FactoredShapesandAppearancesforPartsbasedObjectUnderstandingSMAliEslamismeslamismsedacukChristopherKIWilliamsckiwinfedacukSchoolofInformaticsUniversityofEdinburghEdinburghUnitedKingd ID: 472622
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ESLAMI,WILLIAMS:FACTOREDSHAPESANDAPPEARANCES1 FactoredShapesandAppearancesforParts-basedObjectUnderstandingS.M.AliEslamis.m.eslami@sms.ed.ac.ukChristopherK.I.Williamsckiw@inf.ed.ac.ukSchoolofInformatics,UniversityofEdinburgh,Edinburgh,UnitedKingdom AbstractWepresentanovelgenerativeframeworkforlearningparts-basedrepresentationsofobjectclasses.Ourmodel,FactoredShapesandAppearances(FSA),employsahighlyfactoredrepresentationtoreasonaboutappearanceandshapevariabilityacrossdatasetsofimages.WeproposeMarkovChainMonteCarlosamplingschemesforefcientin-ferenceandlearning,andevaluatethemodelonanumberofdatasets.Hereweconsiderdatasetsthatexhibitlargeamountsofvariability,bothintheshapesofobjectsinthescene,andintheirappearances.WeshowthattheFSAmodelextractsmeaningfulpartsfromtrainingdata,andthatitsparametersandrepresentationcanbeusedtoperformarangeoftasks,includingobjectparsing,segmentationandne-grainedcategorisation.1IntroductionOneofthelong-standingopenproblemsinmachinevisionhasbeenthetaskofforeground-backgroundsegmentation,inwhichanimageispartitionedintotwosetsofpixels:thosethatbelongtotheobjectofinterestintheforeground,andthosethatdonot.Thereisbroadagree-mentthatthistaskiscoupledtothatofobjectrecognition.Knowledgeoftheobject'sclasscanleadtomoreaccuratesegmentations,andinturnaccuratesegmentationscanbeusedtoobtainhigherrecognitionrates.Inthispaperwefocusononesideofthisrelationship;giventhegroundtruthvalueoftheobject'sidentityinanimageregionspeciedbyaboundingbox,howaccuratelycanwesegmentthatimage?Thereisarichhistoryofworkonprobabilisticmodelsthatsegmentbyonlyconsideringlow-level,pairwisepixelstatisticse.g.[5,27].Toseewhythistypeofapproachisnotsufcientonitsown,oneonlyhastoexaminethekindsofimagesthatthesemodelsnddifculttosegment.Errorscantypicallybeattributedtoalackofhigh-level,cross-imageunderstandingabouttheobjectinquestion.Whentheobject'spixelintensitiesarenearconstantinthedataset(e.g.invideos),statisticsofitsappearancehavebeenusedtoguidesegmentation[7,8,12,28].Howeverformanydatasetsofinteresttheforegroundobject'sappearanceistoovariabletobemodelledeffectivelybythesemethods.Recently,anumberofmodelshavebeenproposedthatobtainmoreaccuratesegmentationsbyincorporatingpriorknowledgeabouttheforegroundobject'sshapeinstead[4,14,17,18,20,21,29].Insuchcases,probabilistictechniquesmainlydifferinhowaccuratelytheyrepresentandlearnaboutthevariabilityintheobject'sshape. c 2011.Thecopyrightofthisdocumentresideswithitsauthors.Itmaybedistributedunchangedfreelyinprintorelectronicforms. ESLAMI,WILLIAMS:FACTOREDSHAPESANDAPPEARANCES3 