Departmen of Computer Science Univ ersit of Massac usettsAmherst Abstract raditional generativ Mark random 57356elds for seg men ting images mo del the image data and corresp onding lab els join tly whic requires extensiv indep endence assumptions f ID: 31784
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SIGNDETECTIONINNATURALIMAGESWITHCONDITIONALRANDOMFIELDSJerodWeinman,AllenHanson,andAndrewMcCallum{weinman,hanson,mccallum}@cs.umass.eduDepartmentofComputerScienceUniversityofMassachusetts-AmherstAbstract.TraditionalgenerativeMarkovrandom eldsforseg-mentingimagesmodeltheimagedataandcorrespondinglabelsjointly,whichrequiresextensiveindependenceassumptionsfortract-ability.Wepresenttheconditionalrandom eldforanapplicationinsigndetection,usingtypicalscaleandorientationselectivetex-ture ltersandanonlineartextureoperatorbasedonthegratingcell.Theresultingmodelcapturesdependenciesbetweenneighbor-ingimageregionlabelsinadata-dependentwaythatescapesthedicultproblemofmodelingimageformation,insteadfocusingef-fortandcomputationonthelabelingtask.Wecomparetheresultsoftrainingthemodelwithpseudo-likelihoodagainstanapproxima-tionofthefulllikelihoodwiththeiterativetreereparameterizationalgorithmanddemonstrateimprovementoverpreviousmethods.INTRODUCTIONAppearinginIEEEInternationalWorkshoponMachineLearningforSig-nalProcessing,S~aoLus,Brazil,Sep.2004.Imagesegmentationandregionlabelingarecommonproblemsincomputervision.Inthiswork,weseektoidentifysignsinnaturalimagesbyclassifyingregionsaccordingtotheirtexturalproperties.Ourgoalistointegratewithawearablesystemthatwillrecognizeanydetectedsignsasanavigationalaidtothevisuallyimpaired.Genericsigndetectionisadicultproblem.Signsmaybelocatedanywhereinanimage,exhibitawiderangeofsizes,andcontainanextraordinarilybroadsetoffonts,colors,arrangements,etc.Forthesereasons,wetreatsignsasageneraltextureclassandseektodiscriminatesuchaclassfromthemanyotherspresentinnaturalimages.Thevalueofcontextincomputervisiontaskshasbeenstudiedinvariouswaysformanyyears.Twotypesofcontextareimportantforthisproblem:labelcontextanddatacontext.Intheabsenceoflabelcontext,localregionsareclassi edindependently,whichisacommonapproachtoobjectdetection.Suchdisregardforthe(unknown)labelsofneighboringregionsoftenleadstoisolatedfalsepositivesandmissingfalsenegatives.Theabsenceofdatacon-textmeansignoringpotentiallyhelpfulimagedatafromanyneighborsofthe regionbeingclassi ed.Bothcontextsaresimultaneouslyimportant.Forin-stance,sinceneighboringregionsoftenhavethesamelabel,wecouldpenalizelabeldiscontinuityinanimage.Ifsuchregularityisimposedwithoutregardfortheactualdatainaregionandlocalevidenceforalabelisweak,thencontinuityconstraintswouldtypicallyoverridethelocaldata.Conversely,localregionevidencefora\sign"labelcouldbeweak,butastrongedgeintheadjoiningregionmightbolsterbeliefinthepresenceofasignatthesitebecausetheedgeindicatesatransition.Thus,consideringboththelabelsanddataofneighboringregionsisimportantforpredictinglabels.Thisisexactlywhattheconditionalrandom