category categorycommonsuper DPM speciccategory Bicycle 46546947 452 Motorbike 311308316 314 Cow 134123137 103 Sheep 2727269 255 Table3Impactofclumpingtogethersimilarcategoriesforcomp ID: 336222
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ments.Informationcanalsobetransferredfromonecate-gorytoanother[1,16].AytarandZisserman[1]useamodeltrainedononecategorytoregularizetraininginadiffer-entcategory,while[16]transfersactualtransformedtrain-ingexamplesfromonecategorytoanother.Endresetal.[9]shares“bodyplans”betweenobjectcategories,whereabodyplanspeciesanarrangementofparts.Outsideofobjectdetection,thenotionofdeformationshassurfacedtimeandagaininthevisioncommunity.Manyoftheideasinthispaperechoactiveappearancemodels[4],wherefacelandmarksareallowedtodeform,andtheap-pearanceafterdeformationismodeledseparately.WinnandJojic[25]proposeagenerativemodelforrecognitionthatusesadeformationeldtomodelintraclassvariation.How-evertheirapproachrequiresrichMRFpriorsandislimitedtosimpleunclutteredscenes,whilewetacklethefull-blownobjectdetectionproblem.Sinceitishardtomatchpixelsacrossdisparateimages,[17]proposetousediscriminativeSIFTfeaturestodothemapping,anideathisworkbuildsupon.Alotofworkinimageclassicationand/ormatching,forinstance[8,3],warpsandalignsimagesforthepurposeofcomputingsim-ilarities.Liuetal.[18]useHOGfeaturestoalignandclus-terimagesandDrayerandBrox[7]trytomatchobjectin-stancesusingHOGfeatureswiththeaimofaligningthem.However,suchalignmentisdifcultintheclutteredandoc-cludedscenesthatarecommoninobjectdetectionsettings.3.ModelOverviewLetusbeginbyconsideringatypicalobjectdetectorbasedonHOG-templates[5].Givenaweightvectorw,wecancomputethescoreofanimagewindowbycomputingitsHOGfeaturesxanddoingadotproductwithw.However,thetemplateandfeaturevectorhaveaspatialstructure:theyaredividedintoagridofcells.Wecanmakethisexplicitbywritingthefeaturesincell(i;j)asxijandthecorrespond-ingweightsaswij.Usingthisnotation,thematchingscoreisgivenby:fw(x)=Xi;jwTijxij(1)Inourapproach,wewanttoconstructadetectorinwhichtheHOGtemplatescandeform.Weaccomplishthisbyal-lowingeachHOGcellinthetemplatetomoveasaunit.Adeformationcanthenbewrittenasaowelddenedoverthecellsinthetemplate.Acell(i;j)movestothelocation(i+uij;j+vij)where(uij;vij)istheowat(i;j).Thescoreofthedeformedtemplatecanthenbewrittenas:fw(x)=Xi;jwTi+uij;j+vijxij(2)Theaboveassumesadiscreteow,whereeachuijandvijisintegral.However,thisisnotnecessary.Wecanallowacontinuousowwithrealvaluesforuijandvijusingbilin-earorbicubicinterpolationtodeformw.Ingeneral,givenacontinuousoweld(u;v),wecanrepresentthescoregivenbyadeformedtemplateas:fw(x)=Xi;jXk;l ijklwTklxij(3)Thecoefcients arethemixingweightsoverwandarede-terminedbytheoweld(u;v).Inpracticetheyarequitesparse.Notethattheaboveequationisstilllinearinbothwandx;thisallowsustowritefw(x)as:fw(x)=wTDx(4)The(sparse)matrixDisdeterminedbytheoweld(u;v).ThedescriptionofhowwendourcandidateoweldsisdeferreduntilSection4.Ourmodelconsidersthedeformationasalatentvariableandmaximizesthescoreoverpossibledeformations:fw(x)=maxD2DwTDx+wTd (D)(5)HereDisourdeformationdictionarycontainingasetofcandidatedeformationsandthetermwTd (D)allowsustoscoreeachdeformationD2D.Thisisuseful,assomedeformationsaremorelikelythanothers.Inpracticeweuseanindicatorfunctionfor (D);thuswTd (D)amountstoassigningeachDabias.NotethatthelinearnatureofEquation5meansthatwecaninterpretiteitherasaxedtemplatewactingonade-formedfeaturevectorDx,oradeformedtemplateDTwactingonx.ThelatterinterpretationimpliesthatattesttimethismodelcanbeseenaschoosingfromasetoftemplatesDTw,oneforeachD2D.3.1.AugmentedModelTakinginspirationfromtheDPM[11],weaugmentourmodelwithafewadditions.Weadda“coarse”roottem-platewrthatdoesnotdeform,inadditiontothe“ne”tem-platewfwhichdoes:fw(x)=wTrx+maxD2DwTfDx+wTd (D)(6)Moreover,whileourdeformationdictionaryallowsustocapturearangeofdeformations,itcannothandleverylargeorextremedeformations,e.g.,changingviewpointfromthefronttothesideviewofacar.Tocapturesuchlargede-formationsweutilizeamixturemodeloveraspectratiossimilarto[11].Specically,weuseaseparatemodelfcw(x)oftheformgiveninEqn.6foreachmixturecomponentc.Ournalmodeltakesontheform:fw(x)=maxcfcw(x)(7)Tosummarize,ourmodeliscomposedofamixtureofcom-ponentscwhereeachcomponentisequippedwith: category category-commonsuper- DPM speciccategory Bicycle 46.546.947 45.2 Motorbike 31.130.831.6 31.4 Cow 13.412.313.7 10.3 Sheep 272726.9 25.5 Table3:Impactofclumpingtogethersimilarcategoriesforcomputingdeformationbasis.3;m=10).Interestingly,usingacommonPCAbasisonlycausesasmalldropinAP,butwearestillonparwithDPM,indicatingthatthedeformationsindifferentobjectcategoriesdohavealotincommon.AcommonsetofPCAbasesisalsolikelytobelessnoisyincasesofinsufcienttrainingexamples.Whentrainingbicycleswithonly100examples,acommonbasisachievesanAPof39:6versusanAPof38:9foracategory-specicbasis(DPMachievesanAPof39:4onthesamedata).Wealsohypothesizethatsimilarcategoriescanbenetfromsharingdeformations.Table3showstheperformanceifwesharethedeformationbasisbetweenmotorbikeandbicycleandbetweencowandsheep.Ineachcaseaccuracyimproves,andinmostcasesAPisevenhigherthanusingacategoryspecicdeformationbasis.6.DiscussionInthispaper,wehaveproposedusingadiscretesetofdeformations.However,wecanalsosearchfortheoptimaldeformationwithinthespacedenedbyoursetof5PCAbases.Usingagreedysearchtechnique,wewereabletoobtainsimilarresultstothatofourdiscretemodel.Whilethediscreteapproachismorecomputationallyefcient,itmayprovebenecialtosearchinacontinuousspaceofde-formationsforsomeobjectcategories.Inconclusion,weproposeanapproachtoobjectdetec-tionthatmodelsdeformationsandappearanceseparately.Wedosobyconstructingadeformationdictionarycontain-ingadiscretesetofcandidateowelds.Interestingly,ourmodelusingasmallnumberofdeformationsisabletoim-proveupontheperformanceofpart-basedmodelsthatarecapableofmodelingaexponentialnumberofdeformations.Inaddition,weshowthatsharingdeformationinformationacrosscategoriescanleadtoimprovedperformance.References[1]Y.AytarandA.Zisserman.Tabularasa:Modeltransferforobjectcategorydetection.InICCV,2011.