Inordertobeabletoallowforpartshapevariability,themodelisdesignedtocaptureadistributionoverml;l=1:::L(m0isxedtoequal1).Specically,theprobabilitydistributionovermlisdenedbyaFactorAnalysis-likemodel:ml=Flv+cl;p(v)=N(0;IHH):(2)HerevisanH-dimensionallatentvariable,FlisaDHmatrixanalogoustothefactorloadingmatrixinFactorAnalysisliteratureandclisthemeanmask.AnL1-normprioronFisusedtoreducetheamountofnoiseinitsvalues.Weadditionallyconsideranalternativeshapevariabilitymodelinwhichweuseseparate,Hdimensionallatentvariablesvlforeverypart(H=LH).Thislocalmodelcanbethoughtofasaspecialcaseoftheglobalmodelpresentedearlier,inwhichmostofthecolumnsofeachFlareforcedtoequal0.Thelocalmodelisusefulincaseswherewebelievetheshapesofanytwopairsofpartsinthedatatobeindependent(e.g.theposeofupperandlowerpartsofhumanbodies),andwewishtoexplicitlybuildthisknowledgeintothemodel. k=1k=2 k=1k=2 background(l=0) foreground(l=1) Figure1:Appearancemodelling:Givenadatasetofimagesandtheirsegmentations,weconstructamodeloftheparts'appearances.Left:Thedataset.Theforegroundandback-groundappearwith2differentstyles.Right:Thecorrespondingappearancemodel.Thetoprowdepictslforthetwopartsandthebottomrowdepicts l.Inthisexample,L=1,K=2andW=5.Appearance:PixelscorrespondingtoeachpartinagivenimageareassumedtohavebeengeneratedbyWxedGaussiansinfeaturespace(inthispaperweonlyuseLabcolourfea-tures).Inthepre-trainingphase,themeansfwgandcovariancesfwgoftheseGaussiansareextractedbytrainingaGaussianmixturemodelwithWcomponentsoneverypixelinthedataset,ignoringimageandpartstructure.ItisalsoassumedthateachoftheLpartshavedifferentappearancesindifferentimages,andthattheseappearancescanbeclusteredintoKclasses.TheclassesdifferinhowlikelytheyaretouseeachoftheWGaussiancomponentswhen`colouringin'thepart.Thegenerativeprocessisasfollows.Forpartlinagivenimage,oneoftheKclassesischosen(representedbya1-of-Kindicatorvariableal).Givenal,theprobabilitydistributiondenedonpixelsassociatedwithpartlisgivenbyaGaussianmixturemodelwithmeansfwgandcovariancesfwgandmixingproportionsf lkwg.Thereforethedistributionontheimagepixelvaluesisgivenbyp(xdjA;sd;)=LYl=0p(xdjal;)sld=LYl=0 KYk=1 WXw=1 lkwN(xdjw;w)!alk!sld(3) 4ESLAMI,WILLIAMS:FACTOREDSHAPESANDAPPEARANCES TheprioronA=falgspeciestheprobabilityofeachappearanceclassbeingselectedforthepartsinanygivenimage:p(Aj)=LYl=0p(alj)=LYl=0KYk=1(lk)alk:(4)SeeFig.1foranillustrationoftheappearancemodel.InourexperimentsthemodeltypicallyperformsbestwhenK'10,andW'30.Weadditionallyplaceahyper-prioron oftheformp( )/expf�E( )gwhereE( )=LXl=00@selfKXk=1H( lk)�othersXm6=lDKL( lk m)+DKL( mk l)1A:(5)HereH( lk)istheentropyofthedistributiondenedby lk(similartothatusedin[6])andDKL( lk m)istheKullback-Leiblerdivergencefromthedistributiondenedby ltothatdenedby m.Thishyper-priorencouragessettingsof thatdenedistributionsontheappearancecomponentsthatare1)low-entropy,and2)dissimilarfromeachother,andcanbeveryeffectiveinacceleratingconvergenceoftheparametersduringtraining.Suitablevaluesofselfandothersarefoundthroughtrialanderror. m0 m1 m2 0 1 (a) 0 1 2 A S X (b) 0 1 2 A S (c) Figure2:Lazyocclusionreasoning:(a)GiventheimageX,themasksaredeformedtotheirmostlikelystates.Inthisexample,themodelhaslearnedthatthecrossandsquarealwaysappearinfrontofthebackgroundandthattheyareequallylikelytobeintheforeground.Thehighlightedpixels(red)areequallylikelytobelongtoeithershapeatthisstage.(b)OnesettingofAandSthatcanexplainX.Notethetwo-toneappearanceforpart1.