Deep Learning of Graph Matching图匹配的深度学习

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1、DeepLearningofGraphMatchingAndreiZanfir2andCristianSminchisescu1,2andrei.zanfir@imar.ro,cristian.sminchisescu@math.lth.se1DepartmentofMathematics,FacultyofEngineering,LundUniversity2InstituteofMathematicsoftheRomanianAcademyAbstractmationthatcanbeusedtomodelcomplexrelationshipsandmorediv

2、ersetransformations.Graphmatchingoper-Theproblemofgraphmatchingundernodeandpair-ateswithaffinitymatricesthatencodesimilaritiesbetweenwiseconstraintsisfundamentalinareasasdiverseascom-unaryandpairwisesetsofnodes(points)inthetwographs.binatorialoptimization,machinelearningorcomputervi-Typi

3、callyitisformulatedmathematicallyasaquadraticin-sion,whererepresentingboththerelationsbetweennodestegerprogram[25,3],subjecttoone-to-onemappingcon-andtheirneighborhoodstructureisessential.Wepresentanstraints,i.e.eachpointinthefirstsetmusthaveanuniqueend-to-endmodelthatmakesitpossibletole

4、arnallparam-correspondenceinthesecondset.ThisisknowntobeNP-etersofthegraphmatchingprocess,includingtheunaryhardsomethodsoftensolveitapproximatelybyrelaxingandpairwisenodeneighborhoods,representedasdeepfea-theconstraintsandfindinglocaloptima[19,38].tureextractionhierarchies.Thechallengeis

5、intheformula-Learningtheparametersofthegraphaffinitymatrixhastionofthedifferentmatrixcomputationlayersofthemodelbeeninvestigatedby[7,20]or,inthecontextofthemoreinawaythatenablestheconsistent,efficientpropagationgeneralhyper-graphmatchingmodel[10],by[21].Inthoseofgradientsinthecompletepipe

6、linefromthelossfunc-cases,thenumberofparametersislow,oftencontrollingge-tion,throughthecombinatorialoptimizationlayersolvingometricaffinitiesbetweenpairsofpointsratherthantheim-thematchingproblem,andthefeatureextractionhierar-agestructureintheneighborhoodofthosepoints.Recentlychy.Ourcomp

7、utervisionexperimentsandablationstudiestherehasbeenagrowinginterestinusingdeepfeaturesforonchallengingdatasetslikePASCALVOCkeypoints,Sin-bothgeometricandsemanticvisualmatchingtasks,eithertelandCUBshowthatmatchingmodelsrefinedend-to-endbytrainingthenetworktodirectlyoptimizeamatch