Global Data Association for MultiObject Tracking Using Network Flows Li Zhang Yuan Li - PDF document

GlobalDataAssociationforMulti-ObjectTrackingUsingNetworkFlowsLiZhang,YuanLiandRamakantNevatiaUniversityofSouthernCaliforniaInstituteofRoboticsandIntelligentSystemsWeproposeanetwork”owbasedoptimizationmethodfordataassociationneededformultipleobjecttracking.Themaximum-a-posteriori(MAP)dataassociationprob-lemismappedintoacost-”ownetworkwithanon-overlapconstraintontrajectories.Theoptimaldataassociationisfoundbyamin-cost”owalgorithminthenetwork.The       Figure1.Detectioninputandtrackingresult:ourmethodcanre-movefalsealarms,recovertrajectoriesandinfereventssuchasmisseddetectionsandocclusions.Inourapproach,dataassociationisde“nedasaMAPes-timationproblemgivenasetofobjectdetectionresultsas 2.RelatedworkTotrackmultipleobjects,oneapproachistomakedataassociationdecisionsframe-by-frame(orinasmalltimewindow)asin[].Whilesuchmethodshaveshownverygoodperformance,consideringmoreframesbeforemakingassociationdecisionsshouldgenerallyhelpbetterovercomeambiguitiescausedbylonger-termocclusionsandfalseormisseddetections.Manyglobalapproachesthatusemoreinformationhavebeenexploredtoovercomeerrorsofdetections.Onestrat-egyistooptimizeonetrajectoryatatimethroughtheen-tiresequence;thishasbeenusedinDynamicProgrammingbasedmethods,suchas[].Greedystrategiesarethenusedtocombinethetrajectoriesandhandlepotentialcon-”icts.Itisdif“cultforthesemethodstomodelocclusionsbecausetrajectoriesareoptimizedseparately.Anotherap-proachistooptimizemultipletrajectoriessimultaneously;multi-HypothesisTracking(MHT)[]andJointProbabilis-ticDataAssociationFilters(JPDAF)[]aretworepresenta-tiveexamples.Alsoin[],detectionandestimationoftra-jectoryhypothesesarecoupledbyQuadraticBooleanPro-gramming.Asthehypothesessearchspaceiscombinato-rial,suchmethodscanonlyoptimizeoveralimitedtimewindow,andhypothesesmuststillbepruned.SamplingmethodssuchasMCMC[]havealsobeenemployedto“ndapproximatesolutions.Occlusionsareusuallymodeledasmergingandsplittingoftrajectoriesinthesemethods.TrackletStitching[]andLinearProgramming(LP)basedtracking[]aretwootherapproachesseekingtoop-timizealltrajectoriessimultaneouslyovertheentirese-quence.[]“rstgeneratestracklets,whicharefragmentsoftracksformedbyconservativegroupingofdetectionre-sponses.ThetrackletsarethenconnectedbyHungarianpartitioningalgorithm.Thismethodassumesalltrackletstocorrespondtotrueobjecttrajectoriesandhenceishardtoextendtorawdetectionsineachframewheremanyfalsealarmsarelikelytobepresent.[]buildsasetofsubgraphsforeveryobjecttrajectorywithedgesbetweenthemrepre-sentingtheobjectinteractions.Amulti-pathsearchproblemonthesubgraphsisthensolvedapproximatelybylinearpro-grammingandrounding.Itassumesinter-objectpositionstoberelativelystable,andthenumberoftargettobe“xed.3.OurapproachWede“nedataassociationasaMAPproblem.Theprob-lemisthenmappedintoacost-”ownetwork,andsolvedwithamin-cost”owalgorithm.Themappingisbasedontheobservationthatthereisananalogybetween“nd-ingnon-overlappingobjecttrajectoriesand“ndingedge-disjointpathsinagraph;thelattercanbesolvedef“cientlybynetwork”owalgorithms.We“rstpresenttheformula-tion,andthenprovidethemin-cost”owsolution.3.1.MAPundernon-overlapconstraintsbeasetofobjectobservations,eachofwhichisadetectionresponse,,whereistheposition,isthescale,istheappearanceandisthetimestep(frameindex)oftheobject.Asingletrajectoryhypothesisisde“nedasanorderedlistofobjectobservations,.Anassociationhypothesisisde“nedasasetofsingletrajectoryhypotheses,Theobjectiveofdataassociationistomaximizethepos-terioriprobabilityofgiventheobservationsetT|XX|TassumingthatthelikelihoodprobabilitiesareconditionallyindependentgiventhehypothesisItisdif“culttooptimizeEqn.directly,becausethespaceofishuge.However,wecanreducethesizeofthesearchspacebyusingtheobservationthatoneobjectcanonlybelongtoonetrajectory.Thistranslatesintotheconstraintthatcannotoverlapwitheachother,Ifwefurtherassumethatmotionofeachobjectisindepen-dent,wecandecomposeEqn.ThetermsinEqn.()arede“nedasfollows:isthelikelihoodfunctionofobservationBernoullidistributionisusedtomodelthecasesofanobser-vationbeingatruedetectionaswellasbeingafalsealarmistheprobabilityforbeingafalsealarm).modeledasaMarkovchain,whichincludesinitialization,terminationprobability,andtran-sitionprobabilities.ThepreciseformofthesefunctionsandtheirestimationfromtrainingdataaredescribedlaterinSection Notethatthelikelihoodfunctioncanmodelnotonlytheobservationsthatareassociatedin.truede-tections,butalsothosethatarenotassociated,.falsealarms.Thisallowsthemethodtoselectobservations,ratherthanassumealltheinputstobetruedetections,with-outadditionalprocessingtoremovefalsetrajectoriesafter3.2.Min-cost”owsolutionTocouplethenon-overlapconstraintswiththeobjectivefunction,thefollowing0-1indicatorvariablesarede“nedstartsfromendsatisrightafterItseasytoseethatthesevariablesaredeterminedforagivenassociationhypothesis,andviceversa.isnon-overlapifandonlyifNext,weincorporateindicatorsinlogarithmoftheob-jectivefunction,log(1subjecttoEqn.,where=log Thisformulationcanbemappedintoacost-”ownetworkwithsourceandsink.Givenanobservationset                       "#  $  $! & ' () $Figure2.Aexampleofthecost-”ownetworkwith3timestepsand9observations:foreveryobservation,createtwonodescreateanarcwithcostand”ow,anarcs,uwithcosts,uand”ows,u,andanarcwithcostand”ow.Foreverytran-,createanarcwithcostand”ow.AnexampleofsuchagraphisshowninFigure.Eqn.isequivalenttothe”owconservationconstraintandEqn.tothecostof”owin.Findingoptimalassociationhypothesisequivalenttosendingthe”owfromsourcetosinkminimizesthecost.Thecost-”ownetworkformulationisanintuitiverepre-sentationofmultipleobjecttracking:each”owpathcanbeinterpretedasanobjecttrajectory,theamountofthe”owsentfromisequaltothenumberofobjecttrajectories,andthetotalcostofthe”owoncorrespondstothelog-likelihoodoftheassociationhypothesis.The”owconser-vationconstraintguaranteesthatno”owpathsshareacom-monedge,andthereforenotrajectoriesoverlap.Ifalltheedgecostsinwerepositive,themin-cost”owwouldbethetrivialemptyzero-cost”ow.However,foranyobserva-thatismorelikelytobeatruedetection(thecostofedgeisnegative;thisallowstheop-timalcosttobecomebelowzerobysending”owsthroughthesenegative-costedges.Theoptimalcostshouldbecalculatedoverallpossible,whereistheamountof”owsentfromsourcetosink.Itisknownthatforagiven,theminimalcostcanbesolvedforinpolynomialtimebyamin-cost”owalgorithm[].Theentireoptimizationprocessisde-scribedasAlgorithm1.Itcanalsobeproventhatthemin-imalcostisaconvexfunctionw.r.t.Hencetheenu-merationoverallpossiblecanbereplacedbyaFi-bonaccisearch,which“ndstheglobalminimalcostbyatexecutionsofthemin-cost”owalgorithm.