数字图像处理MathematicalMorphology课件

MathematicalMorphologyAGeometricApproachtoImageProcessingandAnalysis2ImageAnalysisandProcessingGeometrySpaceAbstractSpaceLinearNonLinearLinearConvolutionFourier,Wavelet

Tomograph

SplinesStatisticalMultivariateanalysisNeuralSets

StereologyMorphological

MorphologicalFiltering

GranulometryRandomsetsWatershedsSyntactical

Semanticapproach

GrammarsIndexation结构元素数学形态学研究几何结构的基本思想是利用“结构元素”（structuringelement）探测图像，看能否将这个结构元素很好地填放在图像的内部，同时验证填放结构元素的方法是否有效。结构元素的设计在处理实际问题中是非常重要的，它决定了抽取信息的结果，构造不同的结构元素，就可以完成不同的分析任务。AB图像形态学初步腐蚀膨胀膨胀与腐蚀的代数意义膨胀与腐蚀的滤波特点小结作业基础——平移概念将一个集合A平移距离x

，表示为A+x

axa+xA+xA二值图像的平移1、腐蚀（erode）定义集合A被集合B“腐蚀”，表示为其中A为输入图像，B为结构元素腐蚀的结果由将B平移x，但仍然包含在A内的所有x点组成。如果将B看作模板，则由在平移过程中，所有可以填入A内部的模板的原点组成。腐蚀还有几种常用表示：E(A,B)，ERODE(A,B)数值举例原点不在结构元素内2、膨胀（dilate）A被B膨胀表示为：

Ac表示A

的补集。膨胀还可以用D(A,B)，DILATE(A,B)表示ABAB利用圆盘对矩形膨胀，尖角被磨圆膨胀ABAB离散情况下的明克夫斯基和（膨胀）小结1、膨胀可以实现图像缝隙的连接；2、腐蚀可以去除小颗粒噪声或毛刺；3、多种组合，实现开、闭、击中、击不中；4、典型的非线性滤波，滤波效果可交互控制；5、模板设计与算法设计膨胀、腐蚀的组合滤波效果

BasicMorphologyOperatorsDilation,Erosion,Opening,Closing

BasicMorphologyAlgorithmsBoundaryextractionRegionfillingHit-or-MisstransformationThinningThickeningPruningApplicationsFilteringSegmentationCoding&CompressionObjectdetectionComputervisionQuestionWhatisMathematicalMorphology?PhysicalSignalanalysistechniquesbasedonsettheoryaimingatthestudyofrelationsbetweenphysicalandstructuralpropertiesSignalProcessingNonlinearsignalprocessingtechniquesbasedonminimumandmaximumoperationsEngineeringAlgorithmandsoftware/hardwaretoolsfordevelopingsignalprocessingapplicationsShapeProcessingandAnalysisVisualperceptionrequirestransformationofimagessoastomakeexplicitparticularshapeinformation.Goal:Distinguishmeaningfulshapeinformationfromirrelevantone.Thevastmajorityofshapeprocessingandanalysistechniquesarebasedondesigningashapeoperatorwhichsatisfiesdesirableproperties.ExampleImageanalysisconsistsofobtainingmeasurementscharacteristictoimagesunderconsideration.Geometricmeasurements(e.g.,objectlocation,orientation,area,lengthofperimeter)GrayscaleImagesBinaryImagesMorphologicalOperatorsErosionsanddilationsarethemostelementaryoperatorsofmathematicalmorphology.Morecomplicatedmorphologicaloperatorscanbedesignedbymeansofcombiningerosionsanddilations.QuestionWhatisMathematicalMorphology?A(precise)MathematicalAnswerAlgebraCompleteLatticesOperatorsErosions-DilationsMathematicalMorphologyTopologyHit-or-MissGeometryConvexity-ConnectivityDistanceApplicationsImageProcessingandAnalysisAmathematicaltoolthatstudiesoperatorsoncompletelatticesMathematicalLatticetheoryforobjectsoroperatorsincontinuousordiscretespacesTopologyandstochasticmodelsTranslationInvariantOperatorsMorphologicalErosion“LINEARITY”TRANSLATIONINVARIANCEMorphologicalErosionMorphologicalErosionPabloPicasso,PasswiththeCape,1960StructuringElementMorphologicalDilation“LINEARITY”TRANSLATIONINVARIANCEMorphologicalDilationMorphologicalDilationPabloPicasso,PasswiththeCape,1960StructuringElementMorphologicalDilationMorphologicalOpeningMorphologicalOpeningPabloPicasso,PasswiththeCape,1960StructuringElementMorphologicalOpeningIsasmoothingfilter!Amountandtypeofsmoothingisdeterminedbytheshapeandsizeofthestructuringelement.Approximatesashapefrombelow,sinceMorphologicalOpening&ClosingDilation,Erosion,Opening,Closing

MorphologicalOpening&ClosingOpeningSmoothesthecontourBreaksnarrowisthmusesEliminatesthinprotrusionsXBisasubsetofXClosing

SmoothesthecontourFusesnarrowbreaksEliminatessmallhollFillgapsinthecontourXBisasubsetofXFilteringExampleBoundaryExtractionQuestionHenriMatisse,WomanwithAmphoraandPomegranates,1952Canweautomaticallyextractthelargestconnectedcomponent(thewoman’sbody)inthisimage?AnswerORIGINALEROSIONMARKERMARKERMARKERMARKERThisisa

morphologicaloperator

thatfiltersoutconnectedimagecomponentsofacertainsizeandshapeCONNECTEDOPERATORS!!ConnectedComponentReconstructionGeodesicReconstructionRegionFilling8-connectedboundaryBeginningwithapointPinsideXandletDoUntilImportantResultsIncreasingOperator+TranslationInvariantOperatorMainIdeaExaminethegeometricalstructureofanimagebymatchingitwithsmallpatternsatvariouslocations.Byvaryingthesizeandshapeofthematchingpatterns,calledstructuringelements,onecanextractusefulinformationabouttheshapeofthedifferentpartsoftheimageandtheirinterrelations.Resultsinimageoperatorswhicharewellsuitedfortheanalysisofthegeometricalandtopologicalstructureofanimage.

QuestionWhataboutgray-scaleimages?GreyscaleErosion“LINEARITY”MINIMUMTRANSLATIONINVARIANCEGrayscaleDilation“LINEARITY”MAXIMUMTRANSLATIONINVARIANCEGrayscaleDilation&Erosion

GrayscaleOpening&Closing

GreyscaleOpeningStructuringElementGrayscaleMorphologyORIGINALEROSIONDILATIONOPENINGRemarkFlatErosionFlatDilationAnApp