LU or DECOMP CHOLESKY method is used, the function returns 1 if src1 (or src1T src1) is non-singular and 0 otherwise; in the latter case dst is not valid. Other methods find some pseudo-solution in the case of singular left-hand side part. Note that if you want to find unity-norm solution of an under-defined singular system src1 · dst = 0, the function solve will not do the work. Use cv::SVD::solveZ instead. See also: cv::invert, cv::SVD, cv::eigen cv::solveCubic (view/add comments) Finds the real roots of a cubic equation. void solveCubic(const Mat& coeffs, Mat& roots); coeffs The equation coefficients, an array of 3 or 4 elements 11.2. OPERATIONS ON ARRAYS 597 roots The destination array of real roots which will have 1 or 3 elements The function solveCubic finds the real roots of a cubic equation: (if coeffs is a 4-element vector) coeffs[0]x3 + coeffs[1]x2 + coeffs[2]x + coeffs[3] = 0 or (if coeffs is 3-element vector): x3 + coeffs[0]x2 + coeffs[1]x + coeffs[2] = 0 The roots are stored to roots array. cv::solvePoly (view/add comments) Finds the real or complex roots of a polynomial equation void solvePoly(const Mat& coeffs, Mat& roots, int maxIters=20, int fig=100); coeffs The array of polynomial coefficients roots The destination (complex) array of roots maxIters The maximum number of iterations the algorithm does fig The function solvePoly finds real and complex roots of a polynomial equation: coeffs[0]xn + coeffs[1]xn−1 + ... + coeffs[n − 1]x + coeffs[n] = 0 cv::sort (view/add comments) Sorts each row or each column of a matrix void sort(const Mat& src, Mat& dst, int flags); 598 CHAPTER 11. CORE. THE CORE FUNCTIONALITY src The source single-channel array dst The destination array of the same size and the same type as src flags The operation flags, a combination of the following values: CV SORT EVERY ROW Each matrix row is sorted independently CV SORT EVERY COLUMN Each matrix column is sorted independently. This flag and the previous one are mutually exclusive CV SORT ASCENDING Each matrix row is sorted in the ascending order CV SORT DESCENDING Each matrix row is sorted in the descending order. This flag and the previous one are also mutually exclusive The function sort sorts each matrix row or each matrix column in ascending or descending order. If you want to sort matrix rows or columns lexicographically, you can use STL std::sort generic function with the proper comparison predicate. See also: cv::sortIdx, cv::randShuffle cv::sortIdx (view/add comments) Sorts each row or each column of a matrix void sortIdx(const Mat& src, Mat& dst, int flags); src The source single-channel array dst The destination integer array of the same size as src flags The operation flags, a combination of the following values: CV SORT EVERY ROW Each matrix row is sorted independently CV SORT EVERY COLUMN Each matrix column is sorted independently. This flag and the previous one are mutually exclusive CV SORT ASCENDING Each matrix row is sorted in the ascending order CV SORT DESCENDING Each matrix row is sorted in the descending order. This flag and the previous one are also mutually exclusive 11.2. OPERATIONS ON ARRAYS 599 The function sortIdx sorts each matrix row or each matrix column in ascending or descend- ing order. Instead of reordering the elements themselves, it stores the indices of sorted elements in the destination array. For example: Mat A = Mat::eye(3,3,CV_32F), B; sortIdx(A, B, CV_SORT_EVERY_ROW + CV_SORT_ASCENDING); // B will probably contain // (because of equal elements in A some permutations are possible): // [[1, 2, 0], [0, 2, 1], [0, 1, 2]] See also: cv::sort, cv::randShuffle cv::split (view/add comments) Divides multi-channel array into several single-channel arrays void split(const Mat& mtx, Mat* mv); void split(const Mat& mtx, vector& mv); void split(const MatND& mtx, MatND* mv); void split(const MatND& mtx, vector& mv); mtx The source multi-channel array mv The destination array or vector of arrays; The number of arrays must match mtx.channels(). The arrays themselves will be reallocated if needed The functions split split multi-channel array into separate single-channel arrays: mv[c](I) = mtx(I)c If you need to extract a single-channel or do some other sophisticated channel permutation, use cv::mixChannels See also: cv::merge, cv::mixChannels, cv::cvtColor cv::sqrt (view/add comments) Calculates square root of array elements 600 CHAPTER 11. CORE. THE CORE FUNCTIONALITY void sqrt(const Mat& src, Mat& dst); void sqrt(const MatND& src, MatND& dst); src The source floating-point array dst The destination array; will have the same size and the same type as src The functions sqrt calculate square root of each source array element. in the case of multi- channel arrays each channel is processed independently. The function accuracy is approximately the same as of the built-in std::sqrt. See also: cv::pow, cv::magnitude cv::subtract (view/add comments) Calculates per-element difference between two arrays or array and a scalar void subtract(const Mat& src1, const Mat& src2, Mat& dst); void subtract(const Mat& src1, const Mat& src2, Mat& dst, const Mat& mask); void subtract(const Mat& src1, const Scalar& sc, Mat& dst, const Mat& mask=Mat()); void subtract(const Scalar& sc, const Mat& src2, Mat& dst, const Mat& mask=Mat()); void subtract(const MatND& src1, const MatND& src2, MatND& dst); void subtract(const MatND& src1, const MatND& src2, MatND& dst, const MatND& mask); void subtract(const MatND& src1, const Scalar& sc, MatND& dst, const MatND& mask=MatND()); void subtract(const Scalar& sc, const MatND& src2, MatND& dst, const MatND& mask=MatND()); src1 The first source array src2 The second source array. It must have the same size and same type as src1 11.2. OPERATIONS ON ARRAYS 601 sc Scalar; the first or the second input parameter dst The destination array; it will have the same size and same type as src1; see Mat::create mask The optional operation mask, 8-bit single channel array; specifies elements of the destina- tion array to be changed The functions subtract compute • the difference between two arrays dst(I) = saturate(src1(I) − src2(I)) if mask(I) 6= 0 • the difference between array and a scalar: dst(I) = saturate(src1(I) − sc) if mask(I) 6= 0 • the difference between scalar and an array: dst(I) = saturate(sc − src2(I)) if mask(I) 6= 0 where I is multi-dimensional index of array elements. The first function in the above list can be replaced with matrix expressions: dst = src1 - src2; dst -= src2; // equivalent to subtract(dst, src2, dst); See also: cv::add, cv::addWeighted, cv::scaleAdd, cv::convertScale, Matrix Expressions, saturate cast. cv::SVD (view/add comments) Class for computing Singular Value Decomposition class SVD { public: enum { MODIFY_A=1, NO_UV=2, FULL_UV=4 }; // default empty constructor SVD(); // decomposes A into u, w and vt: A = u*w*vt; // u and vt are orthogonal, w is diagonal SVD( const Mat& A, int flags=0 ); // decomposes A into u, w and vt. SVD& operator ()( const Mat& A, int flags=0 ); 602 CHAPTER 11. CORE. THE CORE FUNCTIONALITY // finds such vector x, norm(x)=1, so that A*x = 0, // where A is singular matrix static void solveZ( const Mat& A, Mat& x ); // does back-subsitution: // x = vt.t()*inv(w)*u.t()*rhs ˜ inv(A)*rhs void backSubst( const Mat& rhs, Mat& x ) const; Mat u; // the left orthogonal matrix Mat w; // vector of singular values Mat vt; // the right orthogonal matrix }; The class SVD is used to compute Singular Value Decomposition of a floating-point matrix and then use it to solve least-square problems, under-determined linear systems, invert matrices, com- pute condition numbers etc. For a bit faster operation you can pass flags=SVD::MODIFY A|... to modify the decomposed matrix when it is not necessarily to preserve it. If you want to compute condition number of a matrix or absolute value of its determinant - you do not need u and vt, so you can pass flags=SVD::NO UV|.... Another flag FULL UV indicates that full-size u and vt must be computed, which is not necessary most of the time. See also: cv::invert, cv::solve, cv::eigen, cv::determinant cv::SVD::SVD (view/add comments) SVD constructors SVD::SVD(); SVD::SVD( const Mat& A, int flags=0 ); A The decomposed matrix flags Operation flags SVD::MODIFY A The algorithm can modify the decomposed matrix. It can save some space and speed-up processing a bit SVD::NO UV Indicates that only the vector of singular values w is to be computed, while u and vt will be set to empty matrices SVD::FULL UV When the matrix is not square, by default the algorithm produces u and vt matrices of sufficiently large size for the further A reconstruction. If, however, FULL UV flag is specified, u and vt will be full-size square orthogonal matrices. 11.2. OPERATIONS ON ARRAYS 603 The first constructor initializes empty SVD structure. The second constructor initializes empty SVD structure and then calls cv::SVD::operator (). cv::SVD::operator () (view/add comments) Performs SVD of a matrix SVD& SVD::operator ()( const Mat& A, int flags=0 ); A The decomposed matrix flags Operation flags SVD::MODIFY A The algorithm can modify the decomposed matrix. It can save some space and speed-up processing a bit SVD::NO UV Only singular values are needed. The algorithm will not compute u and vt matrices SVD::FULL UV When the matrix is not square, by default the algorithm produces u and vt matrices of sufficiently large size for the further A reconstruction. If, however, FULL UV flag is specified, u and vt will be full-size square orthogonal matrices. The operator performs singular value decomposition of the supplied matrix. The u, vt and the vector of singular values w are stored in the structure. The same SVD structure can be reused many times with different matrices. Each time, if needed, the previous u, vt and w are reclaimed and the new matrices are created, which is all handled by cv::Mat::create. cv::SVD::solveZ (view/add comments) Solves under-determined singular linear system static void SVD::solveZ( const Mat& A, Mat& x ); A The left-hand-side matrix. x The found solution 604 CHAPTER 11. CORE. THE CORE FUNCTIONALITY The method finds unit-length solution x of the under-determined system Ax = 0. Theory says that such system has infinite number of solutions, so the algorithm finds the unit-length solution as the right singular vector corresponding to the smallest singular value (which should be 0). In practice, because of round errors and limited floating-point accuracy, the input matrix can appear to be close-to-singular rather than just singular. So, strictly speaking, the algorithm solves the following problem: x∗ = arg min x:kxk=1 kA· xk cv::SVD::backSubst (view/add comments) Performs singular value back substitution void SVD::backSubst( const Mat& rhs, Mat& x ) const; rhs The right-hand side of a linear system Ax = rhs being solved, where A is the matrix passed to cv::SVD::SVD or cv::SVD::operator () x The found solution of the system The method computes back substitution for the specified right-hand side: x = vtT· diag(w)−1 · uT· rhs ∼ A−1 · rhs Using this technique you can either get a very accurate solution of convenient linear system, or the best (in the least-squares terms) pseudo-solution of an overdetermined linear system. Note that explicit SVD with the further back substitution only makes sense if you need to solve many linear systems with the same left-hand side (e.g. A). If all you need is to solve a single system (pos- sibly with multiple rhs immediately available), simply call cv::solve add pass cv::DECOMP SVD there - it will do absolutely the same thing. cv::sum (view/add comments) Calculates sum of array elements 11.2. OPERATIONS ON ARRAYS 605 Scalar sum(const Mat& mtx); Scalar sum(const MatND& mtx); mtx The source array; must have 1 to 4 channels The functions sum calculate and return the sum of array elements, independently for each channel. See also: cv::countNonZero, cv::mean, cv::meanStdDev, cv::norm, cv::minMaxLoc, cv::reduce cv::theRNG (view/add comments) Returns the default random number generator RNG& theRNG(); The function theRNG returns the default random number generator. For each thread there is separate random number generator, so you can use the function safely in multi-thread environ- ments. If you just need to get a single random number using this generator or initialize an array, you can use cv::randu or cv::randn instead. But if you are going to generate many random num- bers inside a loop, it will be much faster to use this function to retrieve the generator and then use RNG::operator Tp(). See also: cv::RNG, cv::randu, cv::randn cv::trace (view/add comments) Returns the trace of a matrix Scalar trace(const Mat& mtx); mtx The source matrix 606 CHAPTER 11. CORE. THE CORE FUNCTIONALITY The function trace returns the sum of the diagonal elements of the matrix mtx. tr(mtx) = X i mtx(i, i) cv::transform (view/add comments) Performs matrix transformation of every array element. void transform(const Mat& src, Mat& dst, const Mat& mtx ); src The source array; must have as many channels (1 to 4) as mtx.cols or mtx.cols-1 dst The destination array; will have the same size and depth as src and as many channels as mtx.rows mtx The transformation matrix The function transform performs matrix transformation of every element of array src and stores the results in dst: dst(I) = mtx · src(I) (when mtx.cols=src.channels()), or dst(I) = mtx ·[src(I); 1] (when mtx.cols=src.channels()+1) That is, every element of an N-channel array src is considered as N-element vector, which is transformed using a M × N or M × N+1 matrix mtx into an element of M-channel array dst. The function may be used for geometrical transformation of N-dimensional points, arbitrary linear color space transformation (such as various kinds of RGB→YUV transforms), shuffling the image channels and so forth. See also: cv::perspectiveTransform, cv::getAffineTransform, cv::estimateRigidTransform, cv::warpAffine, cv::warpPerspective 11.3. DYNAMIC STRUCTURES 607 cv::transpose (view/add comments) Transposes a matrix void transpose(const Mat& src, Mat& dst); src The source array dst The destination array of the same type as src The function cv::transpose transposes the matrix src: dst(i, j) = src(j, i) Note that no complex conjugation is done in the case of a complex matrix, it should be done separately if needed. 11.3 Dynamic Structures 11.4 Drawing Functions Drawing functions work with matrices/images of arbitrary depth. The boundaries of the shapes can be rendered with antialiasing (implemented only for 8-bit images for now). All the functions include the parameter color that uses a rgb value (that may be constructed with CV RGB or the Scalar constructor ) for color images and brightness for grayscale images. For color images the order channel is normally Blue, Green, Red, this is what cv::imshow, cv::imread and cv::imwrite expect , so if you form a color using Scalar constructor, it should look like: Scalar(blue component, green component, red component[, alpha component]) If you are using your own image rendering and I/O functions, you can use any channel ordering, the drawing functions process each channel independently and do not depend on the channel order or even on the color space used. The whole image can be converted from BGR to RGB or to a different color space using cv::cvtColor. If a drawn figure is partially or completely outside the image, the drawing functions clip it. Also, many drawing functions can handle pixel coordinates specified with sub-pixel accuracy, that is, the coordinates can be passed as fixed-point numbers, encoded as integers. The number of fractional bits is specified by the shift parameter and the real point coordinates are calculated as 608 CHAPTER 11. CORE. THE CORE FUNCTIONALITY Point(x, y) → Point2f(x∗2−shift, y∗2−shift). This feature is especially effective wehn rendering antialiased shapes. Also, note that the functions do not support alpha-transparency - when the target image is 4-channnel, then the color[3] is simply copied to the repainted pixels. Thus, if you want to paint semi-transparent shapes, you can paint them in a separate buffer and then blend it with the main image. cv::circle (view/add comments) Draws a circle void circle(Mat& img, Point center, int radius, const Scalar& color, int thickness=1, int lineType=8, int shift=0); img Image where the circle is drawn center Center of the circle radius Radius of the circle color Circle color thickness Thickness of the circle outline if positive; negative thickness means that a filled circle is to be drawn lineType Type of the circle boundary, see cv::line description shift Number of fractional bits in the center coordinates and radius value The function circle draws a simple or filled circle with a given center and radius. cv::clipLine (view/add comments) Clips the line against the image rectangle bool clipLine(Size imgSize, Point& pt1, Point& pt2); bool clipLine(Rect imgRect, Point& pt1, Point& pt2); 11.4. DRAWING FUNCTIONS 609 imgSize The image size; the image rectangle will be Rect(0, 0, imgSize.width, imgSize.height) imgSize The image rectangle pt1 The first line point pt2 The second line point The functions clipLine calculate a part of the line segment which is entirely within the spec- ified rectangle. They return false if the line segment is completely outside the rectangle and true otherwise. cv::ellipse (view/add comments) Draws a simple or thick elliptic arc or an fills ellipse sector. void ellipse(Mat& img, Point center, Size axes, double angle, double startAngle, double endAngle, const Scalar& color, int thickness=1, int lineType=8, int shift=0); void ellipse(Mat& img, const RotatedRect& box, const Scalar& color, int thickness=1, int lineType=8); img The image center Center of the ellipse axes Length of the ellipse axes angle The ellipse rotation angle in degrees startAngle Starting angle of the elliptic arc in degrees endAngle Ending angle of the elliptic arc in degrees box Alternative ellipse representation via a RotatedRect , i.e. the function draws an ellipse inscribed in the rotated rectangle color Ellipse color 610 CHAPTER 11. CORE. THE CORE FUNCTIONALITY thickness Thickness of the ellipse arc outline if positive, otherwise this indicates that a filled ellipse sector is to be drawn lineType Type of the ellipse boundary, see cv::line description shift Number of fractional bits in the center coordinates and axes’ values The functions ellipse with less parameters draw an ellipse outline, a filled ellipse, an ellip- tic arc or a filled ellipse sector. A piecewise-linear curve is used to approximate the elliptic arc boundary. If you need more control of the ellipse rendering, you can retrieve the curve using cv::ellipse2Poly and then render it with cv::polylines or fill it with cv::fillPoly. If you use the first variant of the function and want to draw the whole ellipse, not an arc, pass startAngle=0 and endAngle=360. The picture below explains the meaning of the parameters. Parameters of Elliptic Arc cv::ellipse2Poly (view/add comments) Approximates an elliptic arc with a polyline void ellipse2Poly( Point center, Size axes, int angle, int startAngle, int endAngle, int delta, vector& pts ); center Center of the arc axes Half-sizes of the arc. See cv::ellipse angle Rotation angle of the ellipse in degrees. See cv::ellipse 11.4. DRAWING FUNCTIONS 611 startAngle Starting angle of the elliptic arc in degrees endAngle Ending angle of the elliptic arc in degrees delta Angle between the subsequent polyline vertices. It defines the approximation accuracy. pts The output vector of polyline vertices The function ellipse2Poly computes the vertices of a polyline that approximates the speci- fied elliptic arc. It is used by cv::ellipse. cv::fillConvexPoly (view/add comments) Fills a convex polygon. void fillConvexPoly(Mat& img, const Point* pts, int npts, const Scalar& color, int lineType=8, int shift=0); img Image pts The polygon vertices npts The number of polygon vertices color Polygon color lineType Type of the polygon boundaries, see cv::line description shift The number of fractional bits in the vertex coordinates The function fillConvexPoly draws a filled convex polygon. This function is much faster than the function fillPoly and can fill not only convex polygons but any monotonic polygon without self-intersections, i.e., a polygon whose contour intersects every horizontal line (scan line) twice at the most (though, its top-most and/or the bottom edge could be horizontal). 