eld(CRF)modelprovides.Theadvantageofthediscriminativecontextualmodeloveragenerativeonefordetectiontaskshasrecentlybeenshownin[8].Wedemonstrateatrainingmethodthatimprovespredictionresults,andweapplythemodeltoachallengingreal-worldtask.Firstthedetailsofthemodelandhowitdi ersfromthetypicalrandom eldaredescribed,followedbyadescriptionoftheimagefeaturesweuse.Weclosewithexperimentsandconclusions.RANDOMFIELDSModelFormanycomputervisiontasks,thepriorprobabilityofthedatabeingob-servedisinconsequential.Imageshappen.Weareprimarilyinterestedinwhatmaybeinferredwhengiventheimages.However,probabilitydistribu-tionsoverlabelsyandanimagexhavetraditionallybeenmodeledjointly,withtheimagepriorprobabilitybeingignoredatclassi cationtime.Forthatreason,generativejointmodelsrequireunnecessarymodelinge ortandmorecomputationthantheirconditionalcounterparts.Markovrandom eldsareprobabilitydistributionsparameterizedbyagraphtopologyG=(V;E).Fortractabilityreasons,typicalgenerativeran-dom eldstreattheinteractionbetweenlocaldataanditslabelindependentlyoftheinteractionbetweenneighboringlabels.Thejointdistributionisthusfactoredintotheprioronlabelassignmentsandtheprobabilityoflocallyobserveddata,conditionedonthesinglesitelabel:p(y;x)=p(xjy)p(y),1ZYC2C C(yC)Yv2V v(yv;xv);(1)where ()arecompatibilityfunctions,Zisanormalizingconstantmakingtheexpressionaprobabilitydistribution,Cisafamilyofcliquesofthegraph,andyCarethevariablesinagivencliqueCV.Inthismodel,objectsx(e.g.,patchstatistics,salientfeatures,etc.)fromeachclassy2Yaregener-atedbyaclass-conditionalprobabilitydistributionp(xjy).Thisrequiresnotonlyamodelforeveryclasswewishtodistinguish,butanaccurategenerativebackgroundmodelevenforclassesofnointerest;anon-trivialtaskbecausetherealworldcontainsamyriadofimage\classes"(regiontypes,textures, x3y3x4y4x2y2x1y1xyyyy1234Figure1:Left:Traditionaljointrandom eldoverdataxandlabelsy(cf.Eq.1).Right:Conditionalrandom eldwheredataisobserved(cf.Eq.2).objects,etc.).Inshort,itisgenerallymorediculttoexplaintheprocessesthatgenerateclassdatathanitistomodeltheboundariesbetweenclasses.Inthelatterapproach,onlyboundariesamongclassesofinterestmustbedis-tinguished,withtheremaindereasilycollapsingintoasingle\background"class.Modelingtheinteractionsbetweendataandlabelsseparately,as(1)does,isoftentoolimitingformanycomputervisiontasks;wethereforeusearecentlyproposedmodelthathandlestheinteractionbetweensitelabelsinacontext-dependentway[9],describingitnext.Therandom eldgraphtopologycommonlyusedforjointimagelabelingproblemsisthelattice,(Figure1),wherecliquesaresinglenodesandedges.Weuseahomogeneous,anisotropicrandom eld.Thus,cliquesofthesameclassusethesamecompatibilityfunctionsregardlessofimagelocation,buthorizontalandverticaledgesareconsidereddi erentclassesandthushavedistinctcompatibilityfunctions.Anisotropyallowsthemodeltolearnanyorientationalbiasofthelabels.Ourconditionalrandom eldhastheformp(yjx)=1Z(x)Yv2V V(yv;x)Y(u;v)2E E(yu;yv;x)(2)=1Z(x)exp0Xv2VF(yv;x)+X(u;v)2EG(yu;yv;x)1;(3)whereZisnowanobservation-dependentnormalizer.Thecompatibilitiesarefunctionsofcliquelabels,allowingneighboringlabelinteraction,buttheyarealsofunctionsoftheentireobservation.Thisdi