|X|bethenumberofedgesin,which ConstructthegraphV,E,C,ffromobservationsetStartwithempty”owWHILE(canbeaugmented)byone.Findthemincost”owbythealgorithmof[IF(currentmincostglobaloptimalcost)Storecurrentmin-costassignmentasglobaloptimum.Returntheglobaloptimal”owasthebestassociationhypothesis Algorithm1:FindMAPtrajectoriesbymin-cost”ow.growslinearlywith.Letbethenumberofexecu-tionsofthemin-cost”owalgorithm,whichisboundedlog(.Therunningtimeofourmethodisthecomplexityofthemin-cost”owalgorithm.Oneef-“cientmin-cost”owalgorithmisthescalingpush-relabelmethodproposedbyGoldberg[](weusetationfromAndrewGoldbergsNetworkOptimizationLi-braryathttp://www.avglab.com/adrew/soft.html).Thisal-gorithmhasaworst-caserunningtimeof,butusuallytakesmuchlesstimeonrealdata.We“ndthattheruntimegrowsonlylinearlywiththenumberofobserva-tionsasshowninSection;likelybecauseofthenatureofthenetworkwheretransitionsbetweenobservationsaretemporallyconstrained.Algorithm1providesageneralframeworkfordataasso-ciation.Differentfrommethodswhicheitheroptimizeeachtrajectoryseparatelyorsufferfromthecombinatorialexplo-sionofthehypothesesspace,thismethodisableto“ndtheglobaloptimumef“ciently.Next,weextendourmethodtotrackthroughlong-termocclusions.4.Explicitocclusionmodel(EOM)TheformulationinSectioniscapableoftrackingshort-termmisseddetections,includingthosecausedbyocclu-sion.However,long-termocclusions,ifjusttreatedasmissingdata,cannotbehandledwithoutimpairingperfor-mance.Ifweallowassociationofobservationswithalargetemporalgapbetweenthem,thepossibilityofcreatinger-rantassociationalsoincreases.Toeffectivelytrackthroughlong-termocclusions,weproposetoreasonexplicitlyaboutwhichobjectsmaybeoccludingwhichothersbyconstruct-inganExplicitOcclusionModel(EOM).TheEOMgener-atesasetofocclusionhypothesesandcombinesthemwiththeinputobservationsbyasetofocclusionconstraints.Onlyocclusionsbetweentrackedtargetsareaddressed. ))))51x               ,   //// ////51 f Figure3.Anexampleofaddingoccludedobjecthypothesiscorrespondingchangesinthecost-”ownetwork:thesolidrectan-glesareinputobservations;thedashed-linerectangleisancludedobjecthypothesis4.1.OcclusionhypothesesandconstraintsThe“rststepofEOMistoexpandtheobservationsetbyaddingoccludedobjecthypothesisWesaythatobservationdirectlyoccludableandonlyifthedistanceandscaledifferencearebelowcertainthresholds,andde“nethecorrespondingoccludedobjecthypothesisarethepositionandtimestepof,andarethesizeandappearanceofForeverypair)insuchthat)isdirectlyoccludable,generateanewcludedobjecthypothesisandaddittotheobservation.Repeatthisuntilnonewhypothesescanbegener-ated.Theprocedureofaddinghypothesesisillustratedinbetheobservationsetobtainedbyexpandingtheasabove.NotethatX||X|afteralldu-plicatehypothesesareremoved;thenumberofobservationdoesnotgrowexponentially.Inpractice,hypothesesthataresimilarinappearanceandsizearemergedbymean-shiftclusteringtofurtherreducethesizeofInthesecondstepofEOM,theproposedMAPformu-)isappliedagaintotheset,exceptfortwodifferences:“rst,thereisnoobservationlikelihoodtermforanyhypothesis;second,asetofocclusionconstraintsareimposedasistheindicatorfunctionforthehypothesisAsanycanbeonly0or1,theseconstraintsguarantee thatanoccludedobjecthypothesiscanbeused()inassociationonlyiftheobjectthatoccludesitisalsousedSincetheobjectivefunctionremainsunchangedthroughtheextension,wecanstilloptimizeEqn.,subjecttoandthenewconstraintEqn..WesolvetheEOM-baseddataassociationbyusinganiterativeapproachbuiltonAlgorithm1.4.2.AniterativesolutionAlgorithm1providesanoptimalsolutionwhenobjectsarenotoccluded.Toaccountforocclusions,wetakethetra-jectoriesfoundbytheAlgorithm1tobetruetrajectoriesandaddhypothesesthatareoccludedbythesetruetrajectoriestothenetwork.Algorithm1isthenappliedtotheexpandednetwork.Thisprocessisrepeatedtoinferocclusionsandassociationsiteratively.Moreprecisely,“rsttheoriginalMAPformulationwiththeinputobservationsetissolvedwiththeAlgorithm1.betheoptimalassociationhypoth-esis.Foranyobservation,theindicatoris“xedtobe1.Thenoccludedobjecthypothesisisgen-eratedforanythatisdirectlyoccludable.LettheexpandedobservationsetbeX {.Becauseareboundto1,theocclusionconstraintsforanyholdau-tomatically.Therefore,insteadofhavingasetofocclusionconstraints,wenowhaveisequivalenttoasetoflowerboundconstraintsonthevaluesofinthecost-”ownetwork.Sincethemin-cost”owwithlowerboundconstraintscanstillbesolvedbythesamealgorithm[],Algorithm1canbeap-pliedagaintosolvetheoptimaldataassociationonconstraintsEqn..Theprocedureofestimatingmin-cost”owandexpandingobservationsetisrepeateduntilconver-genceorapresetmaximumnumberofiterationisreached.TheapproachisdescribedasAlgorithm2inTable.Inpractice,we“ndthatthealgorithmusuallyachievesitsop-timalperformanceaftertwoiterations.OcclusioneventscanbeinferredfromtheoutputofAl-gorithm2whenanoccludedobjecthypothesisisusedinthesolution,whileamisseddetectionisinferredwhenthereistemporaldiscontinuityintheassociation.Basedonthis,wecaninfereventsofocclusionandmisseddetectionasshowninourresults(FigureDifferentfrompreviousworkssuchas[],whichmodelocclusionthroughsplittingandmergingofthetra-jectories,ourmethodgeneratesocclusionhypothesesex-plicitlytorecovertheobservationsthatismissingduetoocclusions,andthereforegivesamoreuni“edapproachbe-causerecoveredobservationsaretreatedinthesamewayasinputobservations. betheinputobservationsetLetlowerboundconstraintsetSolveusingAlgorithm1withconstraintForeachforanydirectlyoccludableXX{WHILEnot(convergedormaxnumberofiterationreached)Returnthe“naloptimal”owassignment Algorithm2:FindMAPtrajectorieswithocclusionreasoning.5.ImplementationdetailsInthissection,wedescribetheestimationofthefourinourframework.Astheyaredirectlyrelatedtotheinputobservations,theycanbeestimatedfromthetrainingdatastatistically.arede“nedasmissdetectionrateofthedetectornumberoftrajectories numberofhypothesesAsthenumberoftrajectoriesisdatadependent,anEMap-proachisusedtoestimateduringtheopti-Themodelofisde“nedtoemploytheinformationfromobservationsbyThetermsontherightcorrespondtosize,position,appear-anceandtimegaprespectively,whereconditionalindepen-denceoftheothertermsisassumedgiventimeinterval,exceptbetweenscaleandposition.Thepositionandsizetermsareassumedtobenormaldistributions;theyarelearnedfromtrainingdata.Fortheappearanceterm,twoRGBhistograms,areextractedfromthedetectionresponsestively,andisde“nedbasedontheBhattacharyya arethenormaldistri-butionsofbetweenthesameobjectanddifferentobjectsrespectively;theyarelearnedfromtrainingdata. Thetimegapcomponentisde“nedbyanexponentialmodelbasedonthemissingrateofthedetectorasisthemaximalallowedtimegap.6.EvaluationsInthissection,weshowresultsofourmethodontwodatasets:theCAVIARvideos[]andtheETHMobileScene(ETHMS)[].Bothdatasetareverychallengingbe-causeoftheheavyocclusionsandpoorimagecontrastfrombackground.Ourmethodisevaluatedbyitstrackingper-formance,detectionperformanceandspeed.OurmethodiscomparedwithWuetal.s[]onCAVIAR,astheyhavere-portedthebesttrackingresultonthedataset.OnETHMSitiscomparedwithEssetal.sdetectionmethod[],asitistheonlymethodevaluatedonthedataset.Theresultsshowgoodperformance,withfewerfalsealarmsandtrajectoryfragmentsthanthepreviousmethods.Ourmethodisalsomoreef“cientcomparedtootherglobalmethods.6.1.ExperimentsettingsTheCAVIARdatasetincludes26videosequencesofawalkwayinashoppingcentertakenbyasinglecamerawithframesizeofandframerateof25fps.TheETHMSdatasetincludes4videosequencesofstreetscenestakenbyamovingcamera,withframesizeofframerateof15fps.Bothdatasetincludemanyinter-personocclusionsincrowdedscenes,withpoorcontrastbetweenobjectsandbackground.ForCAVIAR,weteston20videos(25587framestotal)andusetheother6videosfortraining.ForETHMS,wetestonsequence#1(999frames)andusetheother3videosfortraining.Theinputobservationsetisfromtheoutput“lesofthehumandetectorbyWuetalal2].However,wedonotmakeuseofthepart-basedreason-ingproposedin[],buttakeallthedetectionresponsesinthe“lesasourinputset.Peoplethataretoosmallintheimages(lessthan24pixelinwidth)orpartiallyoutofthescenearenotcountedintheevaluation.6.2.TrackingPerformanceWeevaluatethetrackingperformanceaccordingtothefollowing“vemetricsproposedin[mostlytrackedtrajectories(MT),thenumberoftrajec-toriesthataresuccessfullytrackedformorethan80%;mostlylosttrajectories(ML),thenumberoftrajecto-riesthataretrackedforlessthan20%;partiallytrackedtrajectories(PT),thenumberoftrajec-toriesthataretrackedbetween20%and80%;fragmentation(FRMT),thenumberoftimesatrajec-toryisinterrupted;IDswitches(IDS),thenumberoftimestwotrajectoriesswitchtheirIDs.TheresultsonCAVIARareshowninTable,whereGTisthenumberoftrajectoriesinthegroundtruth. GT MT PT ML FRMT IDS etal 140 106 25 9 35 17 Algorithm1 140 104 29 7 58 7 Algorithm2 140 120 15 5 20 15 Table1.ComparisonofthetrackingresultsonCAVIARdatasetComparedtotheresultin[],Algorithm1outputsmorePTandmoreFRMTbecauseithasnoocclusionmodel,whileEOM-basedAlgorithm2connectsalargeportionofthetrajectoryfragmentstoyieldmoreMT.SomepictorialresultsaregiveninFiguretoshowthattheEOM-basedAlgorithm2canrecovertrajectoriesfromfullocclusions.InFigure,Object#4isoccludedbyobject#5foralongtimebetweenframe301and389,butisstilltrackedbyAl-gorithm2.Resultimagesalsoshowourmethodprovidereasoningofocclusionsandmisseddetectionsexplicitly.showsthatourmethodcanrecovertrajectoriesinsomecomplicatedcaseswithmanyfullocclusions.6.3.DetectionPerformanceWecomparethedetectionrateandfalsealarmsofourmethodwiththeinputobservationsetandpreviousresultsresults2,14]inTable.ItshowsthatAlgorithm1increasesthedetectionrateandreducesfalsealarmssigni“cantlycom-paredtotheinputobservationset;Algorithm2furtherim-provesthedetectionratebutwithaslightlyhigherfalsealarmrate.TheimprovementofAlgorithm2ondetectionrateisnotsigni“cantbecausethenumberoffullyoccludedhumansintheentiretestsetisrelativelysmall.BothAlgo-rithm1and2givebigimprovementsinthefalsealarmratescomparedtothepreviousmethods,whilethedetectionratesaresimilar.Becauseourmethoddoesnotuseadditionalwaysto“lldetectiongapssuchasthemean-shifttrackerinin2],itcannotrecoveratrajectoryifanobjectisnotdetectedformanyconsecutiveframes.6.4.SpeedWehavemeasuredexecutionspeedofthemethodonsomeCAVIARvideoswhichtypicallyhaveseveralobjectstobetrackedineachframe,thetrajectoriesareusuallylongaspeoplewalkalongthecorridorandtherearepersistentocclusions.Theprocessingtimeoftheobjectdetectorisnotcountedhere.Eventhoughthetheoreticalcomplexityforthemin-cost”owalgorithmispolynomial,we“ndthat 0   0   0   0   Figure4.DetectioninputsandtrackingresultsonCAVIAR[]:ourmethodcanremovefalsealarmssuchasinframe301,recovermisseddetectionsuchasinframe258,andtrackthroughheavyocclusionssuchasinframe301and389. Dataset Method Detectionrate FalseAlarmperframe CAVIAR