612 CHAPTER 11. CORE. THE CORE FUNCTIONALITY cv::fillPoly (view/add comments) Fills the area bounded by one or more polygons void fillPoly(Mat& img, const Point** pts, const int* npts, int ncontours, const Scalar& color, int lineType=8, int shift=0, Point offset=Point() ); img Image pts Array of polygons, each represented as an array of points npts The array of polygon vertex counters ncontours The number of contours that bind the filled region color Polygon color lineType Type of the polygon boundaries, see cv::line description shift The number of fractional bits in the vertex coordinates The function fillPoly fills an area bounded by several polygonal contours. The function can fills complex areas, for example, areas with holes, contours with self-intersections (some of thier parts), and so forth. cv::getTextSize (view/add comments) Calculates the width and height of a text string. Size getTextSize(const string& text, int fontFace, double fontScale, int thickness, int* baseLine); text The input text string 11.4. DRAWING FUNCTIONS 613 fontFace The font to use; see cv::putText fontScale The font scale; see cv::putText thickness The thickness of lines used to render the text; see cv::putText baseLine The output parameter - y-coordinate of the baseline relative to the bottom-most text point The function getTextSize calculates and returns size of the box that contain the specified text. That is, the following code will render some text, the tight box surrounding it and the baseline: // Use "y" to show that the baseLine is about string text = "Funny text inside the box"; int fontFace = FONT_HERSHEY_SCRIPT_SIMPLEX; double fontScale = 2; int thickness = 3; Mat img(600, 800, CV_8UC3, Scalar::all(0)); int baseline=0; Size textSize = getTextSize(text, fontFace, fontScale, thickness, &baseline); baseline += thickness; // center the text Point textOrg((img.cols - textSize.width)/2, (img.rows + textSize.height)/2); // draw the box rectangle(img, textOrg + Point(0, baseline), textOrg + Point(textSize.width, -textSize.height), Scalar(0,0,255)); // ... and the baseline first line(img, textOrg + Point(0, thickness), textOrg + Point(textSize.width, thickness), Scalar(0, 0, 255)); // then put the text itself putText(img, text, textOrg, fontFace, fontScale, Scalar::all(255), thickness, 8); cv::line (view/add comments) Draws a line segment connecting two points 614 CHAPTER 11. CORE. THE CORE FUNCTIONALITY void line(Mat& img, Point pt1, Point pt2, const Scalar& color, int thickness=1, int lineType=8, int shift=0); img The image pt1 First point of the line segment pt2 Second point of the line segment color Line color thickness Line thickness lineType Type of the line: 8 (or omitted) 8-connected line. 4 4-connected line. CV AA antialiased line. shift Number of fractional bits in the point coordinates The function line draws the line segment between pt1 and pt2 points in the image. The line is clipped by the image boundaries. For non-antialiased lines with integer coordinates the 8-connected or 4-connected Bresenham algorithm is used. Thick lines are drawn with rounding endings. Antialiased lines are drawn using Gaussian filtering. To specify the line color, the user may use the macro CV RGB(r, g, b). cv::LineIterator (view/add comments) Class for iterating pixels on a raster line class LineIterator { public: // creates iterators for the line connecting pt1 and pt2 // the line will be clipped on the image boundaries // the line is 8-connected or 4-connected // If leftToRight=true, then the iteration is always done // from the left-most point to the right most, 11.4. DRAWING FUNCTIONS 615 // not to depend on the ordering of pt1 and pt2 parameters LineIterator(const Mat& img, Point pt1, Point pt2, int connectivity=8, bool leftToRight=false); // returns pointer to the current line pixel uchar* operator *(); // move the iterator to the next pixel LineIterator& operator ++(); LineIterator operator ++(int); // internal state of the iterator uchar* ptr; int err, count; int minusDelta, plusDelta; int minusStep, plusStep; }; The class LineIterator is used to get each pixel of a raster line. It can be treated as versatile implementation of the Bresenham algorithm, where you can stop at each pixel and do some extra processing, for example, grab pixel values along the line, or draw a line with some effect (e.g. with XOR operation). The number of pixels along the line is store in LineIterator::count. // grabs pixels along the line (pt1, pt2) // from 8-bit 3-channel image to the buffer LineIterator it(img, pt1, pt2, 8); vector buf(it.count); for(int i = 0; i < it.count; i++, ++it) buf[i] = *(const Vec3b)*it; cv::rectangle (view/add comments) Draws a simple, thick, or filled up-right rectangle. void rectangle(Mat& img, Point pt1, Point pt2, const Scalar& color, int thickness=1, int lineType=8, int shift=0); img Image pt1 One of the rectangle’s vertices 616 CHAPTER 11. CORE. THE CORE FUNCTIONALITY pt2 Opposite to pt1 rectangle vertex color Rectangle color or brightness (grayscale image) thickness Thickness of lines that make up the rectangle. Negative values, e.g. CV FILLED, mean that the function has to draw a filled rectangle. lineType Type of the line, see cv::line description shift Number of fractional bits in the point coordinates The function rectangle draws a rectangle outline or a filled rectangle, which two opposite corners are pt1 and pt2. cv::polylines (view/add comments) Draws several polygonal curves void polylines(Mat& img, const Point** pts, const int* npts, int ncontours, bool isClosed, const Scalar& color, int thickness=1, int lineType=8, int shift=0 ); img The image pts Array of polygonal curves npts Array of polygon vertex counters ncontours The number of curves isClosed Indicates whether the drawn polylines are closed or not. If they are closed, the function draws the line from the last vertex of each curve to its first vertex color Polyline color thickness Thickness of the polyline edges lineType Type of the line segments, see cv::line description shift The number of fractional bits in the vertex coordinates The function polylines draws one or more polygonal curves. 11.5. XML/YAML PERSISTENCE 617 cv::putText (view/add comments) Draws a text string void putText( Mat& img, const string& text, Point org, int fontFace, double fontScale, Scalar color, int thickness=1, int lineType=8, bool bottomLeftOrigin=false ); img The image text The text string to be drawn org The bottom-left corner of the text string in the image fontFace The font type, one of FONT HERSHEY SIMPLEX, FONT HERSHEY PLAIN, FONT HERSHEY DUPLEX, FONT HERSHEY COMPLEX, FONT HERSHEY TRIPLEX, FONT HERSHEY COMPLEX SMALL, FONT HERSHEY SCRIPT SIMPLEX or FONT HERSHEY SCRIPT COMPLEX, where each of the font id’s can be combined with FONT HERSHEY ITALIC to get the slanted letters. fontScale The font scale factor that is multiplied by the font-specific base size color The text color thickness Thickness of the lines used to draw the text lineType The line type; see line for details bottomLeftOrigin When true, the image data origin is at the bottom-left corner, otherwise it’s at the top-left corner The function putText renders the specified text string in the image. Symbols that can not be rendered using the specified font are replaced by question marks. See cv::getTextSize for a text rendering code example. 11.5 XML/YAML Persistence cv::FileStorage (view/add comments) The XML/YAML file storage class 618 CHAPTER 11. CORE. THE CORE FUNCTIONALITY class FileStorage { public: enum { READ=0, WRITE=1, APPEND=2 }; enum { UNDEFINED=0, VALUE_EXPECTED=1, NAME_EXPECTED=2, INSIDE_MAP=4 }; // the default constructor FileStorage(); // the constructor that opens the file for reading // (flags=FileStorage::READ) or writing (flags=FileStorage::WRITE) FileStorage(const string& filename, int flags); // wraps the already opened CvFileStorage* FileStorage(CvFileStorage* fs); // the destructor; closes the file if needed virtual ˜FileStorage(); // opens the specified file for reading (flags=FileStorage::READ) // or writing (flags=FileStorage::WRITE) virtual bool open(const string& filename, int flags); // checks if the storage is opened virtual bool isOpened() const; // closes the file virtual void release(); // returns the first top-level node FileNode getFirstTopLevelNode() const; // returns the root file node // (it’s the parent of the first top-level node) FileNode root(int streamidx=0) const; // returns the top-level node by name FileNode operator[](const string& nodename) const; FileNode operator[](const char* nodename) const; // returns the underlying CvFileStorage* CvFileStorage* operator *() { return fs; } const CvFileStorage* operator *() const { return fs; } // writes the certain number of elements of the specified format // (see DataType) without any headers void writeRaw( const string& fmt, const uchar* vec, size_t len ); // writes an old-style object (CvMat, CvMatND etc.) void writeObj( const string& name, const void* obj ); // returns the default object name from the filename // (used by cvSave() with the default object name etc.) 11.5. XML/YAML PERSISTENCE 619 static string getDefaultObjectName(const string& filename); Ptr fs; string elname; vector structs; int state; }; cv::FileNode (view/add comments) The XML/YAML file node class class CV_EXPORTS FileNode { public: enum { NONE=0, INT=1, REAL=2, FLOAT=REAL, STR=3, STRING=STR, REF=4, SEQ=5, MAP=6, TYPE_MASK=7, FLOW=8, USER=16, EMPTY=32, NAMED=64 }; FileNode(); FileNode(const CvFileStorage* fs, const CvFileNode* node); FileNode(const FileNode& node); FileNode operator[](const string& nodename) const; FileNode operator[](const char* nodename) const; FileNode operator[](int i) const; int type() const; int rawDataSize(const string& fmt) const; bool empty() const; bool isNone() const; bool isSeq() const; bool isMap() const; bool isInt() const; bool isReal() const; bool isString() const; bool isNamed() const; string name() const; size_t size() const; operator int() const; operator float() const; operator double() const; operator string() const; FileNodeIterator begin() const; FileNodeIterator end() const; 620 CHAPTER 11. CORE. THE CORE FUNCTIONALITY void readRaw( const string& fmt, uchar* vec, size_t len ) const; void* readObj() const; // do not use wrapper pointer classes for better efficiency const CvFileStorage* fs; const CvFileNode* node; }; cv::FileNodeIterator (view/add comments) The XML/YAML file node iterator class class CV_EXPORTS FileNodeIterator { public: FileNodeIterator(); FileNodeIterator(const CvFileStorage* fs, const CvFileNode* node, size_t ofs=0); FileNodeIterator(const FileNodeIterator& it); FileNode operator *() const; FileNode operator ->() const; FileNodeIterator& operator ++(); FileNodeIterator operator ++(int); FileNodeIterator& operator --(); FileNodeIterator operator --(int); FileNodeIterator& operator += (int); FileNodeIterator& operator -= (int); FileNodeIterator& readRaw( const string& fmt, uchar* vec, size_t maxCount=(size_t)INT_MAX ); const CvFileStorage* fs; const CvFileNode* container; CvSeqReader reader; size_t remaining; }; 11.6 Clustering cv::kmeans (view/add comments) Finds the centers of clusters and groups the input samples around the clusters. 11.6. CLUSTERING 621 double kmeans( const Mat& samples, int clusterCount, Mat& labels, TermCriteria termcrit, int attempts, int flags, Mat* centers ); samples Floating-point matrix of input samples, one row per sample clusterCount The number of clusters to split the set by labels The input/output integer array that will store the cluster indices for every sample termcrit Specifies maximum number of iterations and/or accuracy (distance the centers can move by between subsequent iterations) attempts How many times the algorithm is executed using different initial labelings. The algo- rithm returns the labels that yield the best compactness (see the last function parameter) flags It can take the following values: KMEANS RANDOM CENTERS Random initial centers are selected in each attempt KMEANS PP CENTERS Use kmeans++ center initialization by Arthur and Vassilvitskii KMEANS USE INITIAL LABELS During the first (and possibly the only) attempt, the function uses the user-supplied labels instaed of computing them from the initial centers. For the second and further attempts, the function will use the random or semi-random centers (use one of KMEANS * CENTERS flag to specify the exact method) centers The output matrix of the cluster centers, one row per each cluster center The function kmeans implements a k-means algorithm that finds the centers of clusterCount clusters and groups the input samples around the clusters. On output, labelsi contains a 0- based cluster index for the sample stored in the ith row of the samples matrix. The function returns the compactness measure, which is computed as X i ksamplesi − centerslabelsi k2 after every attempt; the best (minimum) value is chosen and the corresponding labels and the compactness value are returned by the function. Basically, the user can use only the core of the function, set the number of attempts to 1, initialize labels each time using some custom algorithm and pass them with (flags=KMEANS USE INITIAL LABELS) flag, and then choose the best (most-compact) clus- tering. 622 CHAPTER 11. CORE. THE CORE FUNCTIONALITY cv::partition (view/add comments) Splits an element set into equivalency classes. template int partition( const vector< Tp>& vec, vector& labels, EqPredicate predicate= EqPredicate()); vec The set of elements stored as a vector labels The output vector of labels; will contain as many elements as vec. Each label labels[i] is 0-based cluster index of vec[i] predicate The equivalence predicate (i.e. pointer to a boolean function of two arguments or an instance of the class that has the method bool operator()(const Tp& a, const Tp& b). The predicate returns true when the elements are certainly if the same class, and false if they may or may not be in the same class The generic function partition implements an O(N2) algorithm for splitting a set of N el- ements into one or more equivalency classes, as described in http://en.wikipedia.org/ wiki/Disjoint-set_data_structure. The function returns the number of equivalency classes. 11.7 Utility and System Functions and Macros cv::alignPtr (view/add comments) Aligns pointer to the specified number of bytes template Tp* alignPtr( Tp* ptr, int n=sizeof( Tp)); ptr The aligned pointer n The alignment size; must be a power of two The function returns the aligned pointer of the same type as the input pointer: ( Tp*)(((size t)ptr + n-1) & -n) 11.7. UTILITY AND SYSTEM FUNCTIONS AND MACROS 623 cv::alignSize (view/add comments) Aligns a buffer size to the specified number of bytes size t alignSize(size t sz, int n); sz The buffer size to align n The alignment size; must be a power of two The function returns the minimum number that is greater or equal to sz and is divisble by n: (sz + n-1) & -n cv::allocate (view/add comments) Allocates an array of elements template Tp* allocate(size t n); n The number of elements to allocate The generic function allocate allocates buffer for the specified number of elements. For each element the default constructor is called. cv::deallocate (view/add comments) Allocates an array of elements template void deallocate( Tp* ptr, size t n); ptr Pointer to the deallocated buffer n The number of elements in the buffer The generic function deallocate deallocates the buffer allocated with cv::allocate. The number of elements must match the number passed to cv::allocate. 624 CHAPTER 11. CORE. THE CORE FUNCTIONALITY CV Assert (view/add comments) Checks a condition at runtime. CV Assert(expr) #define CV_Assert( expr ) ... #define CV_DbgAssert(expr) ... expr The checked expression The macros CV Assert and CV DbgAssert evaluate the specified expression and if it is 0, the macros raise an error (see cv::error). The macro CV Assert checks the condition in both Debug and Release configurations, while CV DbgAssert is only retained in the Debug configuration. cv::error (view/add comments) Signals an error and raises the exception void error( const Exception& exc ); #define CV Error( code, msg ) <...> #define CV Error ( code, args ) <...> exc The exception to throw code The error code, normally, a negative value. The list of pre-defined error codes can be found in cxerror.h msg Text of the error message args printf-like formatted error message in parantheses The function and the helper macros CV Error and CV Error call the error handler. Currently, the error handler prints the error code (exc.code), the context (exc.file, exc.line and the error message exc.err to the standard error stream stderr. In Debug configuration it then 11.7. UTILITY AND SYSTEM FUNCTIONS AND MACROS 625 provokes memory access violation, so that the execution stack and all the parameters can be analyzed in debugger. In Release configuration the exception exc is thrown. The macro CV Error can be used to construct the error message on-fly to include some dynamic information, for example: // note the extra parentheses around the formatted text message CV_Error_(CV_StsOutOfRange, ("the matrix element (%d,%d)=%g is out of range", i, j, mtx.at(i,j))) cv::Exception (view/add comments) The exception class passed to error class Exception { public: // various constructors and the copy operation Exception() { code = 0; line = 0; } Exception(int _code, const string& _err, const string& _func, const string& _file, int _line); Exception(const Exception& exc); Exception& operator = (const Exception& exc); // the error code int code; // the error text message string err; // function name where the error happened string func; // the source file name where the error happened string file; // the source file line where the error happened int line; }; The class Exception encapsulates all or almost all the necessary information about the er- ror happened in the program. The exception is usually constructed and thrown implicitly, via CV Error and CV Error macros, see cv::error. cv::fastMalloc (view/add comments) Allocates aligned memory buffer 626 CHAPTER 11. CORE. THE CORE FUNCTIONALITY void* fastMalloc(size t size); size The allocated buffer size The function allocates buffer of the specified size and returns it. When the buffer size is 16 bytes or more, the returned buffer is aligned on 16 bytes. cv::fastFree (view/add comments) Deallocates memory buffer void fastFree(void* ptr); ptr Pointer to the allocated buffer The function deallocates the buffer, allocated with cv::fastMalloc. If NULL pointer is passed, the function does nothing. cv::format (view/add comments) Returns a text string formatted using printf-like expression string format( const char* fmt, ... ); fmt The printf-compatible formatting specifiers The function acts like sprintf, but forms and returns STL string. It can be used for form the error message in cv::Exception constructor. 11.7. UTILITY AND SYSTEM FUNCTIONS AND MACROS 627 cv::getNumThreads (view/add comments) Returns the number of threads used by OpenCV int getNumThreads(); The function returns the number of threads that is used by OpenCV. See also: cv::setNumThreads, cv::getThreadNum. cv::getThreadNum (view/add comments) Returns index of the currently executed thread int getThreadNum(); The function returns 0-based index of the currently executed thread. The function is only valid inside a parallel OpenMP region. When OpenCV is built without OpenMP support, the function always returns 0. See also: cv::setNumThreads, cv::getNumThreads. cv::getTickCount (view/add comments) Returns the number of ticks int64 getTickCount(); The function returns the number of ticks since the certain event (e.g. when the machine was turned on). It can be used to initialize cv::RNG or to measure a function execution time by reading the tick count before and after the function call. See also the tick frequency. 628 CHAPTER 11. CORE. THE CORE FUNCTIONALITY cv::getTickFrequency (view/add comments) Returns the number of ticks per second double getTickFrequency(); The function returns the number of ticks per second. That is, the following code computes the execution time in seconds. double t = (double)getTickCount(); // do something ... t = ((double)getTickCount() - t)/getTickFrequency(); cv::setNumThreads (view/add comments) Sets the number of threads used by OpenCV void setNumThreads(int nthreads); nthreads The number of threads used by OpenCV The function sets the number of threads used by OpenCV in parallel OpenMP regions. If nthreads=0, the function will use the default number of threads, which is usually equal to the number of the processing cores. See also: cv::getNumThreads, cv::getThreadNum Chapter 12 imgproc. Image Processing 12.1 Histograms cv::calcHist (view/add comments) Calculates histogram of a set of arrays void calcHist( const Mat* arrays, int narrays, const int* channels, const Mat& mask, MatND& hist, int dims, const int* histSize, const float** ranges, bool uniform=true, bool accumulate=false ); void calcHist( const Mat* arrays, int narrays, const int* channels, const Mat& mask, SparseMat& hist, int dims, const int* histSize, const float** ranges, bool uniform=true, bool accumulate=false ); arrays Source arrays. They all should have the same depth, CV 8U or CV 32F, and the same size. Each of them can have an arbitrary number of channels narrays The number of source arrays channels The list of dims channels that are used to compute the histogram. The first array chan- nels are numerated from 0 to arrays[0].channels()-1, the second array channels are 629 630 CHAPTER 12. IMGPROC. IMAGE PROCESSING counted from arrays[0].channels() to arrays[0].channels() + arrays[1].channels()-1 etc. mask The optional mask. If the matrix is not empty, it must be 8-bit array of the same size as arrays[i]. The non-zero mask elements mark the array elements that are counted in the histogram hist The output histogram, a dense or sparse dims-dimensional array dims The histogram dimensionality; must be positive and not greater than CV MAX DIMS(=32 in the current OpenCV version) histSize The array of histogram sizes in each dimension ranges The array of dims arrays of the histogram bin boundaries in each dimension. When the histogram is uniform (uniform=true), then for each dimension i it’s enough to spec- ify the lower (inclusive) boundary L0 of the 0-th histogram bin and the upper (exclusive) boundary UhistSize[i]−1 for the last histogram bin histSize[i]-1. That is, in the case of uniform histogram each of ranges[i] is an array of 2 elements. When the histogram is not uniform (uniform=false), then each of ranges[i] contains histSize[i]+1 ele- ments: L0,U0 = L1,U1 = L2, ..., UhistSize[i]−2 = LhistSize[i]−1,UhistSize[i]−1. The array elements, which are not between L0 and UhistSize[i]−1, are not counted in the histogram uniform Indicates whether the histogram is uniform or not, see above accumulate Accumulation flag. If it is set, the histogram is not cleared in the beginning (when it is allocated). This feature allows user to compute a single histogram from several sets of arrays, or to update the histogram in time The functions calcHist calculate the histogram of one or more arrays. The elements of a tuple that is used to increment a histogram bin are taken at the same location from the corre- sponding input arrays. The sample below shows how to compute 2D Hue-Saturation histogram for a color imag #include #include using namespace cv; int main( int argc, char** argv ) { Mat src, hsv; if( argc != 2 || !