ersmarkedlyfrom(1)byallowingdata-dependentlabelinteraction(seeFigure1).FandGarevector-valuedfeaturefunctions,andandarevectorsofparametersfornodesandedges,respectively.Nodelabelscomefromadiscrete, nitealphabetY.Weuseonesetofobservationfeaturesfornodesandedgesandtransformthemintofeaturefunctions(observation,labelpairs)usingtherelationshipfky(yv;x)=(y;yv)fk(x)gjy;y0(yu;yv;x)=(y;yu)(y0;yv)gj(x);wheref= fkk=1:::Kisavectorofnodefeatures(i.e.,texturestatisticsof aregion)andg= gjj=1:::Jisavectorofedgefeatures(i.e.,di erencesbetweenstatisticsofneighboringregions),sothatF= fkyk=1:::K;y2YandG=gjy;y0j=1:::J;y;y02YY:Thus2RKjYjand2RJjYj2.WhenE=;,themodelusesnolabelcontextandiscommonlycalledaconditionalmaximumentropyclassi er(hence,MaxEnt),orlogisticregression.TrainingandInferenceParametersforprobabilisticmodelslikeCRFsaregenerallysetbymaximiz-ingthelikelihoodofadatasample.Unfortunately,inferenceforanyrandom eldwiththelatticetopologyisintractableduetoZ(anexponentialsum).MarkovchainMonteCarlo(MCMC)(seee.g.,[16])isoftenusedtoapproxi-mateZinsimilargenerativemodels.However,inourconditionalmodelZisdependentontheimagedataxandmustbeestimatedforeachobservationinthesample.Asimplerapproximationistomaximizethepseudo-likelihood(PL)[1],whichistheproductoftheprobabilitiesofnodesgiventheirneigh-boringlabels.Thenormalizersarethensummationsoverlabelsatasinglenode,ratherthanthepossiblelabelingsofallnodes.ArelativelynewalternativetoMCMCandPLforapproximatinglike-lihoodiscalledtreereparameterization(TRP)[15].Inferenceingraphicalmodelswithoutcycles(unlikethelattice)isveryecient,i.e.,duetothejunctiontreealgorithm(e.g.,[10]).Animportantconsequenceofthejunc-tiontreealgorithmisthatmarginaldistributionsarerevealedonpairsofneighboringnodes,inducinganalternativefactorizationofthejointdistribu-tion.TRPoperatesbyusingjunctiontreetocomputetheexactmarginalsonaspanningtreeofthecyclicgraph.Thespanningtree'sfactorizationisthenplacedbackintotheoriginalgraph,andtheprocessrepeatswithdi erentspanningtreesuntiltheparameterizationconverges,leavingthemarginals.WedemonstrateimproveddetectionperformanceusingTRPtoapproximatethelikelihoodoverpseudo-likelihood.Thelikelihoodfunctionisconvexandmaybeoptimizedgloballyviagradientascent.Pseudo-likelihoodissensitivetoinitialization,however,sonodeparametersareoptimized rst.Weusethequasi-newtonL-BFGSalgorithmformaximization.Topreventtrainingproceduresfromover ttingparametersinconditionalmodels,apriorisintroduced,andtheposteriorismaximizedratherthanlikelihood.Weemployadiagonalzero-centeredGaussianprioronparameters[2](similartoweightdecayinneuralnetworksorridgeregression);variancesareexperimentallydeterminedthroughcross-validation.Giventheimagedata,ourmodelsimplyyieldsajointposteriordistribu-tiononlabelings.Wheninterestedinpickingahardandfastlabelforeachregionoftheimage(nodeinthegraph),thequestionbecomeswhattodowiththatdistribution.Asimple,oft-usedansweristo