Inputobservationset 72.8% 0.270 etal 75.2% 0.281 Algorithm1 74.3% 0.081 Algorithm2 76.4% 0.105 ETHMS Inputobservationset 64.3% 1.54 etal 47% 1.5 Algorithm1 68.3% 0.85 Algorithm2 70.4% 0.97 Table2.DetectionandfalseAlarmrateonCAVIARdatasetthecomplexitygrowsonlylinearlywiththenumberofob-servationsinAlgorithm2.Inoneexample,thereare7000inputobservationsoverasequenceof3500frames,.140seconds,Algorithm1“ndstheglobaloptimumin30sec-ondsusinga3.7GHzPC.Algorithm2,appliedtothesamedata,expandstheinputsetwith11000occludedobjecthy-potheses,and“ndsasolutioninabout2minutes.Henceourmethodisreal-timeandthetotaltimeislikelytobedominatedbythedetectionstep.Becauseoftheef“ciencyofouralgorithms,weprocesseveryvideoinCAVIARdatasetglobally,withoutpartition-ingorusingaslidingwindowaswouldbenecessaryforthepreviouscombinatorialalgorithms.Slidingwindowtech-niquesmaystillbeusefulifmuchlongersequencesaretobeprocessedoronlineresultsarerequired.7.ConclusionWehavepresentedanoveldataassociationframeworkformultipleobjecttrackingthatoptimizestheassociationgloballyusingalltheobservationsfromtheentiresequence.Falsealarms,initializationandterminationofthetrajectory,andinferenceofocclusionsismodeledintrinsicallyinthemethod.Anoptimalsolutionisprovidedbasedonthemin-costnetwork”owalgorithms.Thoughthecomplexityofthealgorithmsispolynomial,inpractice,we“ndthemtobehighlyef“cient.Experimentresultsindicatethatglobaldataassociationishelpful,especiallyforreducingtrajec-toryfragmentsandimprovingtrajectoryconsistency,whilemaintainingef“ciency.Theframeworkisgeneralandcanbeeasilyadaptedtoapplytotrackinganyclassofobjectsforwhichreasonabledetectorsareavailable.8.AcknowledgementThisresearchwassupported,inpart,bytheOf“ceofNavalResearchunderContract#N00014-06-1-0470.Theviewsexpressedheredonotnecessarilyre”ectthepositionorthepolicyoftheUnitedStatesGovernment.ReferencesencesZ.Khan,T.Balch,andF.Dellaert,MCMC-basedparti-cle“lteringfortrackingavariablenumberofinteractingtar-PAMI,vol.27,no.11,2005.2005.B.WuandR.Nevatia,Trackingofmultiple,partiallyoc-cludedhumansbasedonstaticbodypartdetectionŽ,detectionŽ,D.B.Reid,AnalgorithmfortrackingmultipletargetsŽ,Trans.onAutomaticControl,1979.1979.Y.Bar-Shalom,T.Fortmann,andM.Scheffe,Jointprob-abilisticdataassociationformultipletargetsinclutterŽ,inInformationSciencesandSystems,1980.1980.J.Berclaz,F.Fleuret,andP.Fua,RobustpeopletrackingwithglobaltrajectoryoptimizationŽ,in,2006. 0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   Figure5.FirstandsecondrowarethedetectionandtrackingonETHMS[];“fthtoseventhrowaretrackingonCAVIAR[VIAR[L.Zhang,B.Wu,andR.Nevatia,DetectionandtrackingofmultiplehumanswithextensiveposearticulationŽ,ininH.Jiang,S.Fels,andJ.J.Little,AlinearprogrammingapproachformultipleobjecttrackingŽ,,2007.2007.A.G.AmithaPerera,C.Srinivas,A.Hoogs,G.Brooksby,andW.Hu,Multi-objecttrackingthroughsimultaneouslongocclusionsandsplit-mergeconditionsŽ,,2006.2006.Q.Yu,G.Medioni,andI.Cohen,Multipletargettrackingusingspatio-temporalmarkovchainmontecarlodataassoci-,2007.2007.B.Leibe,K.Schindler,andL.VanGool,Coupleddetectionandtrajectoryestimationformulti-objecttrackingŽ,trackingŽ,R.Ahuja,T.Magnanti,andJ.Orlin,NetworkFlows:Theory,Algorithms,andApplications,PrenticeHall,1993.1993.A.V.Goldberg,Anef“cientimplementationofascalingminimum-cost”owalgorithmŽ,J.Algorithms,1997.1997.http://homepages.inf.ed.ac.uk/rbf/CAVIARDATA1Ž.6,7,8[14]A.Ess,B.Leibe,andL.VanGool,DepthandappearanceformobilesceneanalysisŽ,in,2007.