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1、888IEEETRANSACTIONSONPATTERNANALYSISANDMACHINEINTELLIGENCE,VOL.22,NO.8,AUGUST2000NormalizedCutsandImageSegmentationJianboShiandJitendraMalik,Member,IEEEAbstractÐWeproposeanovelapproachforsolvingtheperceptualgroupingprobleminvision.Ratherthanfocusingonlocalfea
2、turesandtheirconsistenciesintheimagedata,ourapproachaimsatextractingtheglobalimpressionofanimage.Wetreatimagesegmentationasagraphpartitioningproblemandproposeanovelglobalcriterion,thenormalizedcut,forsegmentingthegraph.Thenormalizedcutcriterionmeasuresboththe
3、totaldissimilaritybetweenthedifferentgroupsaswellasthetotalsimilaritywithinthegroups.Weshowthatanefficientcomputationaltechniquebasedonageneralizedeigenvalueproblemcanbeusedtooptimizethiscriterion.Wehaveappliedthisapproachtosegmentingstaticimages,aswellasmoti
4、onsequences,andfoundtheresultstobeveryencouraging.IndexTermsÐGrouping,imagesegmentation,graphpartitioning.æ1INTRODUCTIONNEARLY75yearsago,Wertheimer[24]pointedoutthetobedonefromthebigpicturedownward,ratherlikeaimportanceofperceptualgroupingandorganizationpaint
5、erfirstmarkingoutthemajorareasandthenfillingininvisionandlistedseveralkeyfactors,suchassimilarity,thedetails.proximity,andgoodcontinuation,whichleadtovisualPriorliteratureontherelatedproblemsofclustering,grouping.However,eventothisday,manyofthegroupingandimag
6、esegmentationishuge.Theclusteringcomputationalissuesofperceptualgroupinghavere-community[12]hasofferedusagglomerativeanddivisivemainedunresolved.Inthispaper,wepresentageneralalgorithms;inimagesegmentation,wehaveregion-basedframeworkforthisproblem,focusingspec
7、ificallyonthemergeandsplitalgorithms.Thehierarchicaldivisivecaseofimagesegmentation.approachthatweadvocateproducesatree,thedendrogram.SincetherearemanypossiblepartitionsofthedomainIWhilemostoftheseideasgobacktothe1970s(andearlier),ofanimageintosubsets,howdowe
8、picktheªrightºone?the1980sbroughtintheuseofMarkovRandomFields[10]Therearetwoaspectstobeconsideredhere.Thefirstisthatandvariationalformulations[17],[2],[14].TheMRFandtheremaynotbeasingleco