(c)ThemostlikelysettingofAandS.Outofallsuchcompetingsegmentations,themostlikelySistheoneforwhichthecorrespondingchoiceofappearancesismostprobable.Handlingocclusion:Insteadofmodellingpartocclusionusinganexplicitrandomvariable,FSAcapturesknowledgeaboutpart-orderingimplicitlyintheshapeparameters.Byincreas-ingthemagnitudeofmldforaparticularl,themodelcancapturetheincreasedlikelihoodofpartloccludingotherpartsatpixeld.Incaseswherethemultiplepartsareequallylikelytooccludeeachother,theappearancemodelisusedtoresolvethisambiguityintheposterior.SeeFig.2foranillustrationofthiseffect.Combinedmodel:Tosummarise,thelatentvariablesZiforimageXiareAi,Siandvi,themodel'sactiveparametersincludeshapeparameterss=ffFlg;fclggandappearanceparametersa=fflkg;f lkwgg,andp(Xi;Ai;Si;vij)=p(vi)p(Aija)DYd=1p(sdjvi;s)p(xidjA;sid;a):(6) 6ESLAMI,WILLIAMS:FACTOREDSHAPESANDAPPEARANCES FortheM-stepwearelookingtondargmaxQ(;old),whereQ(;old)=lnp()+nXi=1XZip(ZijXi;old)lnp(Xi;Zij):(9)Todothis,wecomputethederivativeofQwithrespecttoaands.ThegradientsareusedinanumericaloptimisationroutinetondthesettingsoftheparametersatwhichQismaximised.Weuseindependentscaledconjugategradients(SCG)routinestoup-datetheshapeandappearanceparameters.Notethatspecialcareneedstobetakentoen-surethattheand variablessumto1.Were-parametrisethemodelsuchthatlk=expf lkg=PKc=1expf lcgand lkw=expflkwg=PWv=1expflkvg,andoptimiseQwithrespectto andinstead.4RelatedworkExistingparts-basedimagemodelscanbecategorisedbytheamountofvariabilitytheyex-pecttoencounterinthedataandbyhowtheymodelthisvariability.Forexample,intheLayeredSubspaceManifold(LSM)ofFreyetal.[12]videosarepartitionedintolayersthattranslateindependentlyofeachother.Thelayersexhibitlimitedshapeandappearancevari-abilityfromframetoframe,andaremodelledusingFactorAnalysersandaxed,explicitocclusionordering.WiththeSpritesmodel[28],WilliamsandTitsiasshowhowsuchlay-eredmodelscanbeefcientlylearnedonelayeratatime,howevertheydonotmodelshapeorappearancevariability.Bycontrast,FSAisdesignedtoworkondatasetsofimagesthatex-hibitsignicantshapeandappearancevariabilityfromimagetoimage,anddoesnotimposeanylayerorderingintothemodel.WithMultipleCauseVectorQuantisation(MCVQ)[26],RossandZemelpresentanalternativepart-basedrepresentationofimages.Themodellearnsaxedpartitioningoftheimage,anditisassumedthataxednumberofappearancetemplatesgeneratethepixelswithineachpart.Whenappliedtohighlyvariabledata,themodelndsitdifculttolearnmeaningfulpartsasitcanonlymakeverylimitedvariationinthepartitioningsfromimagetoimage.TheauthorsalsopresentMultipleCauseFactorAnalysis(MCFA),whichusesaFactorAnalysismodelforpartappearances,howeverthisremainstoorestrictiveformostdatasetsofinterest.Bycontrast,FSAexplicitlymodelsthevariabilityofpixelassignmentstoparts,thereforelearningsharppartitions,anditmodelspartappearancevariationinamoreexibleway.Table1:Comparisonofanumberofdifferentparts-basedmodels.FACTOREDFACTOREDSHAPESHAPEAPPEARANCEPARTSANDAPPEARANCEVARIABILITYVARIABILITY LSM[12]X(layers)-X(FA)X(FA)Sprites[28]X(layers)---LOCUS[29]-XX(deformation)X(colours)MCVQ[26]-X-X(templates)SCA[18]-XX(convex)X(histograms) FSAX(softmax)XX(FA)X(histograms) ESLAMI,WILLIAMS:FACTOREDSHAPESANDAPPEARANCES7 