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1、IEEETRANSACTIONSONPATTERNANALYSISANDMACHINEINTELLIGENCE,VOL.33,NO.8,AUGUST20111633RobustPointSetRegistrationUsingGaussianMixtureModelsBingJian,Member,IEEEComputerSociety,andBabaC.Vemuri,Fellow,IEEEAbstract—Inthispaper,wepresentaunifiedframeworkfortherigidand
2、nonrigidpointsetregistrationprobleminthepresenceofsignificantamountsofnoiseandoutliers.ThekeyideaofthisregistrationframeworkistorepresenttheinputpointsetsusingGaussianmixturemodels.Then,theproblemofpointsetregistrationisreformulatedastheproblemofaligningtwoG
3、aussianmixturessuchthatastatisticaldiscrepancymeasurebetweenthetwocorrespondingmixturesisminimized.Weshowthatthepopulariterativeclosestpoint(ICP)method[1]andseveralexistingpointsetregistrationmethods[2],[3],[4],[5],[6],[7]inthefieldarecloselyrelatedandcanber
4、einterpretedmeaningfullyinourgeneralframework.OurinstantiationofthisgeneralframeworkisbasedonthetheL2distancebetweentwoGaussianmixtures,whichhastheclosed-formexpressionandinturnleadstoacomputationallyefficientregistrationalgorithm.Theresultingregistrationalg
5、orithmexhibitsinherentstatisticalrobustness,hasanintuitiveinterpretation,andissimpletoimplement.Wealsoprovidetheoreticalandexperimentalcomparisonswithotherrobustmethodsforpointsetregistration.IndexTerms—Pointsetregistration,nonrigidregistration,Gaussianmixtu
6、res,robustmatching.Ç1INTRODUCTIONOINTsetrepresentationsfrequentlyariseinavarietyofcomputationalgeometryandpatternrecognitioncommu-Papplicationsofcomputervision,medicalimageanalysis,nities.Thereisalargebodyofresearchworkonpointpatternrecognition,andcomputergr
7、aphics.Manyproblemspatternmatchingfromtheviewpointofstructuralpatterninthesefieldscanbesolvedbyalgorithmsoperatingontherecognitionaswell.Forexample,traditionalprobabilisticpointsetsextractedfromtheinputdata.Inthispaper,werelaxationmethodsemployrandomizedalgo
8、rithmsalongfocusontheimportantproblemofpointsetregistration,withtheneighborhoodinformationtofindthecorrespon-whichisoftenencounteredinstereocorrespondence,shapedencebetweenpatternsinthemodelandt
