树莓大礼包数字图像处理课件chapter09brief

ChapterMorphologicaloperationsContent::DilationandOpeningand:TheHit-or-Miss:Somebasicmorphological:Morphologicaloperationsongray作业：9.7（答案后发）,选作ImageProcessing——Image——ComputerLow-levelProcessing:bothinputandoutputareNoiseReduction;ImageEnhancement;ImageMid-levelProcessing:inputimages,outputattributesofthoseimagesImageHigh-levelProcessing:relatedtocomputer ysisandThematerialsinthischapterisatransitionfromafocusonpurelyimageprocessingmethods,whoseinputandoutputarebothimages,toprocessesinwhichtheinputareimages,buttheoutputsareattributesextractedfromthoseimages,inthesensedefinedbefore.Toolssuchasmorphologyandrelatedconceptareacornerstoneofthemathematicalfoundationthatisutilizedforextracting“meaning”fromanimage.Otherapproachesaredevelopedandappliedintheremainingchaptersofthebook.:Set

AB

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AB{p|pAandpAc{p|pA}AB{p|pA,pB}A(ASpecialsetoperationsfor

z{p|paz,aˆ{w|wb,bLogicOperationsInvolvingBinaryDilationandTerminologiesandex nations:structureelementshavetoberectangulararrays.9.2DilationandTerminologiesand nations:structurehavetoberectangular9.2DilationandDilationofAbyB:直观定义：给定图像A，任选一个结构元素（structuringBˆ(B)的中心点贴着A的Boundary滑动，从而把A（或扩展WithAandBassetsinZ2,thedilationofAbyB,isdefinedAB{z|(ˆ)zAABz|(ˆ)Az Someexamplesof左边A，左边A，右边B。内的1是B的中心元黑色是A，红色是用膨胀出去的部ˆBridgingErosionForsetsAandBinZ2,theerosionofAbyB,definedA⊖B={z|(B)z⊆A Question:ifA=B? FigureBinaryimagewithsquaresofsize1,3,5,7,9andTheresultoferodingimage(a)withastructuringelementsizeTheresultofdilatingthe3spotinimage(b)byaelementofsize

白色表示0（黑）色表示OpeningandOpeningtheopeningAbyBistheerosionofAbyB,followedbyadilationoftheresultbyB.A∘B=(A⊖OpeninggenerallysmoothesthecontourofanbreaknarrowisthmusesandeliminatesthinSinceA∘B=∪{(B)z|(B)z⊆A},→A∘B⊆A.Opening的主要功能就是把外轮廓磨得较圆滑，但也会把connectedobjectsClosingTheclosingofsetAbystructuringelementBissimplythedilationofAbyB,followedbytheerosionoftheresultbyBA·B=(A⊕B)⊖Closinggenerallyfusesnarrowbreaksandlongthingulfs,eliminatessmallhole,andfillgapsinthecontour.ClosingApplicationExampleofOpeningandClosingOpeningandclosingarefrequentlyusedtoremovenoisesandtoconnectcomponentsfragmentedbynoises.Inthefollowingexample,noisesarefirstremovedbyopening,followedbyaclosingtore-connectfragmentedlines.TheHit-or-MissTheHit-or-misstransformisusedtoallocate(match)agivenreferencepatterninatestimage.ForinstancetofindthebodyXinaninputimage.However,thisapproachrequiresthattheXintheinputimageexactlymatchesthereferenceimageXwithoutanydistortion,henceitsdirectpracticalapplicationsareverylimited.However,itdoesleadstosomeotherinterestingmethodsthatmightbeusefulinpracticalapplications(suchasconvexhull).STEP2:FindSTEP3:ErodeAbyXtoget

STEP1:DesignawindowW⊃XtoobtainW-XBeforethenextstep,pleasenoticethat,whencenterof(W-isatpositionSTEP4:ErodeAcbyW-XgetAc⊖(W-※wehaveP∈Ac⊖(W-※Similarly,theshapeofZcanbecomple ycoveredbytheshapeofX,hencethereexistsasubsetof Zsso

(WX)pˆAifˆZsZˆ[Ac(WX)]STEP5:togetA9.6Morphologicaloperationsongray9.6.1DilationA⊕BofgrayLetAbethegrayimagedilatedbythestructuringelementB,betheresultantgrayimageandb(x,y)∈B,g(s,t)∈G,g(s,t)=(fb)(s,t)max{f(sx,ty)b(x,y)(sx),(ty)DA;(x,y)Onemayfollowthreestepstoobtaintheintensityofg(s,t)atpixelcoordinate(s,Foreachgiven(s,t),translateAaroundB(i.e.,changeandy)suchthat(sx),(ty) (x,y)ateachposition(x,y),obtainA(s−x,t−y)+b(x,y)withgiven(s,Forthegiven(s,t),compareallintensityvalueA(s−x,t−+b(x,y)undertheconditionthat(sx),(ty)

and(x,y)DB,choosethe umvalueofA(s−x,t−y)+b(x,y)asthevalueofg(s,t).PleasenoticeResultantintensityis alofA(s−x,t−y)+b(x,yhencedilationgenerallyincreasetheintensityofagrayimage.（图像变亮）Inthelimitingcasewhenthegrayimageisbinary,theabovedefinitionreducesexactlytothatdefinedforbinaryimages.However,inthecaseofgrayimages,allpixelsarechanged(intermsofintensity)whilebinaryoperationschangesonlythosepixelsontheboundary.Thefollowingexampleisa1-D9.6.2ErosionA⊖BofgrayLetAbethegrayimageerodedbyB,Gbetheresultantimageandb(x,y)∈B,g(s,t)∈G,Onemayfollowthreestepstoobtaintheintensityofg(s,t)ataForeachgiven(s,t),translateAaroundB(i.e.,changeand suchthat(sx),(ty)DA

(x,y)ateachposition(x,y),obtainA(s+x,t+y)-b(x,y)withgiven(s,Forthegiven(s,t),compareallintensityvalueA(s+x,t++b(x,y)underthecondition

(sx),(ty)and(x,y)DB,andchoosetheminimumvalueofA(s+x,t+y)-b(x,y)asthevalueofg(s,t).PleasenoticeResultantintensityisminimalofA(s+x,t+y)−b(x,y),henceerosiongenerallydecreasetheintensityofagrayimage.Inthelimitingcasewhenthegrayimageisbinary,theabovedefinitionreducesexactlytothatdefinedforbinaryimages.However,inthecaseofgrayimages,allpixelsarechanged(intermsofintensity)whilebinaryoperationschangesonlythosepixelsontheboundary.9.6.3OpeningandOpening:erosionfollowedbyRemovesmalllightdetails,whileleavingoverallgraylevelsandlargerrightClosing:dilationfollowedbyRemovedarkdetailsfromanimageApplicationofgray-scaleopeningand9.6.4SomeApplicationsofGray-ScaleMorphologicalsmoothing=opening+Toremoveallisolatedbrightspots(open)andallisolateddarkspotsMorphologicalgradient=(A⊕B)–(A⊖MorphologicalgradientcanbeusedforedgeTop-hattransformToenhancedetailsinshadowwhilesuppressingbrightTexturalTofindtheboundarylargeblobsandsmallSTEP1:Use