nditsmaximum.Thatis,usemaximumaposteriori(MAP)estimation:^y=argmaxy2YjVjp(yjx): Thissearchspaceisintractable.However,aslightalterationofTRPallowsMAPestimatestobequicklycalculated.Asimpleralternativeistosearchforalocalmaximumoftheposterior,anestimatecallediteratedconditionalmodes(ICM).Givensomeinitiallabelingy0,subsequentlabelsaregivenbyyk+1v=argmaxyv2YpyvjykN(v);x;8v2Vuntilyk+1=ykoraniterationlimitisexceeded.Often,theinitiallabelingcomesfromthelocalcompatibilitymaximumy0v=argmaxyv2Y (yv;x):Likemanypointestimates,theMAPestimationhasanimportantcaveat:poorpredictionscanresultwhenthemaximumoftheposteriorisnotrepre-sentativeofmostoftheotherlikelylabelings[6].Analternativemethodforpredictioniscalledmaximumposteriormarginal(MPM)estimation,^yv=argmaxyv2Yp(yvjx);8v2V;whichaccountsfortheprobabilityofalllabelings,notsimplythemaxi-mal(joint)labeling,bychoosingthelabelateachnodethatmaximizesitsmarginalprobability.MAPandMPMareequivalentintheMaxEntclassi- ersincenodelabelsareindependent.Marginalizationsu ersfromthesamecomputationalcomplexityproblemsasMAP,butsinceTRPreveals(ap-proximate)marginalsonthenodes,itiseasilyusedforMPM.ComparisonsbetweenICMandMAPestimatedwithTRParegivenintheexperiments.IMAGEFEATURESFORSIGNDETECTIONTextandsigndetectionhasbeenthesubjectofmuchresearch.Earlierap-proacheseitheruseindependent,localclassi cations(i.e.,[5,7,11])oruseheuristicmethods,suchasconnectedcomponentanalysis(i.e.,[4,14]).Muchworkhasbeenbasedonedgedetectorsormoregeneraltexturefeatures,aswellascolor.Ourapproachcalculatesajointlabelingofimagepatches,ratherthanlabelingpatchesindependently,anditobviateslayoutheuristicsbyallowingtheCRFtolearnthecharacteristicsofregionsthatcontaintext.Ratherthansimplyusingfunctionsofsingle lters(e.g.,moments)oredges,weusearicherrepresentationthatcapturesimportantrelationshipsbetweenresponsestodi erentscale-andorientation-selective lters.Tomeasurethegeneraltexturalpropertiesofbothsignandespeciallynon-sign(hence,background)imageregions,weuseresponsesofscaleandori-entationselective lters.Speci cally,weusethestatisticsof lterresponsesdescribedin[13],wherecorrelationsbetweensteerablepyramidresponsesofdi erentscalesandorientationsaretheprominentfeatures.Abiologicallyinspirednon-lineartextureoperatorfordetectinggratingsofbarsataparticularorientationandscaleisdescribedin[12].Scaleandorientationselective lters,suchasthesteerablepyramidorGabor lters,respondindiscriminatelytobothsingleedgesandoneormorebars.Grating FTIPrimarySimpleFiltersSecondaryOrthogonalFilterWeightedSimpleFiltersReceptiveFieldMaximumsGratingAND-likeIndicatorFinalGratingResponseQPMMMMMMFTIRFigure2:Gratingcelldata\rowforasinglescaleandorientation.TwoboxesatI,T,andFrepresentcenteronandcentero lters,whiletheboxesatMareforthesixreceptive elds.cells,ontheotherhand,respondselectivelyonlytomultiple(threeormore)bars.Thispropertyisanidealmatchfordetectingtext,whichisgener-allycharacterizedbya\grating"ofstrokes.Theoriginalmodeliscontrast-normalized,butweexpecttextinsignstohavehighcontrastforreadability,soweomitanynormalizationwhencalculatingI;!; ,theresponseofanin-putimagetoa lterwithpreferredorientation,spatialfrequency!,andphase (Figure3,upper-right).Furthermore,lettershavealimitedaspectratio,thusthebarsintexthaveboundedheight.ForthisreasonwesubjecttheresponsesI;!; toasecondroundof lteringwithoutputT;!; ,where;!; stillindicatestheparametersoftheprimarysimple lter.Thesec-ondary lterhasanorthogonalorientation+2,acenter-onphaseof,andshouldhaveafrequencyofnomorethan!