TheclosestworkstooursareLOCUS[29]andStelComponentAnalysis(SCA)[18].InthebasicformulationofLOCUS,themodelusesonlyone`part'toaccountforthefore-groundobject,butthisrestrictioncanberelaxedwiththedeformableprobabilisticindexmap(dPIM)[29].Shapevariabilitybetweenimagesisaccountedforusingadeformationeldthatwarpsthepartitioningtoteachimage.Sincetheformulationimposesonlylocalsmoothnessconstraintsondeformations,samplesfromthemodelintheabsenseofanimageareunlikelytocaptureglobalpropertiesoftheobjectinconsideration(e.g.poseofahorse).TheSCAmodel,ontheotherhand,accountsforshapevariabilitybylearningaxednumberoftemplatesforeachpart.Thetemplatesarerestrictedsuchthatanypixelwise,convexcombinationoftemplatesresultsinavalidprobabilisticindexmap(i.e.oneinwhichtheprobabilitiesofpartassignmentsforeachpixelsumto1).TheSCAdistributionoversegmentationsisaccurateonlyintheposterior–intheabsenceofanimage,thedeneddis-tributionoversegmentationsis`blurry'.ThussamplesofpartitioningsgeneratedbyLOCUSandSCAwillnothavemuchresemblancetotheirtrainingimages,eventhoughthearebothgenerativemodelsofimagepartitionings.InFSApartshapesvaryaccuratelyeveninthepriorandsegmentationsrandomlysam-pledbythemodelaresimilartothosefoundinthetrainingdata.Additionally,bothLOCUS(withdPIMs)andSCAdeneglobaldistributionsoverpartitioningsthatdonotfactoriseoverpartshape.InFSApartscanbemodelledindependentlyofeachotherallowingfurtherdevelopmentstobemadebyincorporatingspecialisedpartmodelsthatconcentrateontheshape,positionandscaleofeachindividually.WesummarisethesedifferencesinTable1.5ExperimentsFSA,asagenerativemodelforimagesofobjects,canbeusedtoaccomplishavarietyoftasksincomputervision.Herewedemonstrateitsperformanceonseveraldatasets.FSAsegmentsallimagesacrossthedatasetsimultaneouslytolearnaparts-basedobjectmodel.Inadditiontothesegmentationsmadebythealgorithm,weinspecttheparameterslearnedbythemodel.Weshowthattheseparametersformanintuitivereectionofthealgorithm's`understanding'oftheobjectclass.Carsdataset:Therstrealdatasetweconsider1contains20imagesofcarsthathavebeendownloadedfromamanufacturer'swebsite2.Inadditiontoappearancevariability,thecarsexhibitsignicantshapevariabilityacrossthedataset(e.g.hatchback,SUV,convert-iblecoupé,saloon,estate).ThesegmentationsinferredbyanunsupervisedFSAmodelwithL=3andH=2areshowninFig.4(a).ItisinformativetoinspecthowthelatentvvariableisprojectedbyFlandclintomasksfortheparts.InFig.4(b)weplotcolumnsofoneoftheFmatrices,andinFig.4(c)weplotthecarbody'smaskforagridofvvaluesin2-dimensionallatentspace.NoticehowFSAlearnsamodelofshapethatgraduallymorphsbetweentheparts'possibleoutlines.Indoingsoitlearnsamodelofobjectclassshapethatismoreinformativethanjustamean3.Alsonotethatthemodellearnsamaskfortheroof-less`convertible-coupé'bodytype.AdeformationeldliketheoneusedinLOCUS[29]wouldndthiskindofvariabilitydifculttorepresent.Finally,weobservethattheinferredvscanbeusedasdiscriminativeindicators 1Seesupplementarymaterialforillustrativeresultsonsyntheticdata.2http://bmw.com3SeesupplementarymaterialforsamplesfromasupervisedFSAmodelonthesamedataset. 8ESLAMI,WILLIAMS:FACTOREDSHAPESANDAPPEARANCES (a) (b) +3 0 -3 +3 0 -3 (c) Figure4:(a)Asubsetofthetrainingimageswiththeirinferredsegmentations.Distinctcoloursindicateassignmentsofpixelstodifferentparts.(b)HintondiagramsofthetwocolumnsofF2correspondingtothecarbody(cyan).