數(shù)字圖像處理

（DigitalImageProcessing）圖像分割I(lǐng)magesegmentationdividesanimageintoregionsthatareconnectedandhavesomesimilaritywithintheregionandsomedifferencebetweenadjacentregions.

Thegoalisusuallytofindindividualobjectsinanimage.Forthemostparttherearefundamentallytwokindsofapproachestosegmentation:discontinuityandsimilarity.Similaritymaybeduetopixelintensity,colorortexture.Differencesaresuddenchanges(discontinuities)inanyofthese,butespeciallysuddenchangesinintensityalongaboundaryline,whichiscalledanedge.ConceptsandApproachesWhatisImageSegmentation?ImageSegmentationMethodsThresholdingBoundary-basedRegion-based:regiongrowing,splittingandmergingConceptsandApproachesPartitionanimageintoregions,eachassociatedwithanobjectbutwhatdefinesanobject?Howtodefinethesimilaritybetweenregions?FromProf.XinLiAssumption:therangeofintensitylevelscoveredbyobjectsofinterestisdifferentfromthebackground.ThresholdingMethodThresholdingMethodthresholdinghistogramsinglethresholdmultiplethresholdsFrom[Gonzalez&Woods]GlobalThresholdingThresholdingMethod:BasicGlobalThresholding選取一個(gè)全局閾值T的初始估計(jì)用T分割圖像為兩部分：G1和G2計(jì)算區(qū)域G1和G2中的灰度均值m1和m2計(jì)算新的閾值：T=0.5(m1+m2)重復(fù)步驟2-4，直至T值收斂全局閾值估計(jì)基本算法GlobalThresholdingThresholdingMethod:BasicGlobalThresholdingThismethodtreatspixelvaluesasprobabilitydensityfunctions.Thegoalofthismethodistominimizetheprobabilityofmisclassifyingpixelsaseitherobjectorbackground.Therearetwokindsoferror:mislabelinganobjectpixelasbackground,andmislabelingabackgroundpixelasobject.OptimalGlobalThresholding計(jì)算圖像歸一化直方圖，pi(i=0,1,2,…,L-1)計(jì)算累積直方圖P1，令P2=1-P1計(jì)算累積灰度均值m1和m2計(jì)算全局灰度mG計(jì)算類間方差var(k)取使得var(k)最大的k值，即為Otsu閾值k*Otsu最佳全局閾值估計(jì)算法Otsu’sThresholdingThresholdingTheRoleofIlluminationThresholdingTheRoleofNoiseThresholdingTheRoleofNoise---DenosingThresholdingMethod:BasicGlobalThresholdingGlobalThresholding:WhendoesItNOTWork?AmeaningfulglobalthresholdmaynotexistImage-dependentglobalthresholdingBasicAdaptiveThresholdingBasicAdaptiveThresholdingThresholdingT=4.5ThresholdingT=5.5trueobjectboundaryBasicAdaptiveThresholdingThresholdingT=4.5ThresholdingT=5.5trueobjectboundarySplitSolutionSpatiallyadaptivethresholdingLocalizedprocessingBasicAdaptiveThresholdingThresholdingT=4ThresholdingT=7ThresholdingT=4ThresholdingT=7spatiallyadaptivethresholdselectionBasicAdaptiveThresholdingmergemergemergemergemergelocalsegmentationresultsBasicAdaptiveThresholdingAdaptiveThresholdingMultipleThresholdsColorimagesegmentationandclusteringColorimagesegmentationandclusteringRegion-BasedMethod:RegionGrowingFrom[Gonzalez&Woods]Key:similaritymeasureRegionGrowingStartfromaseed,andletitgrow(includesimilarneighborhood)Region-BasedMethod:SplitandMergeSplitandMergeIterativelysplit(non-similarregion)andmerge(similarregions)Example:quadtreeapproachFrom[Gonzalez&Woods]Region-BasedMethod:SplitandMergeoriginalimage4regions4regions(nothingtomerge)splitmergeExample:QuadtreeSplitandMergeProcedureIteration1SplitStep

spliteverynon-uniformregionto4Merge

Step

mergealluniformadjacentregionsRegion-BasedMethod:SplitandMergefromIteration113regions4regionssplitmergeExample:QuadtreeSplitandMergeProcedureIteration2SplitStep

spliteverynon-uniformregionto4Merge

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mergealluniformadjacentregionsRegion-BasedMethod:SplitandMergefromIteration210regionssplitmergeExample:QuadtreeSplitandMergeProcedureIteration3finalsegmentationresult2regionsSplitStep

spliteverynon-uniformregionto4Merge

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mergealluniformadjacentregionsRegion-BasedMethod:SplitandMergeHardProblem:TexturesSimilaritymeasuremakesthedifferenceFromProf.XinLiedgedetectionboundarydetectionclassificationandlabelingimagesegmentationBoundary-BasedMethodDetectionofDiscontinuitiesTherearethreekindsofdiscontinuitiesofintensity:points,linesandedges.Themostcommonwaytolookfordiscontinuitiesistoscanasmallmaskovertheimage.Themaskdetermineswhichkindofdiscontinuitytolookfor.