(src=imread(argv[1], 1)).data ) return -1; 12.1. HISTOGRAMS 631 cvtColor(src, hsv, CV_BGR2HSV); // let’s quantize the hue to 30 levels // and the saturation to 32 levels int hbins = 30, sbins = 32; int histSize[] = {hbins, sbins}; // hue varies from 0 to 179, see cvtColor float hranges[] = { 0, 180 }; // saturation varies from 0 (black-gray-white) to // 255 (pure spectrum color) float sranges[] = { 0, 256 }; const float* ranges[] = { hranges, sranges }; MatND hist; // we compute the histogram from the 0-th and 1-st channels int channels[] = {0, 1}; calcHist( &hsv, 1, channels, Mat(), // do not use mask hist, 2, histSize, ranges, true, // the histogram is uniform false ); double maxVal=0; minMaxLoc(hist, 0, &maxVal, 0, 0); int scale = 10; Mat histImg = Mat::zeros(sbins*scale, hbins*10, CV_8UC3); for( int h = 0; h < hbins; h++ ) for( int s = 0; s < sbins; s++ ) { float binVal = hist.at(h, s); int intensity = cvRound(binVal*255/maxVal); rectangle( histImg, Point(h*scale, s*scale), Point( (h+1)*scale - 1, (s+1)*scale - 1), Scalar::all(intensity), CV_FILLED ); } namedWindow( "Source", 1 ); imshow( "Source", src ); namedWindow( "H-S Histogram", 1 ); imshow( "H-S Histogram", histImg ); waitKey(); } 632 CHAPTER 12. IMGPROC. IMAGE PROCESSING cv::calcBackProject (view/add comments) Calculates the back projection of a histogram. void calcBackProject( const Mat* arrays, int narrays, const int* channels, const MatND& hist, Mat& backProject, const float** ranges, double scale=1, bool uniform=true ); void calcBackProject( const Mat* arrays, int narrays, const int* channels, const SparseMat& hist, Mat& backProject, const float** ranges, double scale=1, bool uniform=true ); arrays Source arrays. They all should have the same depth, CV 8U or CV 32F, and the same size. Each of them can have an arbitrary number of channels narrays The number of source arrays channels The list of channels that are used to compute the back projection. The number of channels must match the histogram dimensionality. The first array channels are numer- ated from 0 to arrays[0].channels()-1, the second array channels are counted from arrays[0].channels() to arrays[0].channels() + arrays[1].channels()-1 etc. hist The input histogram, a dense or sparse backProject Destination back projection aray; will be a single-channel array of the same size and the same depth as arrays[0] ranges The array of arrays of the histogram bin boundaries in each dimension. See cv::calcHist scale The optional scale factor for the output back projection uniform Indicates whether the histogram is uniform or not, see above The functions calcBackProject calculate the back project of the histogram. That is, similarly to calcHist, at each location (x, y) the function collects the values from the selected channels in the input images and finds the corresponding histogram bin. But instead of incrementing it, the function reads the bin value, scales it by scale and stores in backProject(x,y). In terms of statistics, the function computes probability of each element value in respect with the empirical 12.1. HISTOGRAMS 633 probability distribution represented by the histogram. Here is how, for example, you can find and track a bright-colored object in a scene: 1. Before the tracking, show the object to the camera such that covers almost the whole frame. Calculate a hue histogram. The histogram will likely have a strong maximums, corresponding to the dominant colors in the object. 2. During the tracking, calculate back projection of a hue plane of each input video frame using that pre-computed histogram. Threshold the back projection to suppress weak colors. It may also have sense to suppress pixels with non sufficient color saturation and too dark or too bright pixels. 3. Find connected components in the resulting picture and choose, for example, the largest component. That is the approximate algorithm of cv::CAMShift color object tracker. See also: cv::calcHist cv::compareHist (view/add comments) Compares two histograms double compareHist( const MatND& H1, const MatND& H2, int method ); double compareHist( const SparseMat& H1, const SparseMat& H2, int method ); H1 The first compared histogram H2 The second compared histogram of the same size as H1 method The comparison method, one of the following: CV COMP CORREL Correlation CV COMP CHISQR Chi-Square CV COMP INTERSECT Intersection CV COMP BHATTACHARYYA Bhattacharyya distance The functions compareHist compare two dense or two sparse histograms using the specified method: 634 CHAPTER 12. IMGPROC. IMAGE PROCESSING Correlation (method=CV COMP CORREL) d(H1,H2) = P I(H1(I) − ¯H1)(H2(I) − ¯H2) qP I(H1(I) − ¯H1)2 P I(H2(I) − ¯H2)2 where ¯Hk = 1 N X J Hk(J) and N is the total number of histogram bins. Chi-Square (method=CV COMP CHISQR) d(H1,H2) = X I (H1(I) − H2(I))2 H1(I) + H2(I) Intersection (method=CV COMP INTERSECT) d(H1,H2) = X I min(H1(I),H2(I)) Bhattacharyya distance (method=CV COMP BHATTACHARYYA) d(H1,H2) = s 1 − 1 p ¯H1 ¯H2N2 X I pH1(I)·H2(I) The function returns d(H1,H2). While the function works well with 1-, 2-, 3-dimensional dense histograms, it may not be suit- able for high-dimensional sparse histograms, where, because of aliasing and sampling problems the coordinates of non-zero histogram bins can slightly shift. To compare such histograms or more general sparse configurations of weighted points, consider using the cv::calcEMD function. cv::equalizeHist (view/add comments) Equalizes the histogram of a grayscale image. void equalizeHist( const Mat& src, Mat& dst ); 12.2. IMAGE FILTERING 635 src The source 8-bit single channel image dst The destination image; will have the same size and the same type as src The function equalizes the histogram of the input image using the following algorithm: 1. calculate the histogram H for src. 2. normalize the histogram so that the sum of histogram bins is 255. 3. compute the integral of the histogram: H0 i = X 0≤j& _filter2D, const Ptr& _rowFilter, const Ptr& _columnFilter, int srcType, int dstType, int bufType, int _rowBorderType=BORDER_REPLICATE, int _columnBorderType=-1, // use _rowBorderType by default const Scalar& _borderValue=Scalar()); virtual ˜FilterEngine(); // separate function for the engine initialization void init(const Ptr& _filter2D, const Ptr& _rowFilter, const Ptr& _columnFilter, int srcType, int dstType, int bufType, int _rowBorderType=BORDER_REPLICATE, int _columnBorderType=-1, const Scalar& _borderValue=Scalar()); // starts filtering of the ROI in an image of size "wholeSize". // returns the starting y-position in the source image. virtual int start(Size wholeSize, Rect roi, int maxBufRows=-1); // alternative form of start that takes the image // itself instead of "wholeSize". Set isolated to true to pretend that // there are no real pixels outside of the ROI // (so that the pixels will be extrapolated using the specified border modes) virtual int start(const Mat& src, const Rect& srcRoi=Rect(0,0,-1,-1), bool isolated=false, int maxBufRows=-1); // processes the next portion of the source image, // "srcCount" rows starting from "src" and // stores the results to "dst". // returns the number of produced rows virtual int proceed(const uchar* src, int srcStep, int srcCount, uchar* dst, int dstStep); // higher-level function that processes the whole // ROI or the whole image with a single call virtual void apply( const Mat& src, Mat& dst, const Rect& srcRoi=Rect(0,0,-1,-1), Point dstOfs=Point(0,0), bool isolated=false); bool isSeparable() const { return filter2D.empty(); } // how many rows from the input image are not yet processed int remainingInputRows() const; // how many output rows are not yet produced int remainingOutputRows() const; ... // the starting and the ending rows in the source image int startY, endY; 640 CHAPTER 12. IMGPROC. IMAGE PROCESSING // pointers to the filters Ptr filter2D; Ptr rowFilter; Ptr columnFilter; }; The class FilterEngine can be used to apply an arbitrary filtering operation to an image. It contains all the necessary intermediate buffers, it computes extrapolated values of the ”virtual” pixels outside of the image etc. Pointers to the initialized FilterEngine instances are returned by various create*Filter functions, see below, and they are used inside high-level functions such as cv::filter2D, cv::erode, cv::dilate etc, that is, the class is the workhorse in many of OpenCV filtering functions. This class makes it easier (though, maybe not very easy yet) to combine filtering operations with other operations, such as color space conversions, thresholding, arithmetic operations, etc. By combining several operations together you can get much better performance because your data will stay in cache. For example, below is the implementation of Laplace operator for a floating-point images, which is a simplified implementation of cv::Laplacian: void laplace_f(const Mat& src, Mat& dst) { CV_Assert( src.type() == CV_32F ); dst.create(src.size(), src.type()); // get the derivative and smooth kernels for d2I/dx2. // for d2I/dy2 we could use the same kernels, just swapped Mat kd, ks; getSobelKernels( kd, ks, 2, 0, ksize, false, ktype ); // let’s process 10 source rows at once int DELTA = std::min(10, src.rows); Ptr Fxx = createSeparableLinearFilter(src.type(), dst.type(), kd, ks, Point(-1,-1), 0, borderType, borderType, Scalar() ); Ptr Fyy = createSeparableLinearFilter(src.type(), dst.type(), ks, kd, Point(-1,-1), 0, borderType, borderType, Scalar() ); int y = Fxx->start(src), dsty = 0, dy = 0; Fyy->start(src); const uchar* sptr = src.data + y*src.step; // allocate the buffers for the spatial image derivatives; // the buffers need to have more than DELTA rows, because at the // last iteration the output may take max(kd.rows-1,ks.rows-1) // rows more than the input. Mat Ixx( DELTA + kd.rows - 1, src.cols, dst.type() ); Mat Iyy( DELTA + kd.rows - 1, src.cols, dst.type() ); 12.2. IMAGE FILTERING 641 // inside the loop we always pass DELTA rows to the filter // (note that the "proceed" method takes care of possibe overflow, since // it was given the actual image height in the "start" method) // on output we can get: // * < DELTA rows (the initial buffer accumulation stage) // * = DELTA rows (settled state in the middle) // * > DELTA rows (then the input image is over, but we generate // "virtual" rows using the border mode and filter them) // this variable number of output rows is dy. // dsty is the current output row. // sptr is the pointer to the first input row in the portion to process for( ; dsty < dst.rows; sptr += DELTA*src.step, dsty += dy ) { Fxx->proceed( sptr, (int)src.step, DELTA, Ixx.data, (int)Ixx.step ); dy = Fyy->proceed( sptr, (int)src.step, DELTA, d2y.data, (int)Iyy.step ); if( dy > 0 ) { Mat dstripe = dst.rowRange(dsty, dsty + dy); add(Ixx.rowRange(0, dy), Iyy.rowRange(0, dy), dstripe); } } } If you do not need that much control of the filtering process, you can simply use the FilterEngine::apply method. Here is how the method is actually implemented: void FilterEngine::apply(const Mat& src, Mat& dst, const Rect& srcRoi, Point dstOfs, bool isolated) { // check matrix types CV_Assert( src.type() == srcType && dst.type() == dstType ); // handle the "whole image" case Rect _srcRoi = srcRoi; if( _srcRoi == Rect(0,0,-1,-1) ) _srcRoi = Rect(0,0,src.cols,src.rows); // check if the destination ROI is inside the dst. // and FilterEngine::start will check if the source ROI is inside src. CV_Assert( dstOfs.x >= 0 && dstOfs.y >= 0 && dstOfs.x + _srcRoi.width <= dst.cols && dstOfs.y + _srcRoi.height <= dst.rows ); // start filtering int y = start(src, _srcRoi, isolated); 642 CHAPTER 12. IMGPROC. IMAGE PROCESSING // process the whole ROI. Note that "endY - startY" is the total number // of the source rows to process // (including the possible rows outside of srcRoi but inside the source image) proceed( src.data + y*src.step, (int)src.step, endY - startY, dst.data + dstOfs.y*dst.step + dstOfs.x*dst.elemSize(), (int)dst.step ); } Unlike the earlier versions of OpenCV, now the filtering operations fully support the notion of image ROI, that is, pixels outside of the ROI but inside the image can be used in the filtering operations. For example, you can take a ROI of a single pixel and filter it - that will be a filter response at that particular pixel (however, it’s possible to emulate the old behavior by passing isolated=false to FilterEngine::start or FilterEngine::apply). You can pass the ROI explicitly to FilterEngine::apply, or construct a new matrix headers: // compute dI/dx derivative at src(x,y) // method 1: // form a matrix header for a single value float val1 = 0; Mat dst1(1,1,CV_32F,&val1); Ptr Fx = createDerivFilter(CV_32F, CV_32F, 1, 0, 3, BORDER_REFLECT_101); Fx->apply(src, Rect(x,y,1,1), Point(), dst1); // method 2: // form a matrix header for a single value float val2 = 0; Mat dst2(1,1,CV_32F,&val2); Mat pix_roi(src, Rect(x,y,1,1)); Sobel(pix_roi, dst2, dst2.type(), 1, 0, 3, 1, 0, BORDER_REFLECT_101); printf("method1 = %g, method2 = %g\n", val1, val2); Note on the data types. As it was mentioned in cv::BaseFilter description, the specific fil- ters can process data of any type, despite that Base*Filter::operator() only takes uchar pointers and no information about the actual types. To make it all work, the following rules are used: • in case of separable filtering FilterEngine::rowFilter applied first. It transforms the input image data (of type srcType) to the intermediate results stored in the internal buffers 12.2. IMAGE FILTERING 643 (of type bufType). Then these intermediate results are processed as single-channel data with FilterEngine::columnFilter and stored in the output image (of type dstType). Thus, the input type for rowFilter is srcType and the output type is bufType; the input type for columnFilter is CV MAT DEPTH(bufType) and the output type is CV MAT DEPTH(dstType). • in case of non-separable filtering bufType must be the same as srcType. The source data is copied to the temporary buffer if needed and then just passed to FilterEngine::filter2D. That is, the input type for filter2D is srcType (=bufType) and the output type is dstType. See also: cv::BaseColumnFilter, cv::BaseFilter, cv::BaseRowFilter, cv::createBoxFilter, cv::createDerivFilter, cv::createGaussianFilter, cv::createLinearFilter, cv::createMorphologyFilter, cv::createSeparableLinearFilter cv::bilateralFilter (view/add comments) Applies bilateral filter to the image void bilateralFilter( const Mat& src, Mat& dst, int d, double sigmaColor, double sigmaSpace, int borderType=BORDER DEFAULT ); src The source 8-bit or floating-point, 1-channel or 3-channel image dst The destination image; will have the same size and the same type as src d The diameter of each pixel neighborhood, that is used during filtering. If it is non-positive, it’s computed from sigmaSpace sigmaColor Filter sigma in the color space. Larger value of the parameter means that farther colors within the pixel neighborhood (see sigmaSpace) will be mixed together, resulting in larger areas of semi-equal color sigmaSpace Filter sigma in the coordinate space. Larger value of the parameter means that far- ther pixels will influence each other (as long as their colors are close enough; see sigmaColor). Then d>0, it specifies the neighborhood size regardless of sigmaSpace, otherwise d is pro- portional to sigmaSpace The function applies bilateral filtering to the input image, as described in http://www.dai. ed.ac.uk/CVonline/LOCAL_COPIES/MANDUCHI1/Bilateral_Filtering.html 644 CHAPTER 12. IMGPROC. IMAGE PROCESSING cv::blur (view/add comments) Smoothes image using normalized box filter void blur( const Mat& src, Mat& dst, Size ksize, Point anchor=Point(-1,-1), int borderType=BORDER DEFAULT ); src The source image dst The destination image; will have the same size and the same type as src ksize The smoothing kernel size anchor The anchor point. The default value Point(-1,-1) means that the anchor is at the kernel center borderType The border mode used to extrapolate pixels outside of the image The function smoothes the image using the kernel: K = 1 ksize.width*ksize.height   1 1 1 ··· 1 1 1 1 1 ··· 1 1 ................... 1 1 1 ··· 1 1   The call blur(src, dst, ksize, anchor, borderType) is equivalent to boxFilter(src, dst, src.type(), anchor, true, borderType). See also: cv::boxFilter, cv::bilateralFilter, cv::GaussianBlur, cv::medianBlur. cv::borderInterpolate (view/add comments) Computes source location of extrapolated pixel int borderInterpolate( int p, int len, int borderType ); p 0-based coordinate of the extrapolated pixel along one of the axes, likely ¡0 or ¿=len 12.2. IMAGE FILTERING 645 len length of the array along the corresponding axis borderType the border type, one of the BORDER *, except for BORDER TRANSPARENT and BORDER ISOLATED. When borderType==BORDER CONSTANT the function always returns -1, regardless of p and len The function computes and returns the coordinate of the donor pixel, corresponding to the specified extrapolated pixel when using the specified extrapolation border mode. For example, if we use BORDER WRAP mode in the horizontal direction, BORDER REFLECT 101 in the vertical direction and want to compute value of the ”virtual” pixel Point(-5, 100) in a floating-point image img, it will be float val = img.at(borderInterpolate(100, img.rows, BORDER_REFLECT_101), borderInterpolate(-5, img.cols, BORDER_WRAP)); Normally, the function is not called directly; it is used inside cv::FilterEngine and cv::copyMakeBorder to compute tables for quick extrapolation. See also: cv::FilterEngine, cv::copyMakeBorder cv::boxFilter (view/add comments) Smoothes image using box filter void boxFilter( const Mat& src, Mat& dst, int ddepth, Size ksize, Point anchor=Point(-1,-1), bool normalize=true, int borderType=BORDER DEFAULT ); src The source image dst The destination image; will have the same size and the same type as src ksize The smoothing kernel size anchor The anchor point. The default value Point(-1,-1) means that the anchor is at the kernel center normalize Indicates, whether the kernel is normalized by its area or not borderType The border mode used to extrapolate pixels outside of the image 646 CHAPTER 12. IMGPROC. IMAGE PROCESSING The function smoothes the image using the kernel: K = α   1 1 1 ··· 1 1 1 1 1 ··· 1 1 ................... 1 1 1 ··· 1 1   where α =  1 ksize.width*ksize.height when normalize=true 1 otherwise Unnormalized box filter is useful for computing various integral characteristics over each pixel neighborhood, such as covariation matrices of image derivatives (used in dense optical flow algo- rithms, Harris corner detector etc.). If you need to compute pixel sums over variable-size windows, use cv::integral. See also: cv::boxFilter, cv::bilateralFilter, cv::GaussianBlur, cv::medianBlur, cv::integral. cv::buildPyramid (view/add comments) Constructs Gaussian pyramid for an image void buildPyramid( const Mat& src, vector& dst, int maxlevel ); src The source image; check cv::pyrDown for the list of supported types dst The destination vector of maxlevel+1 images of the same type as src; dst[0] will be the same as src, dst[1] is the next pyramid layer, a smoothed and down-sized src etc. maxlevel The 0-based index of the last (i.e. the smallest) pyramid layer; it must be non-negative The function constructs a vector of images and builds the gaussian pyramid by recursively applying cv::pyrDown to the previously built pyramid layers, starting from dst[0]==src. cv::copyMakeBorder (view/add comments) Forms a border around the image 12.2. IMAGE FILTERING 647 void copyMakeBorder( const Mat& src, Mat& dst, int top, int bottom, int left, int right, int borderType, const Scalar& value=Scalar() ); src The source image dst The destination image; will have the same type as src and the size Size(src.cols+left+right, src.rows+top+bottom) top, bottom, left, right Specify how much pixels in each direction from the source im- age rectangle one needs to extrapolate, e.g. top=1, bottom=1, left=1, right=1 mean that 1 pixel-wide border needs to be built borderType The border type; see cv::borderInterpolate value The border value if borderType==BORDER CONSTANT The function copies the source image into the middle of the destination image. The areas to the left, to the right, above and below the copied source image will be filled with extrapolated pixels. This is not what cv::FilterEngine or based on it filtering functions do (they extrapolate pixels on-fly), but what other more complex functions, including your own, may do to simplify image boundary handling. The function supports the mode when src is already in the middle of dst. In this case the function does not copy src itself, but simply constructs the border, e.g.: // let border be the same in all directions int border=2; // constructs a larger image to fit both the image and the border Mat gray_buf(rgb.rows + border*2, rgb.cols + border*2, rgb.depth()); // select the middle part of it w/o copying data Mat gray(gray_canvas, Rect(border, border, rgb.cols, rgb.rows)); // convert image from RGB to grayscale cvtColor(rgb, gray, CV_RGB2GRAY); // form a border in-place copyMakeBorder(gray, gray_buf, border, border, border, border, BORDER_REPLICATE); // now do some custom filtering ... ... See also: cv::borderInterpolate 648 CHAPTER 12. IMGPROC. IMAGE PROCESSING cv::createBoxFilter (view/add comments) Returns box filter engine Ptr createBoxFilter( int srcType, int dstType, Size ksize, Point anchor=Point(-1,-1), bool normalize=true, int borderType=BORDER DEFAULT); Ptr getRowSumFilter(int srcType, int sumType, int ksize, int anchor=-1); Ptr getColumnSumFilter(int sumType, int dstType, int ksize, int anchor=-1, double scale=1); srcType The source image type sumType The intermediate horizontal sum type; must have as many channels as srcType dstType The destination image type; must have as many channels as srcType ksize The aperture size anchor The anchor position with the kernel; negative values mean that the anchor is at the kernel center normalize Whether the sums are normalized or not; see cv::boxFilter scale Another way to specify normalization in lower-level getColumnSumFilter borderType Which border type to use; see cv::borderInterpolate The function is a convenience function that retrieves horizontal sum primitive filter with cv::getRowSumFilter, vertical sum filter with cv::getColumnSumFilter, constructs new cv::FilterEngine and passes both of the primitive filters there. The constructed filter engine can be used for image filtering with normalized or unnormalized box filter. The function itself is used by cv::blur and cv::boxFilter. See also: cv::FilterEngine, cv::blur, cv::boxFilter. 