/2.Toelicitstrongerresponsesfrombarsoflimitedheight,theoriginalsimple lterresponseisweightedbytheperpendicularresponsewiththeSchurproductF;!; ,I;!; T;!; .Oncetheweightedresponsesarecalculated,abinarygratingcellsubunitQ;!indicatesthepresenceofagratingateachimagelocation.Tomakesuchadetermination,alternatingstrongmaximumcenter-on( =)andcenter-o ( =0)responsesM;!;narerequiredinreceptive eldregionsR;!;n( 3n2)oflength1/(2!)alongalinewithorientation(Figure3,bottom).Weletthe naloutputP;!bethemeanresponseamongthereceptive eldswhereQ;!indicatesagratingandzeroelsewhere.Thisalsodi ersfromtheoriginalmodel,whichsimplygivesthespatialaverageofthegratingindicator.Useofactual lterresponsesintheoutputisimportantbecauseitrepresentsthestrengthofthegrating,ratherthanonlyitspres-ence.Aftertakingmaximumresponsesoverasetofscales,weusethemean,max,variance,skewandkurtosisoftheoutputsinaregionasfeatures.Additionally,histogramsofpatchhueandsaturationareused,whichalsoallowsustomeasurecolordiscontinuitiesbetweenpatches.Usinganalgorithm[3]thatranksdiscriminativepowerofrandom eldmodelfeatures,wefoundthetopthreeintheedge-less,context-freeMaxEntmodeltobe(i)thelevelofgreenhue(easilyidentifyingvegetationasback-ground),(ii)meangratingcellresponse(easilyidentifyingtext),and(iii)correlationbetweenaverticallyanddiagonallyoriented lterofmoderatescale(thesinglemostusefulother`textural'feature). Figure3:Gratingoperatorontext.UpperLeft:Inputimage.UpperRight:Center-onandcenter-o simple lterresponses(=0).Bottom:Sliceofsimple lterresponsesandreceptiveregionsforamarkedpoint.Figure4:Multi-scaletextdetectionwithgratingcells.Left:Inputimagewithsignareasoutlined.Right:Gratingcellresponses.EXPERIMENTSOursignexperimentsarebasedonahand-labeleddatabaseof309imagescollectedfromaNorthAmericandowntownareawithastillcamera.1Weviewthe1024x768pixelimagesasan8x6gridof128x128pixelpatchesoverwhichthefeaturesarecomputed.Thisouterscalewaschosentobalancecomputationalburdenagainsttypicalsignsize;somepatchescontainmoresignthanothers.Letfprepresentthestatisticsofthesteerablepyramid,fgthegratingstatistics,andfh,fsthehueandsaturationhistograms,respec-tively.Ournodefeaturesaretheconcatenatedvectorsf=hfp;fg;fh;fs;1i1Availableat&#xhttp;&#x://v;&#xis-w;&#xww.c;&#xs.um; ss.;íu/;&#xproj;ìts;&#x/vid;&#xi000;. Classi erPredictionRecallPrecisionF1MaxEntMAP48.3668.0256.45ICM49.4270.2357.90PLMAP49.5370.2357.97MPM49.9769.7758.13CRFICM54.0166.5459.49TRPMAP54.5866.0759.57MPM54.5866.0759.65Table1:Predictionresultsforsigns.PLindicatestrainingwithpseudo-likelihood,andTRPtrainingwithapproximatedfulllikelihood.MAPandMPMfortheCRFisestimatedwithTRP.00.20.40.60.8100.20.40.60.81False Alarm RateDetection Rate50%- 75% : 0.909100.20.40.60.8100.20.40.60.81False Alarm RateDetection RateMaxEnt : 0.7061Figure5:Discriminativepower.Left:ROCcurvesandareasforMaxEntonpatchesthatarenearlyall(75%-100%)signormostly(50-75%)sign.Right:ROCcurvesandareasforMaxEntandCRFinpatchescontaininglessthan25%sign.plusabiasfeature.EdgefeaturesaretheL2normsofdi