PointDetection點(diǎn)檢測(cè)（拉普拉斯）模板LineDetectionOnlyslightlymorecommonthanpointdetectionistofindaonepixelwidelineinanimage.Fordigitalimagestheonlythreepointstraightlinesareonlyhorizontal,vertical,ordiagonal(+or–45

).LineDetectionEdgeDetectionEdgeDetectionEdgeDetectionEdgeDetection:GradientOperatorsFirst-orderderivatives:Thegradientofanimagef(x,y)atlocation(x,y)isdefinedasthevector:Themagnitudeofthisvector:Thedirectionofthisvector:EdgeDetection:GradientOperatorsEdgeDetection:GradientOperatorsEdgeDetection:GradientOperatorsRobertscross-gradientoperatorsPrewittoperatorsSobeloperatorsGradientOperators:ExampleGradientOperators:ExampleGradientOperators:ExampleEdgeDetection:GradientOperatorsSecond-orderderivatives:(TheLaplacian)TheLaplacianofan2Dfunctionf(x,y)isdefinedasTwoformsinpractice:EdgeDetection:Marr-HildrethEdgeDetectorConsiderthefunction:TheLaplacianofhisTheLaplacianofaGaussiansometimesiscalledtheMexicanhatfunction.Italsocanbecomputedby

smoothingtheimagewiththeGaussiansmoothingmask,followedbyapplicationoftheLaplacianmask.TheLaplacianofaGaussian(LoG)AGaussianfunctionEdgeDetection:Marr-HildrethEdgeDetectorEdgeDetection:Marr-HildrethEdgeDetectorZerocrossingofthesecondderivativeofafunctionindicatesthepresenceofamaximaEdgeDetection:Marr-HildrethEdgeDetectorStepsSmooththeimageusingGaussianfilterEnhancetheedgesusingLaplacianoperatorZerocrossingsdenotetheedgelocationUselinearinterpolationtodeterminethesub-pixellocationoftheedgeMarr-HildrethEdgeDetector:ExampleZeroCrossingsDetectionEdgeImageZeroCrossingsMarr-HildrethEdgeDetector:ExampleSobelgradientLaplacianmaskGaussiansmoothfunctionMarr-HildrethEdgeDetector:ExampleEdgeDetection:CannyEdgeDetectorOptimaledgedetectordependingonLowerrorrate–edgesshouldnotbemissedandtheremustnotbespuriousresponsesLocalization–distancebetweenpointsmarkedbythedetectorandtheactualcenteroftheedgeshouldbeminimumResponse–OnlyoneresponsetoasingleedgeOnedimensionalformulationAssumethat2DimageshaveconstantcrosssectioninsomedirectionEdgeDetection:CannyEdgeDetectorDependingontheaboveprinciples,severaloptimaledgedetectorsarecalculatedBestapproximationtotheabovedetectorsistheFirstDerivativeofGaussianItischosenbecauseoftheeaseofcomputationin2dimensionsImplementationofCannyEdgeDetectorStep1Noiseisfilteredout–usuallyaGaussianfilterisusedWidthischosencarefullyStep2EdgestrengthisfoundoutbytakingthegradientoftheimageARobertsmaskoraSobelmaskcanbeusedImplementationofCannyEdgeDetectorStep3FindtheedgedirectionStep4ResolveedgedirectionImplementationofCannyEdgeDetectorStep5Non-maximasuppression–tracealongtheedgedirectionandsuppressanypixelvaluenotconsideredtobeanedge.GivesathinlineforedgeStep6Usedouble/hysterisisthresholdingtoeliminatestreakingCannyEdgeDetectorWewishtomarkpointsalongthecurvewherethemagnitudeisbiggest.Wecandothisbylookingforamaximumalongaslicenormaltothecurve(non-maximumsuppression).Thesepointsshouldformacurve.Therearethentwoalgorithmicissues:atwhichpointisthemaximum,andwhereisthenextone?Non-MaximumSuppressionNon-MaximumSuppressionSuppressthepixelsin‘GradientMagnitudeImage’whicharenotlocalmaximumNon-MaximumSuppressionNon-MaximumSuppressionHysteresisThresholdingHysteresisThresholdingIfthegradientatapixelisabove‘High’,declareitan‘edgepixel’Ifthegradientatapixelisbelow‘Low’,declareita‘non-edge-pixel’Ifthegradientatapixelisbetween‘Low’and‘High’thendeclareitan‘edgepixel’ifandonlyifitisconnectedtoan‘edgepixel’directlyorviapixelsbetween‘Low’and‘High’HysteresisThresholdingCannyEdgeDetector:ExampleCannySobelEdgeDetection:CannyAlgorithmEdgeLinkingandBoundaryDetection:LocalProcessingTwopropertiesofedgepointsareusefulforedgelinking:thestrength(ormagnitude)ofthedetectededgepointstheirdirections(determinedfromgradientdirections)Thisisusuallydoneinlocalneighborhoods.Adjacentedgepointswithsimilar

magnitudeanddirectionarelinked.Forexample,anedgepixelwithcoordinates(x0,y0)inapredefinedneighborhoodof(x,y)issimilartothepixelat(x,y)ifEdgeLinkingandBoundaryDetection:LocalProcessingInthisexample,wecanfindthelicenseplatecandidateafteredgelinkingprocess.HoughTransformMethodtoisolatetheshapesfromanimagePerformedafteredgedetectionNotaffectedbynoiseorgapsintheedgesTechniqueThresholdingisusedtoisolatepixelswithstrongedgegradientParametricequationofstraightlineisusedtomaptheedgepointstotheHoughparameterspacePointsofintersectionintheHoughparameterspacegivestheequationoflineonactualimageEdgeLinkingandB