(c)Aplotofthejointsegmentationforagridofvvaluesin2Dlatentspace.Prototypicalshapesof4ofthedifferentcartypeshavebeenhighlightedinred.oftheobject'stype.Inourexperiments,usingaleave-one-outSVMclassierononlytheinferredvs,wecanclassifythecarsintothe5distinctcategorieswith100%accuracy.Otherdatasets:WeapplytheFSAmodeltoanumberofotherdatasetsincluding100MITpedestrians[25],200UMISTfaces[13]and127Caltechmotorbikes[9],aswellas138imagesofdressesobtainedfromafashionretailer'swebsite4;5.TheresultsoftheseexperimentscanbeseeninFig.5.Themodeldoesagoodjoboflearningaboutclassshapeacrossthedataset.Inourexperimentsweobservedthatitusesthisinformationeffectivelytoguideinferencesformoredifcultimagesthatcannotbesegmentedbasedonappearancecuesalone.Thefactthatithastheexibilitytolearnaboutshapedeformationsincreasesitschancesoftransferringshapeinformationinausefulway.Forexample,havingcorrectlylearnedabouttheshapeofahumaninanunusualposeinanimagewithstrongappearancecues,themodelusesthisinformationtocorrectlysegmentmoredifcultimagesofhumanswiththesamepose.Themeanposeinthiscasewoulddomoreharmthangoodinprovidingcuesforsegmentation.Segmentationaccuracy:WeadditionallyevaluatetheperformanceoftheFSAmodelatsegmentingtheWeizmannhorse[4]andCaltech4[10]datasets,wherethegroundtruthsarereadilyavailable.Thetrain-testsplitforthedatasetswereasfollows.Weizmannhorses:127-200;Caltechcars:63-60;faces:335-100;motorbikes698-100andairplanes:700-100.ThebaselineweconsideristhebatchGrabCutalgorithmdescribedbyAlexeetal.[1].GrabCutisinitialisedbytrainingaforegroundcolourmodelonthecentral25%ofeachtestimageandabackgroundcolourmodelusingtheremainderofitspixels.InsupervisedFSA,trainingisperformedgiventheground-truthsegmentationsforeachimage(L=1).TheresultsoftheseexperimentscanbeseeninTable2.ForcomparisonwealsoincludeaccuraciesreportedbyBorensteinetal.[4](supervised),WinnandJojic[29](unsupervised,colourmodel)andAlexeetal.[1](unsupervised).FSAusesknowledgeaboutshapetoin-creasetheaverageaccuracyoverthebaseline.ThediscrepancywithLOCUSandBorensteinetal.'sapproachontheWeizmanndatasetislikelyduetothelackoflow-leveledgefeaturesinourimplementationofFSA.SupervisedFSAoutperformstheothermodelsonthefaceandmotorbikedatasets,inpartduetothewayinwhichitlearnstoclassifypixelsbelonging 4http://marksandspencer.com5Pedestrians:L=3,H=2;faces:L=2,H=2;motorbikes:L=3,H=20;dresses:L=1,H=5. 10ESLAMI,WILLIAMS:FACTOREDSHAPESANDAPPEARANCES ditionally,FSArepresentsthestatisticsofpartappearanceinawaythatignoresthespatialstructureofthepixelswithinparts.Wewouldliketoinvestigatehowmorestructuredmod-elsoftexturecanbeusedtorepresentpartappearances.Finally,wishtondoutifefcientalgorithmscanbedevelopedtoautomaticallydeterminesuitablechoicesofLandH.Table2:Averagesegmentationaccuracies.Herewereporttheaccuracyofthealgorithmastheaveragepercentageofcorrectlylabelledpixelsacrossallthetestimages.WeizmannCaltech4 HorsesCarsFacesMotorbikesAirplanes GrabCut[1]83.9%45.1%83.7%82.4%84.5%Borensteinetal.[4]93.6%----LOCUS[29]93.1%91.4%---Aroraetal.[2]-95.1%92.4%83.1%93.1%ClassCut[1]86.2%93.1%89.0%90.3%89.8% UnsupervisedFSA87.3%82.9%88.3%85.7%88.7%SupervisedFSA88.0%93.6%93.3%92.1%90.9% 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