erencesbetweenstatisticsatneighboringpatches,g=\n\rfp f0p\r;kfh f0hk;kfs f0sk;1 .Theimagesetissplitevenlywithhalfeachfortrainingandtesting.Ta-ble1containstheaveragepredictionresultsof20suchsplits.Sincethisisadetectiontask,wereportprecisionandrecall(commonininformationretrieval)foreachpredictionmethod.LetDSbethenumberoftruesignpatchesdetectedwithDthetotalnumberofdetectionsandStheactualnumberoftruesignpatches.PrecisionisP=DS/D,thepercentageofdetectionsthatarecorrect(notthecomplementoffalsealarm).RecallisR=DS/S,thedetectionrate.TheharmonicmeanofrecallandprecisionF1=2PR/(P+R)re\rectsthebalance(orlackthereof)betweentherateandaccuracyofdetections;higherF1indicatesbetteroverallperformance.MAPandICMarepointestimatesoftheunwieldyjointposteriorprob-ability,butthemarginalposteriorofalabel(i.e.,\sign")atanodeisarealquantitythatmaybeeasilyvaried.Figure5(left)demonstratesthatoveralldiscriminationisverygoodeveninthecontext-freeMaxEntclassi erwhen Figure6:Exampledetectionresults.Left-Right:MaxEnt,CRFICMandMAP.apatchcontainsnearlyallsign,butperformancedegradesastheamountofsigninapatchdecreases.Figure5(right)showsthataddingcontextwithaCRFimprovestheabilitytoidentifyallregionsofasign,especiallythoseontheborderwherethepatchcontainsmorebackground.UsingaCRFsigni cantlyimprovesF1overthelocalMaxEntclassi er.2TrainingwithTRPalsoimprovesrecall.Becauseitisgiventrueneighboringlabels,whichareunavailableattesttime,PLtrainingtendstobeovercon- dentwithedgeparameters,leadingtohigherprecision(exceptingMPM)asaresultofover-smoothingthelabels.TRPtrainingyieldshigherF1andrecalloverPLforallpredictionmethods.CONCLUSIONSconditionalrandom eldisapowerfulnewmodelforvisionapplica-tionsthatdoesnotrequirethestrongindependenceassumptionsofgenera-tivemodels.Withit,wedemonstratesigndetectioninnaturalimagesusingbothgeneraltexturefeaturesandspecialfeaturesfortext.Addingcontextincreasesthedetectionratefasterthanthefalsealarmratebydrawingonbothobserveddataandunknownlabelsfromneighboringregions.Thecomplexityissuesofcyclicrandom eldsarewellknown.Althoughtrainingtimesaregreater,predictionwithaCRFstillonlyrequiresabout3secondsona3GHzdesktopworkstation.Wehaveshownthesuperiorityoftreereparameterizationoverthepseudo-likelihoodapproximationforparam-eterestimationandpredictionintheCRFmodelforourdetectiontask.Weplantoaddmoreedgefeaturestoincreaseouruseofthemodel'scontextualpowerbyincorporatingfeatureselectionandinductionmethods.Over ttingremainsaconstantprobleminsuchahigh-dimensionalmodel,soregularizationisanimportantareaforstudy.AcknowledgmentsThankstoAronCulotta,KhashayarRohanimanesh,andCharlesSuttonfortheirassistivediscussions.ThisworkwassupportedinpartbyNFSgrant#IIS-0100851,inpartbytheCenterforIntelligentInformationRetrieval,andinpartbyTheCentralIntelligenceAgency,theNationalSecurityAgencyandNationalScienceFoundationunderNSFgrant#IIS-0326249.2Claimsofrelativeperformancearebasedonatwo-sided,pairedsigntest(p4e 5). 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