12.2. IMAGE FILTERING 649 cv::createDerivFilter (view/add comments) Returns engine for computing image derivatives Ptr createDerivFilter( int srcType, int dstType, int dx, int dy, int ksize, int borderType=BORDER DEFAULT ); srcType The source image type dstType The destination image type; must have as many channels as srcType dx The derivative order in respect with x dy The derivative order in respect with y ksize The aperture size; see cv::getDerivKernels borderType Which border type to use; see cv::borderInterpolate The function cv::createDerivFilter is a small convenience function that retrieves linear filter coefficients for computing image derivatives using cv::getDerivKernels and then creates a sep- arable linear filter with cv::createSeparableLinearFilter. The function is used by cv::Sobel and cv::Scharr. See also: cv::createSeparableLinearFilter, cv::getDerivKernels, cv::Scharr, cv::Sobel. cv::createGaussianFilter (view/add comments) Returns engine for smoothing images with a Gaussian filter Ptr createGaussianFilter( int type, Size ksize, double sigmaX, double sigmaY=0, int borderType=BORDER DEFAULT); type The source and the destination image type ksize The aperture size; see cv::getGaussianKernel 650 CHAPTER 12. IMGPROC. IMAGE PROCESSING sigmaX The Gaussian sigma in the horizontal direction; see cv::getGaussianKernel sigmaY The Gaussian sigma in the vertical direction; if 0, then sigmaY ← sigmaX borderType Which border type to use; see cv::borderInterpolate The function cv::createGaussianFilter computes Gaussian kernel coefficients and then returns separable linear filter for that kernel. The function is used by cv::GaussianBlur. Note that while the function takes just one data type, both for input and output, you can pass by this limitation by calling cv::getGaussianKernel and then cv::createSeparableFilter directly. See also: cv::createSeparableLinearFilter, cv::getGaussianKernel, cv::GaussianBlur. cv::createLinearFilter (view/add comments) Creates non-separable linear filter engine Ptr createLinearFilter(int srcType, int dstType, const Mat& kernel, Point anchor=Point(-1,-1), double delta=0, int rowBorderType=BORDER DEFAULT, int columnBorderType=-1, const Scalar& borderValue=Scalar()); Ptr getLinearFilter(int srcType, int dstType, const Mat& kernel, Point anchor=Point(-1,-1), double delta=0, int bits=0); srcType The source image type dstType The destination image type; must have as many channels as srcType kernel The 2D array of filter coefficients anchor The anchor point within the kernel; special value Point(-1,-1) means that the anchor is at the kernel center delta The value added to the filtered results before storing them bits When the kernel is an integer matrix representing fixed-point filter coefficients, the parame- ter specifies the number of the fractional bits 12.2. IMAGE FILTERING 651 rowBorderType, columnBorderType The pixel extrapolation methods in the horizontal and the vertical directions; see cv::borderInterpolate borderValue Used in case of constant border The function returns pointer to 2D linear filter for the specified kernel, the source array type and the destination array type. The function is a higher-level function that calls getLinearFilter and passes the retrieved 2D filter to cv::FilterEngine constructor. See also: cv::createSeparableLinearFilter, cv::FilterEngine, cv::filter2D cv::createMorphologyFilter (view/add comments) Creates engine for non-separable morphological operations Ptr createMorphologyFilter(int op, int type, const Mat& element, Point anchor=Point(-1,-1), int rowBorderType=BORDER CONSTANT, int columnBorderType=-1, const Scalar& borderValue=morphologyDefaultBorderValue()); Ptr getMorphologyFilter(int op, int type, const Mat& element, Point anchor=Point(-1,-1)); Ptr getMorphologyRowFilter(int op, int type, int esize, int anchor=-1); Ptr getMorphologyColumnFilter(int op, int type, int esize, int anchor=-1); static inline Scalar morphologyDefaultBorderValue() return Scalar::all(DBL MAX); op The morphology operation id, MORPH ERODE or MORPH DILATE type The input/output image type element The 2D 8-bit structuring element for the morphological operation. Non-zero elements indicate the pixels that belong to the element esize The horizontal or vertical structuring element size for separable morphological operations anchor The anchor position within the structuring element; negative values mean that the anchor is at the center 652 CHAPTER 12. IMGPROC. IMAGE PROCESSING rowBorderType, columnBorderType The pixel extrapolation methods in the horizontal and the vertical directions; see cv::borderInterpolate borderValue The border value in case of a constant border. The default value, morphologyDefaultBorderValue, has the special meaning. It is transformed + inf for the erosion and to − inf for the dilation, which means that the minimum (maximum) is effec- tively computed only over the pixels that are inside the image. The functions construct primitive morphological filtering operations or a filter engine based on them. Normally it’s enough to use cv::createMorphologyFilter or even higher-level cv::erode, cv::dilate or cv::morphologyEx, Note, that cv::createMorphologyFilter analyses the structuring element shape and builds a separable morphological filter engine when the structuring element is square. See also: cv::erode, cv::dilate, cv::morphologyEx, cv::FilterEngine cv::createSeparableLinearFilter (view/add comments) Creates engine for separable linear filter Ptr createSeparableLinearFilter(int srcType, int dstType, const Mat& rowKernel, const Mat& columnKernel, Point anchor=Point(-1,-1), double delta=0, int rowBorderType=BORDER DEFAULT, int columnBorderType=-1, const Scalar& borderValue=Scalar()); Ptr getLinearColumnFilter(int bufType, int dstType, const Mat& columnKernel, int anchor, int symmetryType, double delta=0, int bits=0); Ptr getLinearRowFilter(int srcType, int bufType, const Mat& rowKernel, int anchor, int symmetryType); srcType The source array type dstType The destination image type; must have as many channels as srcType bufType The inermediate buffer type; must have as many channels as srcType 12.2. IMAGE FILTERING 653 rowKernel The coefficients for filtering each row columnKernel The coefficients for filtering each column anchor The anchor position within the kernel; negative values mean that anchor is positioned at the aperture center delta The value added to the filtered results before storing them bits When the kernel is an integer matrix representing fixed-point filter coefficients, the parame- ter specifies the number of the fractional bits rowBorderType, columnBorderType The pixel extrapolation methods in the horizontal and the vertical directions; see cv::borderInterpolate borderValue Used in case of a constant border symmetryType The type of each of the row and column kernel; see cv::getKernelType. The functions construct primitive separable linear filtering operations or a filter engine based on them. Normally it’s enough to use cv::createSeparableLinearFilter or even higher-level cv::sepFilter2D. The function cv::createMorphologyFilter is smart enough to figure out the symmetryType for each of the two kernels, the intermediate bufType, and, if the filtering can be done in integer arithmetics, the number of bits to encode the filter coefficients. If it does not work for you, it’s possible to call getLinearColumnFilter, getLinearRowFilter directly and then pass them to cv::FilterEngine constructor. See also: cv::sepFilter2D, cv::createLinearFilter, cv::FilterEngine, cv::getKernelType cv::dilate (view/add comments) Dilates an image by using a specific structuring element. void dilate( const Mat& src, Mat& dst, const Mat& element, Point anchor=Point(-1,-1), int iterations=1, int borderType=BORDER CONSTANT, const Scalar& borderValue=morphologyDefaultBorderValue() ); src The source image dst The destination image. It will have the same size and the same type as src 654 CHAPTER 12. IMGPROC. IMAGE PROCESSING element The structuring element used for dilation. If element=Mat(), a 3 × 3 rectangular structuring element is used anchor Position of the anchor within the element. The default value (−1, −1) means that the anchor is at the element center iterations The number of times dilation is applied borderType The pixel extrapolation method; see cv::borderInterpolate borderValue The border value in case of a constant border. The default value has a special meaning, see cv::createMorphologyFilter The function dilates the source image using the specified structuring element that determines the shape of a pixel neighborhood over which the maximum is taken: dst(x, y) = max (x0,y0): element(x0,y0)6=0 src(x + x0, y + y0) The function supports the in-place mode. Dilation can be applied several (iterations) times. In the case of multi-channel images each channel is processed independently. See also: cv::erode, cv::morphologyEx, cv::createMorphologyFilter cv::erode (view/add comments) Erodes an image by using a specific structuring element. void erode( const Mat& src, Mat& dst, const Mat& element, Point anchor=Point(-1,-1), int iterations=1, int borderType=BORDER CONSTANT, const Scalar& borderValue=morphologyDefaultBorderValue() ); src The source image dst The destination image. It will have the same size and the same type as src element The structuring element used for dilation. If element=Mat(), a 3 × 3 rectangular structuring element is used anchor Position of the anchor within the element. The default value (−1, −1) means that the anchor is at the element center 12.2. IMAGE FILTERING 655 iterations The number of times erosion is applied borderType The pixel extrapolation method; see cv::borderInterpolate borderValue The border value in case of a constant border. The default value has a special meaning, see cv::createMorphoogyFilter The function erodes the source image using the specified structuring element that determines the shape of a pixel neighborhood over which the minimum is taken: dst(x, y) = min (x0,y0): element(x0,y0)6=0 src(x + x0, y + y0) The function supports the in-place mode. Erosion can be applied several (iterations) times. In the case of multi-channel images each channel is processed independently. See also: cv::dilate, cv::morphologyEx, cv::createMorphologyFilter cv::filter2D (view/add comments) Convolves an image with the kernel void filter2D( const Mat& src, Mat& dst, int ddepth, const Mat& kernel, Point anchor=Point(-1,-1), double delta=0, int borderType=BORDER DEFAULT ); src The source image dst The destination image. It will have the same size and the same number of channels as src ddepth The desired depth of the destination image. If it is negative, it will be the same as src.depth() kernel Convolution kernel (or rather a correlation kernel), a single-channel floating point matrix. If you want to apply different kernels to different channels, split the image into separate color planes using cv::split and process them individually anchor The anchor of the kernel that indicates the relative position of a filtered point within the kernel. The anchor should lie within the kernel. The special default value (-1,-1) means that the anchor is at the kernel center delta The optional value added to the filtered pixels before storing them in dst 656 CHAPTER 12. IMGPROC. IMAGE PROCESSING borderType The pixel extrapolation method; see cv::borderInterpolate The function applies an arbitrary linear filter to the image. In-place operation is supported. When the aperture is partially outside the image, the function interpolates outlier pixel values according to the specified border mode. The function does actually computes correlation, not the convolution: dst(x, y) = X 0≤x0 1. When ksize == 1, the Laplacian is computed by filtering the image with the following 3 × 3 aperture:   0 1 0 1 −4 1 0 1 0   See also: cv::Sobel, cv::Scharr cv::pyrDown (view/add comments) Smoothes an image and downsamples it. 12.2. IMAGE FILTERING 663 void pyrDown( const Mat& src, Mat& dst, const Size& dstsize=Size()); src The source image dst The destination image. It will have the specified size and the same type as src dstsize Size of the destination image. By default it is computed as Size((src.cols+1)/2, (src.rows+1)/2). But in any case the following conditions should be satisfied: |dstsize.width ∗ 2 − src.cols| ≤ 2 |dstsize.height ∗ 2 − src.rows| ≤ 2 The function performs the downsampling step of the Gaussian pyramid construction. First it convolves the source image with the kernel: 1 16   1 4 6 4 1 4 16 24 16 4 6 24 36 24 6 4 16 24 16 4 1 4 6 4 1   and then downsamples the image by rejecting even rows and columns. cv::pyrUp (view/add comments) Upsamples an image and then smoothes it void pyrUp( const Mat& src, Mat& dst, const Size& dstsize=Size()); src The source image dst The destination image. It will have the specified size and the same type as src dstsize Size of the destination image. By default it is computed as Size(src.cols*2, (src.rows*2). But in any case the following conditions should be satisfied: |dstsize.width − src.cols ∗ 2| ≤ (dstsize.width mod 2) |dstsize.height − src.rows ∗ 2| ≤ (dstsize.height mod 2) 664 CHAPTER 12. IMGPROC. IMAGE PROCESSING The function performs the upsampling step of the Gaussian pyramid construction (it can actu- ally be used to construct the Laplacian pyramid). First it upsamples the source image by injecting even zero rows and columns and then convolves the result with the same kernel as in cv::pyrDown, multiplied by 4. cv::sepFilter2D (view/add comments) Applies separable linear filter to an image void sepFilter2D( const Mat& src, Mat& dst, int ddepth, const Mat& rowKernel, const Mat& columnKernel, Point anchor=Point(-1,-1), double delta=0, int borderType=BORDER DEFAULT ); src The source image dst The destination image; will have the same size and the same number of channels as src ddepth The destination image depth rowKernel The coefficients for filtering each row columnKernel The coefficients for filtering each column anchor The anchor position within the kernel; The default value (−1, 1) means that the anchor is at the kernel center delta The value added to the filtered results before storing them borderType The pixel extrapolation method; see cv::borderInterpolate The function applies a separable linear filter to the image. That is, first, every row of src is filtered with 1D kernel rowKernel. Then, every column of the result is filtered with 1D kernel columnKernel and the final result shifted by delta is stored in dst. See also: cv::createSeparableLinearFilter, cv::filter2D, cv::Sobel, cv::GaussianBlur, cv::boxFilter, cv::blur. 12.2. IMAGE FILTERING 665 cv::Sobel (view/add comments) Calculates the first, second, third or mixed image derivatives using an extended Sobel operator void Sobel( const Mat& src, Mat& dst, int ddepth, int xorder, int yorder, int ksize=3, double scale=1, double delta=0, int borderType=BORDER DEFAULT ); src The source image dst The destination image; will have the same size and the same number of channels as src ddepth The destination image depth xorder Order of the derivative x yorder Order of the derivative y ksize Size of the extended Sobel kernel, must be 1, 3, 5 or 7 scale The optional scale factor for the computed derivative values (by default, no scaling is applied, see cv::getDerivKernels) delta The optional delta value, added to the results prior to storing them in dst borderType The pixel extrapolation method, see cv::borderInterpolate In all cases except 1, an ksize × ksize separable kernel will be used to calculate the deriva- tive. When ksize = 1, a 3 × 1 or 1 × 3 kernel will be used (i.e. no Gaussian smoothing is done). ksize = 1 can only be used for the first or the second x- or y- derivatives. There is also the special value ksize = CV SCHARR (-1) that corresponds to a 3 × 3 Scharr filter that may give more accurate results than a 3 × 3 Sobel. The Scharr aperture is   −3 0 3 −10 0 10 −3 0 3   for the x-derivative or transposed for the y-derivative. The function calculates the image derivative by convolving the image with the appropriate kernel: 666 CHAPTER 12. IMGPROC. IMAGE PROCESSING dst = ∂xorder+yordersrc ∂xxorder∂yyorder The Sobel operators combine Gaussian smoothing and differentiation, so the result is more or less resistant to the noise. Most often, the function is called with (xorder = 1, yorder = 0, ksize = 3) or (xorder = 0, yorder = 1, ksize = 3) to calculate the first x- or y- image derivative. The first case corresponds to a kernel of:   −1 0 1 −2 0 2 −1 0 1   and the second one corresponds to a kernel of:   −1 −2 −1 0 0 0 1 2 1   See also: cv::Scharr, cv::Lapacian, cv::sepFilter2D, cv::filter2D, cv::GaussianBlur cv::Scharr (view/add comments) Calculates the first x- or y- image derivative using Scharr operator void Scharr( const Mat& src, Mat& dst, int ddepth, int xorder, int yorder, double scale=1, double delta=0, int borderType=BORDER DEFAULT ); src The source image dst The destination image; will have the same size and the same number of channels as src ddepth The destination image depth xorder Order of the derivative x yorder Order of the derivative y 12.3. GEOMETRIC IMAGE TRANSFORMATIONS 667 scale The optional scale factor for the computed derivative values (by default, no scaling is applied, see cv::getDerivKernels) delta The optional delta value, added to the results prior to storing them in dst borderType The pixel extrapolation method, see cv::borderInterpolate The function computes the first x- or y- spatial image derivative using Scharr operator. The call Scharr(src, dst, ddepth, xorder, yorder, scale, delta, borderType) is equivalent to Sobel(src, dst, ddepth, xorder, yorder, CV SCHARR, scale, delta, borderType). 12.3 Geometric Image Transformations The functions in this section perform various geometrical transformations of 2D images. That is, they do not change the image content, but deform the pixel grid, and map this deformed grid to the destination image. In fact, to avoid sampling artifacts, the mapping is done in the reverse order, from destination to the source. That is, for each pixel (x, y) of the destination image, the functions compute coordinates of the corresponding ”donor” pixel in the source image and copy the pixel value, that is: dst(x, y) = src(fx(x, y), fy(x, y)) In the case when the user specifies the forward mapping: hgx, gyi : src → dst, the OpenCV functions first compute the corresponding inverse mapping: hfx, fyi : dst → src and then use the above formula. The actual implementations of the geometrical transformations, from the most generic cv::remap and to the simplest and the fastest cv::resize, need to solve the 2 main problems with the above formula: 1. extrapolation of non-existing pixels. Similarly to the filtering functions, described in the pre- vious section, for some (x, y) one of fx(x, y) or fy(x, y), or they both, may fall outside of the image, in which case some extrapolation method needs to be used. OpenCV provides the same selection of the extrapolation methods as in the filtering functions, but also an ad- ditional method BORDER TRANSPARENT, which means that the corresponding pixels in the destination image will not be modified at all. 2. interpolation of pixel values. Usually fx(x, y) and fy(x, y) are floating-point numbers (i.e. hfx, fyi can be an affine or perspective transformation, or radial lens distortion correction 668 CHAPTER 12. IMGPROC. IMAGE PROCESSING etc.), so a pixel values at fractional coordinates needs to be retrieved. In the simplest case the coordinates can be just rounded to the nearest integer coordinates and the correspond- ing pixel used, which is called nearest-neighbor interpolation. However, a better result can be achieved by using more sophisticated interpolation methods, where a polynomial function is fit into some neighborhood of the computed pixel (fx(x, y), fy(x, y)) and then the value of the polynomial at (fx(x, y), fy(x, y)) is taken as the interpolated pixel value. In OpenCV you can choose between several interpolation methods, see cv::resize. cv::convertMaps (view/add comments) Converts image transformation maps from one representation to another void convertMaps( const Mat& map1, const Mat& map2, Mat& dstmap1, Mat& dstmap2, int dstmap1type, bool nninterpolation=false ); map1 The first input map of type CV 16SC2 or CV 32FC1 or CV 32FC2 map2 The second input map of type CV 16UC1 or CV 32FC1 or none (empty matrix), respectively dstmap1 The first output map; will have type dstmap1type and the same size as src dstmap2 The second output map dstmap1type The type of the first output map; should be CV 16SC2, CV 32FC1 or CV 32FC2 nninterpolation Indicates whether the fixed-point maps will be used for nearest-neighbor or for more complex interpolation The function converts a pair of maps for cv::remap from one representation to another. The fol- lowing options ((map1.type(), map2.type()) → (dstmap1.type(), dstmap2.type())) are supported: 1. (CV 32FC1, CV 32FC1) → (CV 16SC2, CV 16UC1). This is the most frequently used conversion operation, in which the original floating-point maps (see cv::remap) are con- verted to more compact and much faster fixed-point representation. The first output array will contain the rounded coordinates and the second array (created only when nninterpolation=false) will contain indices in the interpolation tables. 