[2]H.AzizpourandI.Laptev.Objectdetectionusingstrongly-superviseddeformablepartmodels.InECCV,2012.[3]A.C.Berg,T.L.Berg,andJ.Malik.Shapematchingandobjectrecognitionusinglowdistortioncorrespondences.InCVPR,2005.[4]T.F.Cootes,G.J.Edwards,andC.J.Taylor.Activeappear-ancemodels.PAMI,23(6),2001.[5]N.DalalandB.Triggs.Histogramsoforientedgradientsforhumandetection.InCVPR,2005.[6]S.K.Divvala,A.A.Efros,andM.Hebert.Howimportantare'deformableparts'inthedeformablepartsmodel?InPartsandAttributesWorkshop,ECCV,2012.[7]B.DrayerandT.Brox.Distancesbasedonnon-rigidalign-mentforcomparisonofdifferentobjectinstances.InPatternRecognition,2013.[8]O.Duchenne,A.Joulin,andJ.Ponce.Agraph-matchingkernelforobjectcategorization.InICCV,2011.[9]I.Endres,V.Srikumar,M.-W.Chang,andD.Hoiem.Learn-ingsharedbodyplans.InCVPR,2012.[10]M.Everingham,L.VanGool,C.K.I.Williams,J.Winn,andA.Zisserman.ThePASCALVisualObjectClassesChallenge2012(VOC2012)Results.http://www.pascal-network.org/challenges/VOC/voc2012/workshop/index.html.[11]P.F.Felzenszwalb,R.B.Girshick,D.McAllester,andD.Ra-manan.Objectdetectionwithdiscriminativelytrainedpart-basedmodels.PAMI,32(9),2010.[12]P.F.FelzenszwalbandD.P.Huttenlocher.Pictorialstruc-turesforobjectrecognition.IJCV,61(1),2005.[13]B.Hariharan,J.Malik,andD.Ramanan.Discriminativedecorrelationforclusteringandclassication.InECCV,2012.[14]M.HejratiandD.Ramanan.Analyzing3dobjectsinclut-teredimages.InNIPS,2012.[15]L.Ladicky,P.H.S.Torr,andA.Zisserman.Latentsvmsforhumandetectionwithalocallyafnedeformationeld.InBMVC,2012.[16]J.J.Lim,A.Torralba,andR.Salakhutdinov.Transferlearn-ingbyborrowingexamplesformulticlassobjectdetection.InNIPS,2011.[17]C.Liu,J.Yuen,A.Torralba,J.Sivic,andW.T.Freeman.Siftow:densecorrespondenceacrossdifferentscenes.InECCV,2008.[18]X.Liu,Y.Tong,andF.W.Wheeler.Simultaneousalignmentandclusteringforanimageensemble.InICCV,2009.[19]B.Pepik,P.Gehler,M.Stark,andB.Schiele.3D2PM-3Ddeformablepartmodels.InECCV,2012.[20]B.Pepik,M.Stark,P.Gehler,andB.Schiele.Teaching3Dgeometrytodeformablepartmodels.InCVPR,2012.[21]H.PirsiavashandD.Ramanan.Steerablepartmodels.InCVPR,2012.[22]H.Pirsiavash,D.Ramanan,andC.C.Fowlkes.Bilinearclas-siersforvisualrecognition.InNIPS,2009.[23]A.VedaldiandA.Zisserman.Structuredoutputregressionfordetectionwithpartialocculsion.InNIPS,2009.[24]M.Weber,M.Welling,andP.Perona.Unsupervisedlearningofmodelsforrecognition.InECCV,2000.[25]J.WinnandN.Jojic.LOCUS:Learningobjectclasseswithunsupervisedsegmentation.InICCV,2005.[26]Y.YangandD.Ramanan.Articulatedposeestimationwithexiblemixtures-of-parts.InCVPR,2011.[27]X.Zhu,C.Vondrick,D.Ramanan,andC.Fowlkes.Doweneedmoretrainingdataorbettermodelsforobjectdetec-tion?InBMVC,2012.