数字图像处理,冈萨雷斯,课件英文版Chapter09形态学图像处理

DigitalImageProcessingChapter9:MorphologicalImageProcessing5September2007WhatareMorphologicalOperations?Morphologicaloperationscomefromtheword“morphing”inBiologywhichmeans“changingashape”.MorphingImagemorphologicaloperationsareusedtomanipulateobjectshapessuchasthinning,thickening,andfilling.Binarymorphologicaloperationsarederivedfromsetoperations.(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.BasicSetOperationsConceptofasetinbinaryimagemorphology:Eachsetmayrepresentoneobject.Eachpixel(x,y)hasitsstatus:belongtoasetornotbelongtoaset.TranslationandReflectionOperationsA(A)zz=(z1,z2)TranslationReflectionBˆBBbbwwBfor,ˆAazaccAzfor,(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.LogicalOperations**Forbinaryimagesonly(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.DilationOperationsABzBAzˆ=EmptysetA=ObjecttobedilatedB=StructuringelementDilatemeans“extend”DilationOperations(cont.)StructuringElement(B)Originalimage(A)BˆReflectionIntersectpixelCenterpixelDilationOperations(cont.)ResultofDilationBoundaryofthe“centerpixels”whereintersectsAzBˆ(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.Example:ApplicationofDilation“Repair”brokencharacters(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.ErosionOperationABzBAzA=ObjecttobeerodedB=StructuringelementErosionmeans“trim”ErosionOperations(cont.)StructuringElement(B)Originalimage(A)IntersectpixelCenterpixelErosionOperations(cont.)ResultofErosionBoundaryofthe“centerpixels”whereBisinsideA(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.Example:ApplicationofDilationandErosionRemovesmallobjectssuchasnoiseDualityBetweenDilationandErosionBABAccˆ)(Proof:wherec=complementBAABzABzABzBAcczcczczcˆ)((ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.OpeningOperationBBABA)(ABBBAzzor=CombinationofallpartsofAthatcancompletelycontainBOpeningeliminatesnarrowandsmalldetailsandcorners.(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.ExampleofOpening(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.ClosingOperationBBBA)A(Closingfillsnarrowgapsandnotches(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.ExampleofClosingDualityBetweenOpeningandClosingBABAccˆPropertiesOpeningBABBABDBCDCABA.3thenIf2..1BABBABDBCDCBAA.3thenIf2..1PropertiesClosingIdempotentproperty:can’tchangeanymoreExample:ApplicationofMorphologicalOperations(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.Fingerprintenhancement(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.Hit-or-MissTransformation)(XWAXAXAc*whereX=shapetobedetectedW=windowthatcancontainXHit-or-MissTransformation(cont.))(XWABABAc*(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.BoundaryExtractionBAAβ(A)OriginalimageBoundary(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.RegionFillingckkABXX1OriginalimageResultsofregionfillingwhereX0=seedpixelp(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.ExtractionofConnectedComponentsABXXkk1whereX0=seedpixelpExample:ExtractionofConnectedComponentsX-rayimageofbonesThresholdedimageConnectedcomponents(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.ConvexHulliiDAC41)(4,3,2,1,1iABXXikik*iconviXDConvexhullhasnoconcavepart.ConvexhullAlgorithm:whereExample:ConvexHull(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.ThinningcBAABAABA)()(**))...))((...((21nBBBABAExample:Thinning(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.Makeanobjectthinner.(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.Thickening*)(BAABA.))...))((...((21nBBBABA....Makeanobjectthicker*(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.SkeletonsDotlinesareskeletonsofthisstructureSkeletons(cont.))()(0ASASkKkwithwhere...)))(...((BBBAkB)ABkB)AkB)AASk(()(ktimesandkBAkKmaxSkeletons(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.(ImagesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.PruningBAX1AHXX)(23)(1812kkBXX*314XXX=thinning=findingendpoints=dilationatendpoints=PrunedresultExample:PruningOriginalimagePrunedresultAfterThinning3timesEndpointsDilationofendpoints(TablesfromRafaelC.GonzalezandRichardE.Wood,DigitalImageProcessing,2ndEdition.