12.3. GEOMETRIC IMAGE TRANSFORMATIONS 669 2. (CV 32FC2) → (CV 16SC2, CV 16UC1). The same as above, but the original maps are stored in one 2-channel matrix. 3. the reverse conversion. Obviously, the reconstructed floating-point maps will not be exactly the same as the originals. See also: cv::remap, cv::undisort, cv::initUndistortRectifyMap cv::getAffineTransform (view/add comments) Calculates the affine transform from 3 pairs of the corresponding points Mat getAffineTransform( const Point2f src[], const Point2f dst[] ); src Coordinates of a triangle vertices in the source image dst Coordinates of the corresponding triangle vertices in the destination image The function calculates the 2 × 3 matrix of an affine transform such that: x0 i y0 i  = map matrix ·   xi yi 1   where dst(i) = (x0 i, y0 i), src(i) = (xi, yi), i = 0, 1, 2 See also: cv::warpAffine, cv::transform cv::getPerspectiveTransform (view/add comments) Calculates the perspective transform from 4 pairs of the corresponding points Mat getPerspectiveTransform( const Point2f src[], const Point2f dst[] ); 670 CHAPTER 12. IMGPROC. IMAGE PROCESSING src Coordinates of a quadrange vertices in the source image dst Coordinates of the corresponding quadrangle vertices in the destination image The function calculates the 3 × 3 matrix of a perspective transform such that:   tix0 i tiy0 i ti   = map matrix ·   xi yi 1   where dst(i) = (x0 i, y0 i), src(i) = (xi, yi), i = 0, 1, 2 See also: cv::findHomography, cv::warpPerspective, cv::perspectiveTransform cv::getRectSubPix (view/add comments) Retrieves the pixel rectangle from an image with sub-pixel accuracy void getRectSubPix( const Mat& image, Size patchSize, Point2f center, Mat& dst, int patchType=-1 ); src Source image patchSize Size of the extracted patch center Floating point coordinates of the extracted rectangle center within the source image. The center must be inside the image dst The extracted patch; will have the size patchSize and the same number of channels as src patchType The depth of the extracted pixels. By default they will have the same depth as src The function getRectSubPix extracts pixels from src: dst(x, y) = src(x + center.x − (dst.cols − 1) ∗ 0.5, y + center.y − (dst.rows − 1) ∗ 0.5) 12.3. GEOMETRIC IMAGE TRANSFORMATIONS 671 where the values of the pixels at non-integer coordinates are retrieved using bilinear interpo- lation. Every channel of multiple-channel images is processed independently. While the rectangle center must be inside the image, parts of the rectangle may be outside. In this case, the replica- tion border mode (see cv::borderInterpolate) is used to extrapolate the pixel values outside of the image. See also: cv::warpAffine, cv::warpPerspective cv::getRotationMatrix2D (view/add comments) Calculates the affine matrix of 2d rotation. Mat getRotationMatrix2D( Point2f center, double angle, double scale ); center Center of the rotation in the source image angle The rotation angle in degrees. Positive values mean counter-clockwise rotation (the coor- dinate origin is assumed to be the top-left corner) scale Isotropic scale factor The function calculates the following matrix:  α β (1 − α)· center.x − β · center.y −β α β · center.x − (1 − α)· center.y  where α = scale · cos angle, β = scale · sin angle The transformation maps the rotation center to itself. If this is not the purpose, the shift should be adjusted. See also: cv::getAffineTransform, cv::warpAffine, cv::transform cv::invertAffineTransform (view/add comments) Inverts an affine transformation 672 CHAPTER 12. IMGPROC. IMAGE PROCESSING void invertAffineTransform(const Mat& M, Mat& iM); M The original affine transformation iM The output reverse affine transformation The function computes inverse affine transformation represented by 2 × 3 matrix M: a11 a12 b1 a21 a22 b2  The result will also be a 2 × 3 matrix of the same type as M. cv::remap (view/add comments) Applies a generic geometrical transformation to an image. void remap( const Mat& src, Mat& dst, const Mat& map1, const Mat& map2, int interpolation, int borderMode=BORDER CONSTANT, const Scalar& borderValue=Scalar()); src Source image dst Destination image. It will have the same size as map1 and the same type as src map1 The first map of either (x,y) points or just x values having type CV 16SC2, CV 32FC1 or CV 32FC2. See cv::convertMaps for converting floating point representation to fixed-point for speed. map2 The second map of y values having type CV 16UC1, CV 32FC1 or none (empty map if map1 is (x,y) points), respectively interpolation The interpolation method, see cv::resize. The method INTER AREA is not supported by this function borderMode The pixel extrapolation method, see cv::borderInterpolate. When the borderMode=BORDER TRANSPARENT, it means that the pixels in the destination image that corresponds to the ”outliers” in the source image are not modified by the function 12.3. GEOMETRIC IMAGE TRANSFORMATIONS 673 borderValue A value used in the case of a constant border. By default it is 0 The function remap transforms the source image using the specified map: dst(x, y) = src(mapx(x, y), mapy(x, y)) Where values of pixels with non-integer coordinates are computed using one of the available interpolation methods. mapx and mapy can be encoded as separate floating-point maps in map1 and map2 respectively, or interleaved floating-point maps of (x, y) in map1, or fixed-point maps made by using cv::convertMaps. The reason you might want to convert from floating to fixed- point representations of a map is that they can yield much faster ( 2x) remapping operations. In the converted case, map1 contains pairs (cvFloor(x), cvFloor(y)) and map2 contains indices in a table of interpolation coefficients. This function can not operate in-place. cv::resize (view/add comments) Resizes an image void resize( const Mat& src, Mat& dst, Size dsize, double fx=0, double fy=0, int interpolation=INTER LINEAR ); src Source image dst Destination image. It will have size dsize (when it is non-zero) or the size computed from src.size() and fx and fy. The type of dst will be the same as of src. dsize The destination image size. If it is zero, then it is computed as: dsize = Size(round(fx*src.cols), round(fy*src.rows)) . Either dsize or both fx or fy must be non-zero. fx The scale factor along the horizontal axis. When 0, it is computed as (double)dsize.width/src.cols fy The scale factor along the vertical axis. When 0, it is computed as (double)dsize.height/src.rows 674 CHAPTER 12. IMGPROC. IMAGE PROCESSING interpolation The interpolation method: INTER NEAREST nearest-neighbor interpolation INTER LINEAR bilinear interpolation (used by default) INTER AREA resampling using pixel area relation. It may be the preferred method for image decimation, as it gives moire-free results. But when the image is zoomed, it is similar to the INTER NEAREST method INTER CUBIC bicubic interpolation over 4x4 pixel neighborhood INTER LANCZOS4 Lanczos interpolation over 8x8 pixel neighborhood The function resize resizes an image src down to or up to the specified size. Note that the initial dst type or size are not taken into account. Instead the size and type are derived from the src, dsize, fx and fy. If you want to resize src so that it fits the pre-created dst, you may call the function as: // explicitly specify dsize=dst.size(); fx and fy will be computed from that. resize(src, dst, dst.size(), 0, 0, interpolation); If you want to decimate the image by factor of 2 in each direction, you can call the function this way: // specify fx and fy and let the function to compute the destination image size. resize(src, dst, Size(), 0.5, 0.5, interpolation); See also: cv::warpAffine, cv::warpPerspective, cv::remap. cv::warpAffine (view/add comments) Applies an affine transformation to an image. void warpAffine( const Mat& src, Mat& dst, const Mat& M, Size dsize, int flags=INTER LINEAR, int borderMode=BORDER CONSTANT, const Scalar& borderValue=Scalar()); src Source image dst Destination image; will have size dsize and the same type as src 12.3. GEOMETRIC IMAGE TRANSFORMATIONS 675 M 2 × 3 transformation matrix dsize Size of the destination image flags A combination of interpolation methods, see cv::resize, and the optional flag WARP INVERSE MAP that means that M is the inverse transformation (dst → src) borderMode The pixel extrapolation method, see cv::borderInterpolate. When the borderMode=BORDER TRANSPARENT, it means that the pixels in the destination image that corresponds to the ”outliers” in the source image are not modified by the function borderValue A value used in case of a constant border. By default it is 0 The function warpAffine transforms the source image using the specified matrix: dst(x, y) = src(M11x + M12y + M13,M21x + M22y + M23) when the flag WARP INVERSE MAP is set. Otherwise, the transformation is first inverted with cv::invertAffineTransform and then put in the formula above instead of M. The function can not operate in-place. See also: cv::warpPerspective, cv::resize, cv::remap, cv::getRectSubPix, cv::transform cv::warpPerspective (view/add comments) Applies a perspective transformation to an image. void warpPerspective( const Mat& src, Mat& dst, const Mat& M, Size dsize, int flags=INTER LINEAR, int borderMode=BORDER CONSTANT, const Scalar& borderValue=Scalar()); src Source image dst Destination image; will have size dsize and the same type as src M 3 × 3 transformation matrix dsize Size of the destination image 676 CHAPTER 12. IMGPROC. IMAGE PROCESSING flags A combination of interpolation methods, see cv::resize, and the optional flag WARP INVERSE MAP that means that M is the inverse transformation (dst → src) borderMode The pixel extrapolation method, see cv::borderInterpolate. When the borderMode=BORDER TRANSPARENT, it means that the pixels in the destination image that corresponds to the ”outliers” in the source image are not modified by the function borderValue A value used in case of a constant border. By default it is 0 The function warpPerspective transforms the source image using the specified matrix: dst(x, y) = src M11x + M12y + M13 M31x + M32y + M33 ,M21x + M22y + M23 M31x + M32y + M33  when the flag WARP INVERSE MAP is set. Otherwise, the transformation is first inverted with cv::invert and then put in the formula above instead of M. The function can not operate in-place. See also: cv::warpAffine, cv::resize, cv::remap, cv::getRectSubPix, cv::perspectiveTransform 12.4 Miscellaneous Image Transformations cv::adaptiveThreshold (view/add comments) Applies an adaptive threshold to an array. void adaptiveThreshold( const Mat& src, Mat& dst, double maxValue, int adaptiveMethod, int thresholdType, int blockSize, double C ); src Source 8-bit single-channel image dst Destination image; will have the same size and the same type as src maxValue The non-zero value assigned to the pixels for which the condition is satisfied. See the discussion adaptiveMethod Adaptive thresholding algorithm to use, ADAPTIVE THRESH MEAN C or ADAPTIVE THRESH GAUSSIAN C (see the discussion) thresholdType Thresholding type; must be one of THRESH BINARY or THRESH BINARY INV 12.4. MISCELLANEOUS IMAGE TRANSFORMATIONS 677 blockSize The size of a pixel neighborhood that is used to calculate a threshold value for the pixel: 3, 5, 7, and so on C The constant subtracted from the mean or weighted mean (see the discussion); normally, it’s positive, but may be zero or negative as well The function transforms a grayscale image to a binary image according to the formulas: THRESH BINARY dst(x, y) =  maxValue if src(x, y) > T(x, y) 0 otherwise THRESH BINARY INV dst(x, y) =  0 if src(x, y) > T(x, y) maxValue otherwise where T(x, y) is a threshold calculated individually for each pixel. 1. For the method ADAPTIVE THRESH MEAN C the threshold value T(x, y) is the mean of a blockSize × blockSize neighborhood of (x, y), minus C. 2. For the method ADAPTIVE THRESH GAUSSIAN C the threshold value T(x, y) is the weighted sum (i.e. cross-correlation with a Gaussian window) of a blockSize × blockSize neigh- borhood of (x, y), minus C. The default sigma (standard deviation) is used for the specified blockSize, see cv::getGaussianKernel. The function can process the image in-place. See also: cv::threshold, cv::blur, cv::GaussianBlur cv::cvtColor (view/add comments) Converts image from one color space to another void cvtColor( const Mat& src, Mat& dst, int code, int dstCn=0 ); src The source image, 8-bit unsigned, 16-bit unsigned (CV 16UC...) or single-precision floating- point dst The destination image; will have the same size and the same depth as src 678 CHAPTER 12. IMGPROC. IMAGE PROCESSING code The color space conversion code; see the discussion dstCn The number of channels in the destination image; if the parameter is 0, the number of the channels will be derived automatically from src and the code The function converts the input image from one color space to another. In the case of transfor- mation to-from RGB color space the ordering of the channels should be specified explicitly (RGB or BGR). The conventional ranges for R, G and B channel values are: • 0 to 255 for CV 8U images • 0 to 65535 for CV 16U images and • 0 to 1 for CV 32F images. Of course, in the case of linear transformations the range does not matter, but in the non-linear cases the input RGB image should be normalized to the proper value range in order to get the correct results, e.g. for RGB→L*u*v* transformation. For example, if you have a 32-bit floating- point image directly converted from 8-bit image without any scaling, then it will have 0..255 value range, instead of the assumed by the function 0..1. So, before calling cvtColor, you need first to scale the image down: img *= 1./255; cvtColor(img, img, CV_BGR2Luv); The function can do the following transformations: • Transformations within RGB space like adding/removing the alpha channel, reversing the channel order, conversion to/from 16-bit RGB color (R5:G6:B5 or R5:G5:B5), as well as conversion to/from grayscale using: RGB[A] to Gray: Y ← 0.299 ·R + 0.587 ·G + 0.114 ·B and Gray to RGB[A]: R ← Y,G ← Y,B ← Y,A ← 0 The conversion from a RGB image to gray is done with: cvtColor(src, bwsrc, CV_RGB2GRAY); Some more advanced channel reordering can also be done with cv::mixChannels. 12.4. MISCELLANEOUS IMAGE TRANSFORMATIONS 679 • RGB ↔ CIE XYZ.Rec 709 with D65 white point (CV BGR2XYZ, CV RGB2XYZ, CV XYZ2BGR, CV XYZ2RGB):   X Y Z   ←   0.412453 0.357580 0.180423 0.212671 0.715160 0.072169 0.019334 0.119193 0.950227   ·   R G B     R G B   ←   3.240479 −1.53715 −0.498535 −0.969256 1.875991 0.041556 0.055648 −0.204043 1.057311   ·   X Y Z   X,Y and Z cover the whole value range (in the case of floating-point images Z may exceed 1). • RGB ↔ YCrCb JPEG (a.k.a. YCC) (CV BGR2YCrCb, CV RGB2YCrCb, CV YCrCb2BGR, CV YCrCb2RGB) Y ← 0.299 ·R + 0.587 ·G + 0.114 ·B Cr ← (R − Y)· 0.713 + delta Cb ← (B − Y)· 0.564 + delta R ← Y + 1.403 ·(Cr − delta) G ← Y − 0.344 ·(Cr − delta) − 0.714 ·(Cb − delta) B ← Y + 1.773 ·(Cb − delta) where delta =    128 for 8-bit images 32768 for 16-bit images 0.5 for floating-point images Y, Cr and Cb cover the whole value range. • RGB ↔ HSV (CV BGR2HSV, CV RGB2HSV, CV HSV2BGR, CV HSV2RGB) in the case of 8-bit and 16-bit images R, G and B are converted to floating-point format and scaled to fit the 0 to 1 range V ← max(R, G, B) S ←  V −min(R,G,B) V if V 6= 0 0 otherwise H ←    60(G − B)/S if V = R 120 + 60(B − R)/S if V = G 240 + 60(R − G)/S if V = B 680 CHAPTER 12. IMGPROC. IMAGE PROCESSING if H < 0 then H ← H + 360 On output 0 ≤ V ≤ 1, 0 ≤ S ≤ 1, 0 ≤ H ≤ 360. The values are then converted to the destination data type: 8-bit images V ← 255V,S ← 255S, H ← H/2(to fit to 0 to 255) 16-bit images (currently not supported) V < −65535V, S < −65535S, H < −H 32-bit images H, S, V are left as is • RGB ↔ HLS (CV BGR2HLS, CV RGB2HLS, CV HLS2BGR, CV HLS2RGB). in the case of 8-bit and 16-bit images R, G and B are converted to floating-point format and scaled to fit the 0 to 1 range. Vmax ← max(R, G, B) Vmin ← min(R, G, B) L ← Vmax + Vmin 2 S ← (Vmax−Vmin Vmax+Vmin if L < 0.5 Vmax−Vmin 2−(Vmax+Vmin) if L ≥ 0.5 H ←    60(G − B)/S if Vmax = R 120 + 60(B − R)/S if Vmax = G 240 + 60(R − G)/S if Vmax = B if H < 0 then H ← H + 360 On output 0 ≤ L ≤ 1, 0 ≤ S ≤ 1, 0 ≤ H ≤ 360. The values are then converted to the destination data type: 8-bit images V ← 255 ·V,S ← 255 · S, H ← H/2 (to fit to 0 to 255) 16-bit images (currently not supported) V < −65535 · V, S < −65535 · S, H < −H 32-bit images H, S, V are left as is 12.4. MISCELLANEOUS IMAGE TRANSFORMATIONS 681 • RGB ↔ CIE L*a*b* (CV BGR2Lab, CV RGB2Lab, CV Lab2BGR, CV Lab2RGB) in the case of 8-bit and 16-bit images R, G and B are converted to floating-point format and scaled to fit the 0 to 1 range   X Y Z   ←   0.412453 0.357580 0.180423 0.212671 0.715160 0.072169 0.019334 0.119193 0.950227   ·   R G B   X ← X/Xn, whereXn = 0.950456 Z ← Z/Zn, whereZn = 1.088754 L ←  116 ∗ Y 1/3 − 16 for Y > 0.008856 903.3 ∗ Y for Y ≤ 0.008856 a ← 500(f(X) − f(Y)) + delta b ← 200(f(Y) − f(Z)) + delta where f(t) =  t1/3 for t > 0.008856 7.787t + 16/116 for t ≤ 0.008856 and delta =  128 for 8-bit images 0 for floating-point images On output 0 ≤ L ≤ 100, −127 ≤ a ≤ 127, −127 ≤ b ≤ 127 The values are then converted to the destination data type: 8-bit images L ← L ∗ 255/100, a ← a + 128, b ← b + 128 16-bit images currently not supported 32-bit images L, a, b are left as is • RGB ↔ CIE L*u*v* (CV BGR2Luv, CV RGB2Luv, CV Luv2BGR, CV Luv2RGB) in the case of 8-bit and 16-bit images R, G and B are converted to floating-point format and scaled to fit 0 to 1 range   X Y Z   ←   0.412453 0.357580 0.180423 0.212671 0.715160 0.072169 0.019334 0.119193 0.950227   ·   R G B   L ←  116Y 1/3 for Y > 0.008856 903.3Y for Y ≤ 0.008856 u0 ← 4 ∗ X/(X + 15 ∗ Y + 3Z) 682 CHAPTER 12. IMGPROC. IMAGE PROCESSING v0 ← 9 ∗ Y/(X + 15 ∗ Y + 3Z) u ← 13 ∗ L ∗ (u0 − un) where un = 0.19793943 v ← 13 ∗ L ∗ (v0 − vn) where vn = 0.46831096 On output 0 ≤ L ≤ 100, −134 ≤ u ≤ 220, −140 ≤ v ≤ 122. The values are then converted to the destination data type: 8-bit images L ← 255/100L, u ← 255/354(u + 134), v ← 255/256(v + 140) 16-bit images currently not supported 32-bit images L, u, v are left as is The above formulas for converting RGB to/from various color spaces have been taken from multiple sources on Web, primarily from the Charles Poynton site http://www.poynton. com/ColorFAQ.html • Bayer → RGB (CV BayerBG2BGR, CV BayerGB2BGR, CV BayerRG2BGR, CV BayerGR2BGR, CV BayerBG2RGB, CV BayerGB2RGB, CV BayerRG2RGB, CV BayerGR2RGB) The Bayer pattern is widely used in CCD and CMOS cameras. It allows one to get color pictures from a single plane where R,G and B pixels (sensors of a particular component) are interleaved like this: RGRGR GBGBG RGRGR GBGBG RGRGR The output RGB components of a pixel are interpolated from 1, 2 or 4 neighbors of the pixel having the same color. There are several modifications of the above pattern that can be achieved by shifting the pattern one pixel left and/or one pixel up. The two letters C1 and C2 in the conversion constants CV Bayer C1C2 2BGR and CV Bayer C1C2 2RGB indicate the particular pattern type - these are components from the second row, second and third columns, respectively. For example, the above pattern has very popular ”BG” type. 12.4. MISCELLANEOUS IMAGE TRANSFORMATIONS 683 cv::distanceTransform (view/add comments) Calculates the distance to the closest zero pixel for each pixel of the source image. void distanceTransform( const Mat& src, Mat& dst, int distanceType, int maskSize ); void distanceTransform( const Mat& src, Mat& dst, Mat& labels, int distanceType, int maskSize ); src 8-bit, single-channel (binary) source image dst Output image with calculated distances; will be 32-bit floating-point, single-channel image of the same size as src distanceType Type of distance; can be CV DIST L1, CV DIST L2 or CV DIST C maskSize Size of the distance transform mask; can be 3, 5 or CV DIST MASK PRECISE (the latter option is only supported by the first of the functions). In the case of CV DIST L1 or CV DIST C distance type the parameter is forced to 3, because a 3×3 mask gives the same result as a 5 × 5 or any larger aperture. labels The optional output 2d array of labels - the discrete Voronoi diagram; will have type CV 32SC1 and the same size as src. See the discussion The functions distanceTransform calculate the approximate or precise distance from every binary image pixel to the nearest zero pixel. (for zero image pixels the distance will obviously be zero). When maskSize == CV DIST MASK PRECISE and distanceType == CV DIST L2, the function runs the algorithm described in [9]. In other cases the algorithm [4] is used, that is, for pixel the function finds the shortest path to the nearest zero pixel consisting of basic shifts: horizontal, vertical, diagonal or knight’s move (the latest is available for a 5 × 5 mask). The overall distance is calculated as a sum of these basic distances. Because the distance function should be symmetric, all of the horizontal and vertical shifts must have the same cost (that is denoted as a), all the diagonal shifts must have the same cost (denoted b), and all knight’s moves must have the same cost (denoted c). For CV DIST C and CV DIST L1 types the distance is calculated precisely, whereas for CV DIST L2 (Euclidian distance) the distance can be calculated only with some relative error (a 5 × 5 mask gives more accurate results). For a, b and c OpenCV uses the values suggested in the original paper: 684 CHAPTER 12. IMGPROC. IMAGE PROCESSING CV DIST C(3 × 3) a = 1, b = 1 CV DIST L1 (3 × 3) a = 1, b = 2 CV DIST L2 (3 × 3) a=0.955, b=1.3693 CV DIST L2 (5 × 5) a=1, b=1.4, c=2.1969 Typically, for a fast, coarse distance estimation CV DIST L2, a 3 × 3 mask is used, and for a more accurate distance estimation CV DIST L2, a 5 × 5 mask or the precise algorithm is used. Note that both the precise and the approximate algorithms are linear on the number of pixels. The second variant of the function does not only compute the minimum distance for each pixel (x, y), but it also identifies the nearest the nearest connected component consisting of zero pixels. Index of the component is stored in labels(x, y). The connected components of zero pixels are also found and marked by the function. In this mode the complexity is still linear. That is, the function provides a very fast way to compute Voronoi diagram for the binary image. Currently, this second variant can only use the approximate distance transform algorithm. cv::floodFill (view/add comments) Fills a connected component with the given color. int floodFill( Mat& image, Point seed, Scalar newVal, Rect* rect=0, Scalar loDiff=Scalar(), Scalar upDiff=Scalar(), int flags=4 ); int floodFill( Mat& image, Mat& mask, Point seed, Scalar newVal, Rect* rect=0, Scalar loDiff=Scalar(), Scalar upDiff=Scalar(), int flags=4 ); image Input/output 1- or 3-channel, 8-bit or floating-point image. It is modified by the function unless the FLOODFILL MASK ONLY flag is set (in the second variant of the function; see below) mask (For the second function only) Operation mask, should be a single-channel 8-bit image, 2 pixels wider and 2 pixels taller. The function uses and updates the mask, so the user takes responsibility of initializing the mask content. Flood-filling can’t go across non-zero pixels in the mask, for example, an edge detector output can be used as a mask to stop filling at edges. It is possible to use the same mask in multiple calls to the function to make sure the 12.4. MISCELLANEOUS IMAGE TRANSFORMATIONS 685 filled area do not overlap. Note: because the mask is larger than the filled image, a pixel (x, y) in image will correspond to the pixel (x + 1, y + 1) in the mask seed The starting point newVal New value of the repainted domain pixels loDiff Maximal lower brightness/color difference between the currently observed pixel and one of its neighbors belonging to the component, or a seed pixel being added to the component upDiff Maximal upper brightness/color difference between the currently observed pixel and one of its neighbors belonging to the component, or a seed pixel being added to the component rect The optional output parameter that the function sets to the minimum bounding rectangle of the repainted domain flags The operation flags. Lower bits contain connectivity value, 4 (by default) or 8, used within the function. Connectivity determines which neighbors of a pixel are considered. Upper bits can be 0 or a combination of the following flags: FLOODFILL FIXED RANGE if set, the difference between the current pixel and seed pixel is considered, otherwise the difference between neighbor pixels is considered (i.e. the range is floating) FLOODFILL MASK ONLY (for the second variant only) if set, the function does not change the image (newVal is ignored), but fills the mask The functions floodFill fill a connected component starting from the seed point with the specified color. The connectivity is determined by the color/brightness closeness of the neighbor pixels. The pixel at (x, y) is considered to belong to the repainted domain if: grayscale image, floating range src(x0, y0) − loDiff ≤ src(x, y) ≤ src(x0, y0) + upDiff grayscale image, fixed range src(seed.x, seed.y) − loDiff ≤ src(x, y) ≤ src(seed.x, seed.y) + upDiff color image, floating range src(x0, y0)r − loDiffr ≤ src(x, y)r ≤ src(x0, y0)r + upDiffr src(x0, y0)g − loDiffg ≤ src(x, y)g ≤ src(x0, y0)g + upDiffg src(x0, y0)b − loDiffb ≤ src(x, y)b ≤ src(x0, y0)b + upDiffb 686 CHAPTER 12. IMGPROC. IMAGE PROCESSING color image, fixed range src(seed.x, seed.y)r − loDiffr ≤ src(x, y)r ≤ src(seed.x, seed.y)r + upDiffr src(seed.x, seed.y)g − loDiffg ≤ src(x, y)g ≤ src(seed.x, seed.y)g + upDiffg src(seed.x, seed.y)b − loDiffb ≤ src(x, y)b ≤ src(seed.x, seed.y)b + upDiffb where src(x0, y0) is the value of one of pixel neighbors that is already known to belong to the component. That is, to be added to the connected component, a pixel’s color/brightness should be close enough to the: • color/brightness of one of its neighbors that are already referred to the connected component in the case of floating range • color/brightness of the seed point in the case of fixed range. By using these functions you can either mark a connected component with the specified color in-place, or build a mask and then extract the contour or copy the region to another image etc. Various modes of the function are demonstrated in floodfill.c sample. See also: cv::findContours cv::inpaint (view/add comments) Inpaints the selected region in the image. void inpaint( const Mat& src, const Mat& inpaintMask, Mat& dst, double inpaintRadius, int flags ); src The input 8-bit 1-channel or 3-channel image. inpaintMask The inpainting mask, 8-bit 1-channel image. Non-zero pixels indicate the area that needs to be inpainted. dst The output image; will have the same size and the same type as src inpaintRadius The radius of a circlular neighborhood of each point inpainted that is considered by the algorithm. flags The inpainting method, one of the following: 12.4. MISCELLANEOUS IMAGE TRANSFORMATIONS 687 INPAINT NS Navier-Stokes based method. INPAINT TELEA The method by Alexandru Telea [21] The function reconstructs the selected image area from the pixel near the area boundary. The function may be used to remove dust and scratches from a scanned photo, or to remove undesir- able objects from still images or video. See http://en.wikipedia.org/wiki/Inpainting for more details. cv::integral (view/add comments) Calculates the integral of an image. void integral( const Mat& image, Mat& sum, int sdepth=-1 ); void integral( const Mat& image, Mat& sum, Mat& sqsum, int sdepth=-1 ); void integral( const Mat& image, Mat& sum, Mat& sqsum, Mat& tilted, int sdepth=-1 ); image The source image, W × H, 8-bit or floating-point (32f or 64f) sum The integral image, (W + 1) × (H + 1), 32-bit integer or floating-point (32f or 64f) sqsum The integral image for squared pixel values, (W + 1) × (H + 1), double precision floating- point (64f) tilted The integral for the image rotated by 45 degrees, (W + 1) × (H + 1), the same data type as sum sdepth The desired depth of the integral and the tilted integral images, CV 32S, CV 32F or CV 64F The functions integral calculate one or more integral images for the source image as fol- lowing: sum(X,Y) = X x thresh 0 otherwise THRESH BINARY INV dst(x, y) =  0 if src(x, y) > thresh maxVal otherwise THRESH TRUNC dst(x, y) =  threshold if src(x, y) > thresh src(x, y) otherwise THRESH TOZERO dst(x, y) =  src(x, y) if src(x, y) > thresh 0 otherwise THRESH TOZERO INV dst(x, y) =  0 if src(x, y) > thresh src(x, y) otherwise Also, the special value THRESH OTSU may be combined with one of the above values. In this case the function determines the optimal threshold value using Otsu’s algorithm and uses it instead of the specified thresh. The function returns the computed threshold value. Currently, Otsu’s method is implemented only for 8-bit images. 690 CHAPTER 12. IMGPROC. IMAGE PROCESSING See also: cv::adaptiveThreshold, cv::findContours, cv::compare, cv::min, cv::max cv::watershed (view/add comments) Does marker-based image segmentation using watershed algrorithm void watershed( const Mat& image, Mat& markers ); image The input 8-bit 3-channel image. markers The input/output 32-bit single-channel image (map) of markers. It should have the same size as image The function implements one of the variants of watershed, non-parametric marker-based seg- mentation algorithm, described in [16]. Before passing the image to the function, user has to 12.4. MISCELLANEOUS IMAGE TRANSFORMATIONS 691 outline roughly the desired regions in the image markers with positive (> 0) indices, i.e. every region is represented as one or more connected components with the pixel values 1, 2, 3 etc (such markers can be retrieved from a binary mask using cv::findContoursand cv::drawContours, see watershed.cpp demo). The markers will be ”seeds” of the future image regions. All the other pixels in markers, which relation to the outlined regions is not known and should be defined by the algorithm, should be set to 0’s. On the output of the function, each pixel in markers is set to one of values of the ”seed” components, or to -1 at boundaries between the regions. Note, that it is not necessary that every two neighbor connected components are separated by a watershed boundary (-1’s pixels), for example, in case when such tangent components exist in the initial marker image. Visual demonstration and usage example of the function can be found in OpenCV samples directory; see watershed.cpp demo. See also: cv::findContours cv::grabCut (view/add comments) Runs GrabCut algorithm void grabCut(const Mat& image, Mat& mask, Rect rect, Mat& bgdModel, Mat& fgdModel, int iterCount, int mode ); image The input 8-bit 3-channel image. mask The input/output 8-bit single-channel mask. Its elements may have one of four values. The mask is initialize when mode==GC INIT WITH RECT GC BGD Certainly a background pixel GC FGD Certainly a foreground (object) pixel GC PR BGD Likely a background pixel GC PR BGD Likely a foreground pixel rect The ROI containing the segmented object. The pixels outside of the ROI are marked as ”certainly a background”. The parameter is only used when mode==GC INIT WITH RECT bgdModel, fgdModel Temporary arrays used for segmentation. Do not modify them while you are processing the same image 692 CHAPTER 12. IMGPROC. IMAGE PROCESSING iterCount The number of iterations the algorithm should do before returning the result. Note that the result can be refined with further calls with the mode==GC INIT WITH MASK or mode==GC EVAL mode The operation mode GC INIT WITH RECT The function initializes the state and the mask using the provided rect- angle. After that it runs iterCount iterations of the algorithm GC INIT WITH MASK The function initializes the state using the provided mask. Note that GC INIT WITH RECT and GC INIT WITH MASK can be combined, then all the pixels outside of the ROI are automatically initialized with GC BGD . GC EVAL The value means that algorithm should just resume. The function implements the GrabCut image segmentation algorithm. See the sample grab- cut.cpp on how to use the function. 12.5 Structural Analysis and Shape Descriptors cv::moments (view/add comments) Calculates all of the moments up to the third order of a polygon or rasterized shape. Moments moments( const Mat& array, bool binaryImage=false ); where the class Moments is defined as: class Moments { public: Moments(); Moments(double m00, double m10, double m01, double m20, double m11, double m02, double m30, double m21, double m12, double m03 ); Moments( const CvMoments\& moments ); operator CvMoments() const; // spatial moments double m00, m10, m01, m20, m11, m02, m30, m21, m12, m03; // central moments double mu20, mu11, mu02, mu30, mu21, mu12, mu03; 12.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 693 // central normalized moments double nu20, nu11, nu02, nu30, nu21, nu12, nu03; }; array A raster image (single-channel, 8-bit or floating-point 2D array) or an array (1×N or N ×1) of 2D points (Point or Point2f) binaryImage (For images only) If it is true, then all the non-zero image pixels are treated as 1’s The function computes moments, up to the 3rd order, of a vector shape or a rasterized shape. In case of a raster image, the spatial moments Moments::mji are computed as: mji = X x,y array(x, y)· xj · yi , the central moments Moments::muji are computed as: muji = X x,y array(x, y)·(x − ¯x)j ·(y − ¯y)i where (¯x, ¯y) is the mass center: ¯x = m10 m00 , ¯y = m01 m00 and the normalized central moments Moments::nuij are computed as: nuji = muji m(i+j)/2+1 00 . Note that mu00 = m00, nu00 = 1 nu10 = mu10 = mu01 = mu10 = 0, hence the values are not stored. The moments of a contour are defined in the same way, but computed using Green’s for- mula (see http://en.wikipedia.org/wiki/Green_theorem), therefore, because of a lim- ited raster resolution, the moments computed for a contour will be slightly different from the mo- ments computed for the same contour rasterized. See also: cv::contourArea, cv::arcLength cv::HuMoments (view/add comments) Calculates the seven Hu invariants. 694 CHAPTER 12. IMGPROC. IMAGE PROCESSING void HuMoments( const Moments& moments, double h[7] ); moments The input moments, computed with cv::moments h The output Hu invariants The function calculates the seven Hu invariants, see http://en.wikipedia.org/wiki/ Image_moment, that are defined as: h[0] = η20 + η02 h[1] = (η20 − η02)2 + 4η2 11 h[2] = (η30 − 3η12)2 + (3η21 − η03)2 h[3] = (η30 + η12)2 + (η21 + η03)2 h[4] = (η30 − 3η12)(η30 + η12)[(η30 + η12)2 − 3(η21 + η03)2] + (3η21 − η03)(η21 + η03)[3(η30 + η12)2 − (η21 + η03)2] h[5] = (η20 − η02)[(η30 + η12)2 − (η21 + η03)2] + 4η11(η30 + η12)(η21 + η03) h[6] = (3η21 − η03)(η21 + η03)[3(η30 + η12)2 − (η21 + η03)2] − (η30 − 3η12)(η21 + η03)[3(η30 + η12)2 − (η21 + η03)2] where ηji stand for Moments::nuji. These values are proved to be invariant to the image scale, rotation, and reflection except the seventh one, whose sign is changed by reflection. Of course, this invariance was proved with the assumption of infinite image resolution. In case of a raster images the computed Hu invariants for the original and transformed images will be a bit different. See also: cv::matchShapes cv::findContours (view/add comments) Finds the contours in a binary image. void findContours( const Mat& image, vector >& contours, vector& hierarchy, int mode, int method, Point offset=Point()); void findContours( const Mat& image, vector >& contours, int mode, int method, Point offset=Point()); 12.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 695 image The source, an 8-bit single-channel image. Non-zero pixels are treated as 1’s, zero pixels remain 0’s - the image is treated as binary. You can use cv::compare, cv::inRange, cv::threshold, cv::adaptiveThreshold, cv::Canny etc. to create a binary image out of a grayscale or color one. The function modifies the image while extracting the contours contours The detected contours. Each contour is stored as a vector of points hiararchy The optional output vector that will contain information about the image topology. It will have as many elements as the number of contours. For each contour contours[i], the elements hierarchy[i][0], hiearchy[i][1], hiearchy[i][2], hiearchy[i][3] will be set to 0-based indices in contours of the next and previous contours at the same hierarchical level, the first child contour and the parent contour, respectively. If for some contour i there is no next, previous, parent or nested contours, the corresponding elements of hierarchy[i] will be negative mode The contour retrieval mode CV RETR EXTERNAL retrieves only the extreme outer contours; It will set hierarchy[i][2]=hierarchy[i][3]=-1 for all the contours CV RETR LIST retrieves all of the contours without establishing any hierarchical relation- ships CV RETR CCOMP retrieves all of the contours and organizes them into a two-level hierarchy: on the top level are the external boundaries of the components, on the second level are the boundaries of the holes. If inside a hole of a connected component there is another contour, it will still be put on the top level CV RETR TREE retrieves all of the contours and reconstructs the full hierarchy of nested contours. This full hierarchy is built and shown in OpenCV contours.c demo method The contour approximation method. CV CHAIN APPROX NONE stores absolutely all the contour points. That is, every 2 points of a contour stored with this method are 8-connected neighbors of each other CV CHAIN APPROX SIMPLE compresses horizontal, vertical, and diagonal segments and leaves only their end points. E.g. an up-right rectangular contour will be encoded with 4 points CV CHAIN APPROX TC89 L1,CV CHAIN APPROX TC89 KCOS applies one of the flavors of the Teh-Chin chain approximation algorithm; see [20] offset The optional offset, by which every contour point is shifted. This is useful if the contours are extracted from the image ROI and then they should be analyzed in the whole image context 696 CHAPTER 12. IMGPROC. IMAGE PROCESSING The function retrieves contours from the binary image using the algorithm [19]. The contours are a useful tool for shape analysis and object detection and recognition. See squares.c in the OpenCV sample directory. Note: the source image is modified by this function. cv::drawContours (view/add comments) Draws contours’ outlines or filled contours. void drawContours( Mat& image, const vector >& contours, int contourIdx, const Scalar& color, int thickness=1, int lineType=8, const vector& hierarchy=vector(), int maxLevel=INT MAX, Point offset=Point() ); image The destination image contours All the input contours. Each contour is stored as a point vector contourIdx Indicates the contour to draw. If it is negative, all the contours are drawn color The contours’ color thickness Thickness of lines the contours are drawn with. If it is negative (e.g. thickness=CV FILLED), the contour interiors are drawn. lineType The line connectivity; see cv::line description hierarchy The optional information about hierarchy. It is only needed if you want to draw only some of the contours (see maxLevel) maxLevel Maximal level for drawn contours. If 0, only the specified contour is drawn. If 1, the function draws the contour(s) and all the nested contours. If 2, the function draws the contours, all the nested contours and all the nested into nested contours etc. This parameter is only taken into account when there is hierarchy available. offset The optional contour shift parameter. Shift all the drawn contours by the specified offset = (dx, dy) The function draws contour outlines in the image if thickness ≥ 0 or fills the area bounded by the contours if thickness < 0. Here is the example on how to retrieve connected components from the binary image and label them 12.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 697 #include "cv.h" #include "highgui.h" using namespace cv; int main( int argc, char** argv ) { Mat src; // the first command line parameter must be file name of binary // (black-n-white) image if( argc != 2 || !(src=imread(argv[1], 0)).data) return -1; Mat dst = Mat::zeros(src.rows, src.cols, CV_8UC3); src = src > 1; namedWindow( "Source", 1 ); imshow( "Source", src ); vector > contours; vector hierarchy; findContours( src, contours, hierarchy, CV_RETR_CCOMP, CV_CHAIN_APPROX_SIMPLE ); // iterate through all the top-level contours, // draw each connected component with its own random color int idx = 0; for( ; idx >= 0; idx = hierarchy[idx][0] ) { Scalar color( rand()&255, rand()&255, rand()&255 ); drawContours( dst, contours, idx, color, CV_FILLED, 8, hierarchy ); } namedWindow( "Components", 1 ); imshow( "Components", dst ); waitKey(0); } cv::approxPolyDP (view/add comments) Approximates polygonal curve(s) with the specified precision. 698 CHAPTER 12. IMGPROC. IMAGE PROCESSING void approxPolyDP( const Mat& curve, vector& approxCurve, double epsilon, bool closed ); void approxPolyDP( const Mat& curve, vector& approxCurve, double epsilon, bool closed ); curve The polygon or curve to approximate. Must be 1 × N or N × 1 matrix of type CV 32SC2 or CV 32FC2. You can also convert vector or vector&) constructor. approxCurve The result of the approximation; The type should match the type of the input curve epsilon Specifies the approximation accuracy. This is the maximum distance between the orig- inal curve and its approximation closed If true, the approximated curve is closed (i.e. its first and last vertices are connected), otherwise it’s not The functions approxPolyDP approximate a curve or a polygon with another curve/polygon with less vertices, so that the distance between them is less or equal to the specified precision. It used Douglas-Peucker algorithm http://en.wikipedia.org/wiki/Ramer-Douglas-Peucker_ algorithm cv::arcLength (view/add comments) Calculates a contour perimeter or a curve length. double arcLength( const Mat& curve, bool closed ); curve The input vector of 2D points, represented by CV 32SC2 or CV 32FC2 matrix, or by vector or vector converted to a matrix with Mat(const vector&) constructor closed Indicates, whether the curve is closed or not The function computes the curve length or the closed contour perimeter. 12.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 699 cv::boundingRect (view/add comments) Calculates the up-right bounding rectangle of a point set. Rect boundingRect( const Mat& points ); points The input 2D point set, represented by CV 32SC2 or CV 32FC2 matrix, or by vector or vector converted to the matrix using Mat(const vector&) construc- tor. The function calculates and returns the minimal up-right bounding rectangle for the specified point set. cv::estimateRigidTransform (view/add comments) Computes optimal affine transformation between two 2D point sets Mat estimateRigidTransform( const Mat& srcpt, const Mat& dstpt, bool fullAffine ); srcpt The first input 2D point set dst The second input 2D point set of the same size and the same type as A fullAffine If true, the function finds the optimal affine transformation with no any additional resrictions (i.e. there are 6 degrees of freedom); otherwise, the class of transformations to choose from is limited to combinations of translation, rotation and uniform scaling (i.e. there are 5 degrees of freedom) The function finds the optimal affine transform [A|b](a 2 × 3 floating-point matrix) that approxi- mates best the transformation from srcpti to dstpti: [A∗|b∗] = arg min [A|b] X i kdstpti − Asrcpti T − bk2 700 CHAPTER 12. IMGPROC. IMAGE PROCESSING where [A|b] can be either arbitrary (when fullAffine=true) or have form  a11 a12 b1 −a12 a11 b2  when fullAffine=false. See also: cv::getAffineTransform, cv::getPerspectiveTransform, cv::findHomography cv::estimateAffine3D (view/add comments) Computes optimal affine transformation between two 3D point sets int estimateAffine3D(const Mat& srcpt, const Mat& dstpt, Mat& out, vector& outliers, double ransacThreshold = 3.0, double confidence = 0.99); srcpt The first input 3D point set dstpt The second input 3D point set out The output 3D affine transformation matrix 3 × 4 outliers The output vector indicating which points are outliers ransacThreshold The maximum reprojection error in RANSAC algorithm to consider a point an inlier confidence The confidence level, between 0 and 1, with which the matrix is estimated The function estimates the optimal 3D affine transformation between two 3D point sets using RANSAC algorithm. cv::contourArea (view/add comments) Calculates the contour area 12.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 701 double contourArea( const Mat& contour ); contour The contour vertices, represented by CV 32SC2 or CV 32FC2 matrix, or by vector or vector converted to the matrix using Mat(const vector&) construc- tor. The function computes the contour area. Similarly to cv::moments the area is computed using the Green formula, thus the returned area and the number of non-zero pixels, if you draw the contour using cv::drawContours or cv::fillPoly, can be different. Here is a short example: vector contour; contour.push_back(Point2f(0, 0)); contour.push_back(Point2f(10, 0)); contour.push_back(Point2f(10, 10)); contour.push_back(Point2f(5, 4)); double area0 = contourArea(contour); vector approx; approxPolyDP(contour, approx, 5, true); double area1 = contourArea(approx); cout << "area0 =" << area0 << endl << "area1 =" << area1 << endl << "approx poly vertices" << approx.size() << endl; cv::convexHull (view/add comments) Finds the convex hull of a point set. void convexHull( const Mat& points, vector& hull, bool clockwise=false ); void convexHull( const Mat& points, vector& hull, bool clockwise=false ); void convexHull( const Mat& points, vector& hull, bool clockwise=false ); 702 CHAPTER 12. IMGPROC. IMAGE PROCESSING points The input 2D point set, represented by CV 32SC2 or CV 32FC2 matrix, or by vector or vector converted to the matrix using Mat(const vector&) construc- tor. hull The output convex hull. It is either a vector of points that form the hull (must have the same type as the input points), or a vector of 0-based point indices of the hull points in the original array (since the set of convex hull points is a subset of the original point set). clockwise If true, the output convex hull will be oriented clockwise, otherwise it will be oriented counter-clockwise. Here, the usual screen coordinate system is assumed - the origin is at the top-left corner, x axis is oriented to the right, and y axis is oriented downwards. The functions find the convex hull of a 2D point set using Sklansky’s algorithm [18] that has O(NlogN) or O(N) complexity (where N is the number of input points), depending on how the initial sorting is implemented (currently it is O(NlogN). See the OpenCV sample convexhull.c that demonstrates the use of the different function variants. cv::fitEllipse (view/add comments) Fits an ellipse around a set of 2D points. RotatedRect fitEllipse( const Mat& points ); points The input 2D point set, represented by CV 32SC2 or CV 32FC2 matrix, or by vector or vector converted to the matrix using Mat(const vector&) construc- tor. The function calculates the ellipse that fits best (in least-squares sense) a set of 2D points. It returns the rotated rectangle in which the ellipse is inscribed. cv::fitLine (view/add comments) Fits a line to a 2D or 3D point set. 12.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 703 void fitLine( const Mat& points, Vec4f& line, int distType, double param, double reps, double aeps ); void fitLine( const Mat& points, Vec6f& line, int distType, double param, double reps, double aeps ); points The input 2D point set, represented by CV 32SC2 or CV 32FC2 matrix, or by vector, vector, vector or vector converted to the matrix by Mat(const vector&) constructor line The output line parameters. In the case of a 2d fitting, it is a vector of 4 floats (vx, vy, x0, y0) where (vx, vy) is a normalized vector collinear to the line and (x0, y0) is some point on the line. in the case of a 3D fitting it is vector of 6 floats (vx, vy, vz, x0, y0, z0) where (vx, vy, vz) is a normalized vector collinear to the line and (x0, y0, z0) is some point on the line distType The distance used by the M-estimator (see the discussion) param Numerical parameter (C) for some types of distances, if 0 then some optimal value is chosen reps, aeps Sufficient accuracy for the radius (distance between the coordinate origin and the line) and angle, respectively; 0.01 would be a good default value for both. The functions fitLine fit a line to a 2D or 3D point set by minimizing P i ρ(ri) where ri is the distance between the ith point and the line and ρ(r) is a distance function, one of: distType=CV DIST L2 ρ(r) = r2/2 (the simplest and the fastest least-squares method) distType=CV DIST L1 ρ(r) = r distType=CV DIST L12 ρ(r) = 2 ·( r 1 + r2 2 − 1) distType=CV DIST FAIR ρ (r) = C2 ·  r C − log 1 + r C  where C = 1.3998 704 CHAPTER 12. IMGPROC. IMAGE PROCESSING distType=CV DIST WELSCH ρ (r) = C2 2 ·  1 − exp  −  r C 2 where C = 2.9846 distType=CV DIST HUBER ρ(r) =  r2/2 if r < C C·(r − C/2) otherwise where C = 1.345 The algorithm is based on the M-estimator (http://en.wikipedia.org/wiki/M-estimator) technique, that iteratively fits the line using weighted least-squares algorithm and after each itera- tion the weights wi are adjusted to beinversely proportional to ρ(ri). cv::isContourConvex (view/add comments) Tests contour convexity. bool isContourConvex( const Mat& contour ); contour The tested contour, a matrix of type CV 32SC2 or CV 32FC2, or vector or vector converted to the matrix using Mat(const vector&) constructor. The function tests whether the input contour is convex or not. The contour must be simple, i.e. without self-intersections, otherwise the function output is undefined. cv::minAreaRect (view/add comments) Finds the minimum area rotated rectangle enclosing a 2D point set. RotatedRect minAreaRect( const Mat& points ); points The input 2D point set, represented by CV 32SC2 or CV 32FC2 matrix, or by vector or vector converted to the matrix using Mat(const vector&) construc- tor. The function calculates and returns the minimum area bounding rectangle (possibly rotated) for the specified point set. See the OpenCV sample minarea.c 12.5. STRUCTURAL ANALYSIS AND SHAPE DESCRIPTORS 705 cv::minEnclosingCircle (view/add comments) Finds the minimum area circle enclosing a 2D point set. void minEnclosingCircle( const Mat& points, Point2f& center, float& radius ); points The input 2D point set, represented by CV 32SC2 or CV 32FC2 matrix, or by vector or vector converted to the matrix using Mat(const vector&) construc- tor. center The output center of the circle radius The output radius of the circle The function finds the minimal enclosing circle of a 2D point set using iterative algorithm. See the OpenCV sample minarea.c cv::matchShapes (view/add comments) Compares two shapes. double matchShapes( const Mat& object1, const Mat& object2, int method, double parameter=0 ); object1 The first contour or grayscale image object2 The second contour or grayscale image method Comparison method: CV CONTOUR MATCH I1, CV CONTOURS MATCH I2 or CV CONTOURS MATCH I3 (see the discussion below) parameter Method-specific parameter (is not used now) 706 CHAPTER 12. IMGPROC. IMAGE PROCESSING The function compares two shapes. The 3 implemented methods all use Hu invariants (see cv::HuMoments) as following (A denotes object1,B denotes object2): method=CV CONTOUR MATCH I1 I1(A, B) = X i=1...7 1 mA i − 1 mB i method=CV CONTOUR MATCH I2 I2(A, B) = X i=1...7 mA i − mB i method=CV CONTOUR MATCH I3 I3(A, B) = X i=1...7 mA i − mB i mA i where mA i = sign(hA i )· log hA i mB i = sign(hB i )· log hB i and hA i , hB i are the Hu moments of A and B respectively. cv::pointPolygonTest (view/add comments) Performs point-in-contour test. double pointPolygonTest( const Mat& contour, Point2f pt, bool measureDist ); contour The input contour pt The point tested against the contour measureDist If true, the function estimates the signed distance from the point to the nearest contour edge; otherwise, the function only checks if the point is inside or not. 12.6. PLANAR SUBDIVISIONS 707 The function determines whether the point is inside a contour, outside, or lies on an edge (or coincides with a vertex). It returns positive (inside), negative (outside) or zero (on an edge) value, correspondingly. When measureDist=false, the return value is +1, -1 and 0, respectively. Otherwise, the return value it is a signed distance between the point and the nearest contour edge. Here is the sample output of the function, where each image pixel is tested against the contour. 12.6 Planar Subdivisions 12.7 Motion Analysis and Object Tracking cv::accumulate (view/add comments) Adds image to the accumulator. void accumulate( const Mat& src, Mat& dst, const Mat& mask=Mat() ); src The input image, 1- or 3-channel, 8-bit or 32-bit floating point 708 CHAPTER 12. IMGPROC. IMAGE PROCESSING dst The accumulator image with the same number of channels as input image, 32-bit or 64-bit floating-point mask Optional operation mask The function adds src, or some of its elements, to dst: dst(x, y) ← dst(x, y) + src(x, y) if mask(x, y) 6= 0 The function supports multi-channel images; each channel is processed independently. The functions accumulate* can be used, for example, to collect statistic of background of a scene, viewed by a still camera, for the further foreground-background segmentation. See also: cv::accumulateSquare, cv::accumulateProduct, cv::accumulateWeighted cv::accumulateSquare (view/add comments) Adds the square of the source image to the accumulator. void accumulateSquare( const Mat& src, Mat& dst, const Mat& mask=Mat() ); src The input image, 1- or 3-channel, 8-bit or 32-bit floating point dst The accumulator image with the same number of channels as input image, 32-bit or 64-bit floating-point mask Optional operation mask The function adds the input image src or its selected region, raised to power 2, to the accu- mulator dst: dst(x, y) ← dst(x, y) + src(x, y)2 if mask(x, y) 6= 0 The function supports multi-channel images; each channel is processed independently. See also: cv::accumulateSquare, cv::accumulateProduct, cv::accumulateWeighted 12.7. MOTION ANALYSIS AND OBJECT TRACKING 709 cv::accumulateProduct (view/add comments) Adds the per-element product of two input images to the accumulator. void accumulateProduct( const Mat& src1, const Mat& src2, Mat& dst, const Mat& mask=Mat() ); src1 The first input image, 1- or 3-channel, 8-bit or 32-bit floating point src2 The second input image of the same type and the same size as src1 dst Accumulator with the same number of channels as input images, 32-bit or 64-bit floating-point mask Optional operation mask The function adds the product of 2 images or their selected regions to the accumulator dst: dst(x, y) ← dst(x, y) + src1(x, y)· src2(x, y) if mask(x, y) 6= 0 The function supports multi-channel images; each channel is processed independently. See also: cv::accumulate, cv::accumulateSquare, cv::accumulateWeighted cv::accumulateWeighted (view/add comments) Updates the running average. void accumulateWeighted( const Mat& src, Mat& dst, double alpha, const Mat& mask=Mat() ); src The input image, 1- or 3-channel, 8-bit or 32-bit floating point dst The accumulator image with the same number of channels as input image, 32-bit or 64-bit floating-point alpha Weight of the input image mask Optional operation mask 710 CHAPTER 12. IMGPROC. IMAGE PROCESSING The function calculates the weighted sum of the input image src and the accumulator dst so that dst becomes a running average of frame sequence: dst(x, y) ← (1 − alpha)· dst(x, y) + alpha · src(x, y) if mask(x, y) 6= 0 that is, alpha regulates the update speed (how fast the accumulator ”forgets” about earlier images). The function supports multi-channel images; each channel is processed independently. See also: cv::accumulate, cv::accumulateSquare, cv::accumulateProduct 12.8 Feature Detection cv::Canny (view/add comments) Finds edges in an image using Canny algorithm. void Canny( const Mat& image, Mat& edges, double threshold1, double threshold2, int apertureSize=3, bool L2gradient=false ); image Single-channel 8-bit input image edges The output edge map. It will have the same size and the same type as image threshold1 The first threshold for the hysteresis procedure threshold2 The second threshold for the hysteresis procedure apertureSize Aperture size for the cv::Sobel operator L2gradient Indicates, whether the more accurate L2 norm = p(dI/dx)2 + (dI/dy)2 should be used to compute the image gradient magnitude (L2gradient=true), or a faster default L1 norm = |dI/dx| + |dI/dy| is enough (L2gradient=false) The function finds edges in the input image image and marks them in the output map edges using the Canny algorithm. The smallest value between threshold1 and threshold2 is used for edge linking, the largest value is used to find the initial segments of strong edges, see http: //en.wikipedia.org/wiki/Canny_edge_detector 12.8. FEATURE DETECTION 711 cv::cornerEigenValsAndVecs (view/add comments) Calculates eigenvalues and eigenvectors of image blocks for corner detection. void cornerEigenValsAndVecs( const Mat& src, Mat& dst, int blockSize, int apertureSize, int borderType=BORDER DEFAULT ); src Input single-channel 8-bit or floating-point image dst Image to store the results. It will have the same size as src and the type CV 32FC(6) blockSize Neighborhood size (see discussion) apertureSize Aperture parameter for the cv::Sobel operator boderType Pixel extrapolation method; see cv::borderInterpolate For every pixel p, the function cornerEigenValsAndVecs considers a blockSize × blockSize neigborhood S(p). It calculates the covariation matrix of derivatives over the neighborhood as: M = "P S(p)(dI/dx)2 P S(p)(dI/dxdI/dy)2 P S(p)(dI/dxdI/dy)2 P S(p)(dI/dy)2 # Where the derivatives are computed using cv::Sobel operator. After that it finds eigenvectors and eigenvalues of M and stores them into destination image in the form (λ1, λ2, x1, y1, x2, y2) where λ1, λ2 are the eigenvalues of M; not sorted x1, y1 are the eigenvectors corresponding to λ1 x2, y2 are the eigenvectors corresponding to λ2 The output of the function can be used for robust edge or corner detection. See also: cv::cornerMinEigenVal, cv::cornerHarris, cv::preCornerDetect 712 CHAPTER 12. IMGPROC. IMAGE PROCESSING cv::cornerHarris (view/add comments) Harris edge detector. void cornerHarris( const Mat& src, Mat& dst, int blockSize, int apertureSize, double k, int borderType=BORDER DEFAULT ); src Input single-channel 8-bit or floating-point image dst Image to store the Harris detector responses; will have type CV 32FC1 and the same size as src blockSize Neighborhood size (see the discussion of cv::cornerEigenValsAndVecs) apertureSize Aperture parameter for the cv::Sobel operator k Harris detector free parameter. See the formula below boderType Pixel extrapolation method; see cv::borderInterpolate The function runs the Harris edge detector on the image. Similarly to cv::cornerMinEigenVal and cv::cornerEigenValsAndVecs, for each pixel (x, y) it calculates a 2 × 2 gradient covariation matrix M(x,y) over a blockSize × blockSize neighborhood. Then, it computes the following characteristic: dst(x, y) = detM(x,y) − k · trM(x,y)2 Corners in the image can be found as the local maxima of this response map. cv::cornerMinEigenVal (view/add comments) Calculates the minimal eigenvalue of gradient matrices for corner detection. void cornerMinEigenVal( const Mat& src, Mat& dst, int blockSize, int apertureSize=3, int borderType=BORDER DEFAULT ); 12.8. FEATURE DETECTION 713 src Input single-channel 8-bit or floating-point image dst Image to store the minimal eigenvalues; will have type CV 32FC1 and the same size as src blockSize Neighborhood size (see the discussion of cv::cornerEigenValsAndVecs) apertureSize Aperture parameter for the cv::Sobel operator boderType Pixel extrapolation method; see cv::borderInterpolate The function is similar to cv::cornerEigenValsAndVecs but it calculates and stores only the minimal eigenvalue of the covariation matrix of derivatives, i.e. min(λ1, λ2) in terms of the formulae in cv::cornerEigenValsAndVecs description. cv::cornerSubPix (view/add comments) Refines the corner locations. void cornerSubPix( const Mat& image, vector& corners, Size winSize, Size zeroZone, TermCriteria criteria ); image Input image corners Initial coordinates of the input corners; refined coordinates on output winSize Half of the side length of the search window. For example, if winSize=Size(5,5), then a 5 ∗ 2 + 1 × 5 ∗ 2 + 1 = 11 × 11 search window would be used zeroZone Half of the size of the dead region in the middle of the search zone over which the summation in the formula below is not done. It is used sometimes to avoid possible sin- gularities of the autocorrelation matrix. The value of (-1,-1) indicates that there is no such size criteria Criteria for termination of the iterative process of corner refinement. That is, the pro- cess of corner position refinement stops either after a certain number of iterations or when a required accuracy is achieved. The criteria may specify either of or both the maximum number of iteration and the required accuracy 714 CHAPTER 12. IMGPROC. IMAGE PROCESSING The function iterates to find the sub-pixel accurate location of corners, or radial saddle points, as shown in on the picture below. Sub-pixel accurate corner locator is based on the observation that every vector from the center q to a point p located within a neighborhood of q is orthogonal to the image gradient at p subject to image and measurement noise. Consider the expression: i = DIpi T·(q − pi) where DIpi is the image gradient at the one of the points pi in a neighborhood of q. The value of q is to be found such that i is minimized. A system of equations may be set up with i set to zero: X i (DIpi ·DIpi T) − X i (DIpi ·DIpi T· pi) where the gradients are summed within a neighborhood (”search window”) of q. Calling the first gradient term G and the second gradient term b gives: q = G−1 · b The algorithm sets the center of the neighborhood window at this new center q and then iterates until the center keeps within a set threshold. cv::goodFeaturesToTrack (view/add comments) Determines strong corners on an image. 12.8. FEATURE DETECTION 715 void goodFeaturesToTrack( const Mat& image, vector& corners, int maxCorners, double qualityLevel, double minDistance, const Mat& mask=Mat(), int blockSize=3, bool useHarrisDetector=false, double k=0.04 ); image The input 8-bit or floating-point 32-bit, single-channel image corners The output vector of detected corners maxCorners The maximum number of corners to return. If there are more corners than that will be found, the strongest of them will be returned qualityLevel Characterizes the minimal accepted quality of image corners; the value of the parameter is multiplied by the by the best corner quality measure (which is the min eigen- value, see cv::cornerMinEigenVal, or the Harris function response, see cv::cornerHarris). The corners, which quality measure is less than the product, will be rejected. For example, if the best corner has the quality measure = 1500, and the qualityLevel=0.01, then all the corners which quality measure is less than 15 will be rejected. minDistance The minimum possible Euclidean distance between the returned corners mask The optional region of interest. If the image is not empty (then it needs to have the type CV 8UC1 and the same size as image), it will specify the region in which the corners are detected blockSize Size of the averaging block for computing derivative covariation matrix over each pixel neighborhood, see cv::cornerEigenValsAndVecs useHarrisDetector Indicates, whether to use Harris operator or cv::cornerMinEigenVal k Free parameter of Harris detector The function finds the most prominent corners in the image or in the specified image region, as described in [23]: 1. the function first calculates the corner quality measure at every source image pixel using the cv::cornerMinEigenVal or cv::cornerHarris 2. then it performs non-maxima suppression (the local maxima in 3 × 3 neighborhood are re- tained). 716 CHAPTER 12. IMGPROC. IMAGE PROCESSING 3. the next step rejects the corners with the minimal eigenvalue less than qualityLevel · maxx,y qualityMeasureMap(x, y). 4. the remaining corners are then sorted by the quality measure in the descending order. 5. finally, the function throws away each corner ptj if there is a stronger corner pti (i < j) such that the distance between them is less than minDistance The function can be used to initialize a point-based tracker of an object. Note that the if the function is called with different values A and B of the parameter qualityLevel, and A¿ B, the vector of returned corners with qualityLevel=A will be the prefix of the output vector with qualityLevel=B. See also: cv::cornerMinEigenVal, cv::cornerHarris, cv::calcOpticalFlowPyrLK, cv::estimateRigidMotion, cv::PlanarObjectDetector, cv::OneWayDescriptor cv::HoughCircles (view/add comments) Finds circles in a grayscale image using a Hough transform. void HoughCircles( Mat& image, vector& circles, int method, double dp, double minDist, double param1=100, double param2=100, int minRadius=0, int maxRadius=0 ); image The 8-bit, single-channel, grayscale input image circles The output vector of found circles. Each vector is encoded as 3-element floating-point vector (x, y, radius) method Currently, the only implemented method is CV HOUGH GRADIENT, which is basically 21HT, described in [25]. dp The inverse ratio of the accumulator resolution to the image resolution. For example, if dp=1, the accumulator will have the same resolution as the input image, if dp=2 - accumulator will have half as big width and height, etc minDist Minimum distance between the centers of the detected circles. If the parameter is too small, multiple neighbor circles may be falsely detected in addition to a true one. If it is too large, some circles may be missed 12.8. FEATURE DETECTION 717 param1 The first method-specific parameter. in the case of CV HOUGH GRADIENT it is the higher threshold of the two passed to cv::Canny edge detector (the lower one will be twice smaller) param2 The second method-specific parameter. in the case of CV HOUGH GRADIENT it is the accumulator threshold at the center detection stage. The smaller it is, the more false circles may be detected. Circles, corresponding to the larger accumulator values, will be returned first minRadius Minimum circle radius maxRadius Maximum circle radius The function finds circles in a grayscale image using some modification of Hough transform. Here is a short usage example: #include #include #include using namespace cv; int main(int argc, char** argv) { Mat img, gray; if( argc != 2 && !(img=imread(argv[1], 1)).data) return -1; cvtColor(img, gray, CV_BGR2GRAY); // smooth it, otherwise a lot of false circles may be detected GaussianBlur( gray, gray, Size(9, 9), 2, 2 ); vector circles; HoughCircles(gray, circles, CV_HOUGH_GRADIENT, 2, gray->rows/4, 200, 100 ); for( size_t i = 0; i < circles.size(); i++ ) { Point center(cvRound(circles[i][0]), cvRound(circles[i][1])); int radius = cvRound(circles[i][2]); // draw the circle center circle( img, center, 3, Scalar(0,255,0), -1, 8, 0 ); // draw the circle outline circle( img, center, radius, Scalar(0,0,255), 3, 8, 0 ); } namedWindow( "circles", 1 ); imshow( "circles", img ); return 0; } 718 CHAPTER 12. IMGPROC. IMAGE PROCESSING Note that usually the function detects the circles’ centers well, however it may fail to find the cor- rect radii. You can assist the function by specifying the radius range (minRadius and maxRadius) if you know it, or you may ignore the returned radius, use only the center and find the correct radius using some additional procedure. See also: cv::fitEllipse, cv::minEnclosingCircle cv::HoughLines (view/add comments) Finds lines in a binary image using standard Hough transform. void HoughLines( Mat& image, vector& lines, double rho, double theta, int threshold, double srn=0, double stn=0 ); image The 8-bit, single-channel, binary source image. The image may be modified by the func- tion lines The output vector of lines. Each line is represented by a two-element vector (ρ, θ). ρ is the distance from the coordinate origin (0, 0) (top-left corner of the image) and θ is the line rotation angle in radians (0 ∼ vertical line, π/2 ∼ horizontal line) rho Distance resolution of the accumulator in pixels theta Angle resolution of the accumulator in radians threshold The accumulator threshold parameter. Only those lines are returned that get enough votes (> threshold) srn For the multi-scale Hough transform it is the divisor for the distance resolution rho. The coarse accumulator distance resolution will be rho and the accurate accumulator resolution will be rho/srn. If both srn=0 and stn=0 then the classical Hough transform is used, otherwise both these parameters should be positive. stn For the multi-scale Hough transform it is the divisor for the distance resolution theta The function implements standard or standard multi-scale Hough transform algorithm for line detection. See cv::HoughLinesP for the code example. 12.8. FEATURE DETECTION 719 cv::HoughLinesP (view/add comments) Finds lines segments in a binary image using probabilistic Hough transform. void HoughLinesP( Mat& image, vector& lines, double rho, double theta, int threshold, double minLineLength=0, double maxLineGap=0 ); image The 8-bit, single-channel, binary source image. The image may be modified by the func- tion lines The output vector of lines. Each line is represented by a 4-element vector (x1, y1, x2, y2), where (x1, y1) and (x2, y2) are the ending points of each line segment detected. rho Distance resolution of the accumulator in pixels theta Angle resolution of the accumulator in radians threshold The accumulator threshold parameter. Only those lines are returned that get enough votes (> threshold) minLineLength The minimum line length. Line segments shorter than that will be rejected maxLineGap The maximum allowed gap between points on the same line to link them. The function implements probabilistic Hough transform algorithm for line detection, described in [15]. Below is line detection example: /* This is a standalone program. Pass an image name as a first parameter of the program. Switch between standard and probabilistic Hough transform by changing "#if 1" to "#if 0" and back */ #include #include #include using namespace cv; int main(int argc, char** argv) { Mat src, dst, color_dst; if( argc != 2 || !(src=imread(argv[1], 0)).data) 720 CHAPTER 12. IMGPROC. IMAGE PROCESSING return -1; Canny( src, dst, 50, 200, 3 ); cvtColor( dst, color_dst, CV_GRAY2BGR ); #if 0 vector lines; HoughLines( dst, lines, 1, CV_PI/180, 100 ); for( size_t i = 0; i < lines.size(); i++ ) { float rho = lines[i][0]; float theta = lines[i][1]; double a = cos(theta), b = sin(theta); double x0 = a*rho, y0 = b*rho; Point pt1(cvRound(x0 + 1000*(-b)), cvRound(y0 + 1000*(a))); Point pt2(cvRound(x0 - 1000*(-b)), cvRound(y0 - 1000*(a))); line( color_dst, pt1, pt2, Scalar(0,0,255), 3, 8 ); } #else vector lines; HoughLinesP( dst, lines, 1, CV_PI/180, 80, 30, 10 ); for( size_t i = 0; i < lines.size(); i++ ) { line( color_dst, Point(lines[i][0], lines[i][1]), Point(lines[i][2], lines[i][3]), Scalar(0,0,255), 3, 8 ); } #endif namedWindow( "Source", 1 ); imshow( "Source", src ); namedWindow( "Detected Lines", 1 ); imshow( "Detected Lines", color_dst ); waitKey(0); return 0; } This is the sample picture the function parameters have been tuned for: 12.8. FEATURE DETECTION 721 And this is the output of the above program in the case of probabilistic Hough transform cv::preCornerDetect (view/add comments) Calculates the feature map for corner detection void preCornerDetect( const Mat& src, Mat& dst, int apertureSize, int borderType=BORDER DEFAULT ); src The source single-channel 8-bit of floating-point image dst The output image; will have type CV 32F and the same size as src apertureSize Aperture size of cv::Sobel 722 CHAPTER 12. IMGPROC. IMAGE PROCESSING borderType The pixel extrapolation method; see cv::borderInterpolate The function calculates the complex spatial derivative-based function of the source image dst = (Dxsrc)2 ·Dyysrc + (Dysrc)2 ·Dxxsrc − 2Dxsrc ·Dysrc ·Dxysrc where Dx,Dy are the first image derivatives, Dxx,Dyy are the second image derivatives and Dxy is the mixed derivative. The corners can be found as local maximums of the functions, as shown below: Mat corners, dilated_corners; preCornerDetect(image, corners, 3); // dilation with 3x3 rectangular structuring element dilate(corners, dilated_corners, Mat(), 1); Mat corner_mask = corners == dilated_corners; 12.9 Object Detection cv::matchTemplate (view/add comments) Compares a template against overlapped image regions. void matchTemplate( const Mat& image, const Mat& templ, Mat& result, int method ); image Image where the search is running; should be 8-bit or 32-bit floating-point templ Searched template; must be not greater than the source image and have the same data type result A map of comparison results; will be single-channel 32-bit floating-point. If image is W × H and templ is w × h then result will be (W − w + 1) × (H − h + 1) method Specifies the comparison method (see below) The function slides through image, compares the overlapped patches of size w × h against templ using the specified method and stores the comparison results to result. Here are the formulas for the available comparison methods (I denotes image,T template,R result). The summation is done over template and/or the image patch: x0 = 0...w − 1, y0 = 0...h − 1 12.9. OBJECT DETECTION 723 method=CV TM SQDIFF R(x, y) = X x0,y0 (T(x0, y0) − I(x + x0, y + y0))2 method=CV TM SQDIFF NORMED R(x, y) = P x0,y0 (T(x0, y0) − I(x + x0, y + y0))2 qP x0,y0 T(x0, y0)2 ·P x0,y0 I(x + x0, y + y0)2 method=CV TM CCORR R(x, y) = X x0,y0 (T(x0, y0)·I(x + x0, y + y0)) method=CV TM CCORR NORMED R(x, y) = P x0,y0 (T(x0, y0)·I0(x + x0, y + y0)) qP x0,y0 T(x0, y0)2 ·P x0,y0 I(x + x0, y + y0)2 method=CV TM CCOEFF R(x, y) = X x0,y0 (T 0(x0, y0)·I(x + x0, y + y0)) where T 0(x0, y0) = T(x0, y0) − 1/(w · h)·P x00,y00 T(x00, y00) I0(x + x0, y + y0) = I(x + x0, y + y0) − 1/(w · h)·P x00,y00 I(x + x00, y + y00) method=CV TM CCOEFF NORMED R(x, y) = P x0,y0 (T 0(x0, y0)·I0(x + x0, y + y0)) qP x0,y0 T 0(x0, y0)2 ·P x0,y0 I0(x + x0, y + y0)2 After the function finishes the comparison, the best matches can be found as global minimums (when CV TM SQDIFF was used) or maximums (when CV TM CCORR or CV TM CCOEFF was used) using the cv::minMaxLoc function. In the case of a color image, template summation in the numerator and each sum in the denominator is done over all of the channels (and separate mean values are used for each channel). That is, the function can take a color template and a color image; the result will still be a single-channel image, which is easier to analyze. 724 CHAPTER 12. IMGPROC. IMAGE PROCESSING Chapter 13 features2d. Feature Detection and Descriptor Extraction 13.1 Feature detection and description cv::FAST (view/add comments) Detects corners using FAST algorithm by E. Rosten (”Machine learning for high-speed corner detection”, 2006). void FAST( const Mat& image, vector& keypoints, int threshold, bool nonmaxSupression=true ); image The image. Keypoints (corners) will be detected on this. keypoints Keypoints detected on the image. threshold Threshold on difference between intensity of center pixel and pixels on circle around this pixel. See description of the algorithm. nonmaxSupression If it is true then non-maximum supression will be applied to detected cor- ners (keypoints). cv::MSER (view/add comments) Maximally-Stable Extremal Region Extractor 725 726 CHAPTER 13. FEATURES2D. FEATURE DETECTION AND DESCRIPTOR EXTRACTION class MSER : public CvMSERParams { public: // default constructor MSER(); // constructor that initializes all the algorithm parameters MSER( int _delta, int _min_area, int _max_area, float _max_variation, float _min_diversity, int _max_evolution, double _area_threshold, double _min_margin, int _edge_blur_size ); // runs the extractor on the specified image; returns the MSERs, // each encoded as a contour (vector, see findContours) // the optional mask marks the area where MSERs are searched for void operator()( const Mat& image, vector >& msers, const Mat& mask ) const; }; The class encapsulates all the parameters of MSER (see http://en.wikipedia.org/ wiki/Maximally_stable_extremal_regions) extraction algorithm. cv::StarDetector (view/add comments) Implements Star keypoint detector class StarDetector : CvStarDetectorParams { public: // default constructor StarDetector(); // the full constructor initialized all the algorithm parameters: // maxSize - maximum size of the features. The following // values of the parameter are supported: // 4, 6, 8, 11, 12, 16, 22, 23, 32, 45, 46, 64, 90, 128 // responseThreshold - threshold for the approximated laplacian, // used to eliminate weak features. The larger it is, // the less features will be retrieved // lineThresholdProjected - another threshold for the laplacian to // eliminate edges // lineThresholdBinarized - another threshold for the feature // size to eliminate edges. // The larger the 2 threshold, the more points you get. StarDetector(int maxSize, int responseThreshold, int lineThresholdProjected, int lineThresholdBinarized, int suppressNonmaxSize); 13.1. FEATURE DETECTION AND DESCRIPTION 727 // finds keypoints in an image void operator()(const Mat& image, vector& keypoints) const; }; The class implements a modified version of CenSurE keypoint detector described in [1] cv::SIFT (view/add comments) Class for extracting keypoints and computing descriptors using approach named Scale Invariant Feature Transform (SIFT). class CV_EXPORTS SIFT { public: struct CommonParams { static const int DEFAULT_NOCTAVES = 4; static const int DEFAULT_NOCTAVE_LAYERS = 3; static const int DEFAULT_FIRST_OCTAVE = -1; enum{ FIRST_ANGLE = 0, AVERAGE_ANGLE = 1 }; CommonParams(); CommonParams( int _nOctaves, int _nOctaveLayers, int _firstOctave, int _angleMode ); int nOctaves, nOctaveLayers, firstOctave; int angleMode; }; struct DetectorParams { static double GET_DEFAULT_THRESHOLD() { return 0.04 / SIFT::CommonParams::DEFAULT_NOCTAVE_LAYERS / 2.0; } static double GET_DEFAULT_EDGE_THRESHOLD() { return 10.0; } DetectorParams(); DetectorParams( double _threshold, double _edgeThreshold ); double threshold, edgeThreshold; }; struct DescriptorParams { static double GET_DEFAULT_MAGNIFICATION() { return 3.0; } static const bool DEFAULT_IS_NORMALIZE = true; static const int DESCRIPTOR_SIZE = 128; 728 CHAPTER 13. FEATURES2D. FEATURE DETECTION AND DESCRIPTOR EXTRACTION DescriptorParams(); DescriptorParams( double _magnification, bool _isNormalize, bool _recalculateAngles ); double magnification; bool isNormalize; bool recalculateAngles; }; SIFT(); //! sift-detector constructor SIFT( double _threshold, double _edgeThreshold, int _nOctaves=CommonParams::DEFAULT_NOCTAVES, int _nOctaveLayers=CommonParams::DEFAULT_NOCTAVE_LAYERS, int _firstOctave=CommonParams::DEFAULT_FIRST_OCTAVE, int _angleMode=CommonParams::FIRST_ANGLE ); //! sift-descriptor constructor SIFT( double _magnification, bool _isNormalize=true, bool _recalculateAngles = true, int _nOctaves=CommonParams::DEFAULT_NOCTAVES, int _nOctaveLayers=CommonParams::DEFAULT_NOCTAVE_LAYERS, int _firstOctave=CommonParams::DEFAULT_FIRST_OCTAVE, int _angleMode=CommonParams::FIRST_ANGLE ); SIFT( const CommonParams& _commParams, const DetectorParams& _detectorParams = DetectorParams(), const DescriptorParams& _descriptorParams = DescriptorParams() ); //! returns the descriptor size in floats (128) int descriptorSize() const { return DescriptorParams::DESCRIPTOR_SIZE; } //! finds the keypoints using SIFT algorithm void operator()(const Mat& img, const Mat& mask, vector& keypoints) const; //! finds the keypoints and computes descriptors for them using SIFT algorithm. //! Optionally it can compute descriptors for the user-provided keypoints void operator()(const Mat& img, const Mat& mask, vector& keypoints, Mat& descriptors, bool useProvidedKeypoints=false) const; CommonParams getCommonParams () const { return commParams; } DetectorParams getDetectorParams () const { return detectorParams; } DescriptorParams getDescriptorParams () const { return descriptorParams; } protected: ... }; 13.1. FEATURE DETECTION AND DESCRIPTION 729 cv::SURF (view/add comments) Class for extracting Speeded Up Robust Features from an image. class SURF : public CvSURFParams { public: // default constructor SURF(); // constructor that initializes all the algorithm parameters SURF(double _hessianThreshold, int _nOctaves=4, int _nOctaveLayers=2, bool _extended=false); // returns the number of elements in each descriptor (64 or 128) int descriptorSize() const; // detects keypoints using fast multi-scale Hessian detector void operator()(const Mat& img, const Mat& mask, vector& keypoints) const; // detects keypoints and computes the SURF descriptors for them; // output vector "descriptors" stores elements of descriptors and has size // equal descriptorSize()*keypoints.size() as each descriptor is // descriptorSize() elements of this vector. void operator()(const Mat& img, const Mat& mask, vector& keypoints, vector& descriptors, bool useProvidedKeypoints=false) const; }; The class SURF implements Speeded Up Robust Features descriptor [3]. There is fast multi- scale Hessian keypoint detector that can be used to find the keypoints (which is the default option), but the descriptors can be also computed for the user-specified keypoints. The function can be used for object tracking and localization, image stitching etc. See the find obj.cpp demo in OpenCV samples directory. cv::RandomizedTree (view/add comments) The class contains base structure for RTreeClassifier class CV_EXPORTS RandomizedTree { public: friend class RTreeClassifier; RandomizedTree(); ˜RandomizedTree(); 730 CHAPTER 13. FEATURES2D. FEATURE DETECTION AND DESCRIPTOR EXTRACTION void train(std::vector const& base_set, cv::RNG &rng, int depth, int views, size_t reduced_num_dim, int num_quant_bits); void train(std::vector const& base_set, cv::RNG &rng, PatchGenerator &make_patch, int depth, int views, size_t reduced_num_dim, int num_quant_bits); // following two funcs are EXPERIMENTAL //(do not use unless you know exactly what you do) static void quantizeVector(float *vec, int dim, int N, float bnds[2], int clamp_mode=0); static void quantizeVector(float *src, int dim, int N, float bnds[2], uchar *dst); // patch_data must be a 32x32 array (no row padding) float* getPosterior(uchar* patch_data); const float* getPosterior(uchar* patch_data) const; uchar* getPosterior2(uchar* patch_data); void read(const char* file_name, int num_quant_bits); void read(std::istream &is, int num_quant_bits); void write(const char* file_name) const; void write(std::ostream &os) const; int classes() { return classes_; } int depth() { return depth_; } void discardFloatPosteriors() { freePosteriors(1); } inline void applyQuantization(int num_quant_bits) { makePosteriors2(num_quant_bits); } private: int classes_; int depth_; int num_leaves_; std::vector nodes_; float **posteriors_; // 16-bytes aligned posteriors uchar **posteriors2_; // 16-bytes aligned posteriors std::vector leaf_counts_; void createNodes(int num_nodes, cv::RNG &rng); void allocPosteriorsAligned(int num_leaves, int num_classes); void freePosteriors(int which); // which: 1=posteriors_, 2=posteriors2_, 3=both 13.1. FEATURE DETECTION AND DESCRIPTION 731 void init(int classes, int depth, cv::RNG &rng); void addExample(int class_id, uchar* patch_data); void finalize(size_t reduced_num_dim, int num_quant_bits); int getIndex(uchar* patch_data) const; inline float* getPosteriorByIndex(int index); inline uchar* getPosteriorByIndex2(int index); inline const float* getPosteriorByIndex(int index) const; void convertPosteriorsToChar(); void makePosteriors2(int num_quant_bits); void compressLeaves(size_t reduced_num_dim); void estimateQuantPercForPosteriors(float perc[2]); }; cv::RandomizedTree::train (view/add comments) Trains a randomized tree using input set of keypoints void train(std::vector const& base set, cv::RNG &rng, PatchGenerator &make patch, int depth, int views, size t reduced num dim, int num quant bits); void train(std::vector const& base set, cv::RNG &rng, PatchGenerator &make patch, int depth, int views, size t reduced num dim, int num quant bits); base set Vector of BaseKeypoint type. Contains keypoints from the image are used for train- ing rng Random numbers generator is used for training make patch Patch generator is used for training depth Maximum tree depth reduced num dim Number of dimensions are used in compressed signature num quant bits Number of bits are used for quantization 732 CHAPTER 13. FEATURES2D. FEATURE DETECTION AND DESCRIPTOR EXTRACTION cv::RandomizedTree::read (view/add comments) Reads pre-saved randomized tree from file or stream read(const char* file name, int num quant bits) read(std::istream &is, int num quant bits) file name Filename of file contains randomized tree data is Input stream associated with file contains randomized tree data num quant bits Number of bits are used for quantization cv::RandomizedTree::write (view/add comments) Writes current randomized tree to a file or stream void write(const char* file name) const; void write(std::ostream &os) const; file name Filename of file where randomized tree data will be stored is Output stream associated with file where randomized tree data will be stored 13.1. FEATURE DETECTION AND DESCRIPTION 733 cv::RandomizedTree::applyQuantization (view/add comments) Applies quantization to the current randomized tree void applyQ