基于支持矢量机和信任域的目标跟踪算法

()(),20081,2008203230ActaScientiarumNaturaliumUniversitatisPekinensisOnLineFirst,No.1,Mar.30,2008(PaperCode):pkuxbw2008012http:PPbdxbw.chinajournal.net.cn863(2004AA13020):2007209206;:200721221211,­21,100871;2,100084;­,E2mail:[e-mail],SVM(),SVM,,,QP-TRLaplacian,,,,SVM;;Laplacian;QP-TRTP391ObjectTrackingbyUsingSVMandTrust2RegionMethodthroughScale2SpaceJIAJingping1,ZHANGFeizhou1,­,CHAIYanmei21InstituteofRemoteSensing&GeographicInformationSystem,PekingUniversity,Beijing100871;2DepartmentofComputerScienceandTechnology,TsinghuaUniversity,Beijing100084;­CorrespondingAuthor,E2mail:[e-mail]blemistackledfromtheviewpointofpatternclassification.Anewapproachoftrackingobjectsinimagesequencesisproposed,inwhichtheconstantchangesofthetargetpssizecanbepreciselydescribed.Foreachinputtframe,aprobabilitydistributionimageofthetargetiscreatedthroughtheclassificationofeachpixelbySVM,wherethetargetpsareaturnsintoablob.Thescaleofthisblobcanbedeterminedbasedonlocalmaximumofdifferentialscale2spacefilters.ThentheQP-TRtrustregionalgorithmisemployedtosearchforthelocalmaximaofmulti2scalenormalizedLaplacianfilteroftheprobabilitydistributionimageforlocatingthetargetaswellasdeterminingitsscale.Inthepresentedtrackingexamples,thenewmethodcanbeusedtodescribethetargetmoreaccuratelyandthusachievesmuchbettertrackingprecision.KeywordsSupportVectorMachine;scale2space;multi2scalenormalizedLaplacian;QP-TRtrustregionalgorithm,,,,,[1],[2],,NBohyungHan[3]PCA76[4],,[527],,Lindeberg[8],,MeanShift[6],QP-TR[9],,QP-TRLaplacian,,1(SVM)Vapnik90[10]VC(VC,),,;,,l{(xi,yi),i=1,2,,l},xiRN(),(yi=1),(),(yi=-1),,()x,(x)+b=0,„f(x)=sign[(x)+b],,,[10],1,b,imin,b,i12T+Cli=1i,yi(T(xi)+b)1-i,i0,i=1,,l,(1),bR,i,C,C(1),maxli=1i-12li=1lj=1ijyiyjK(xi,xj),0iC,li=1iyi=0,(2)K(xi,xj)=(xi)(xj),bb=1NNSVxiJNyi-xjJjyjK(xj,xi),(3)NNSV,JN,J:„f(x)=signli=1iyiK(xi,x)+b(4)Mercer,[11]:1)K(xi,x)=xix;2)K(xi,x)=(xix+1)d;3)K(xi,x)=exp(-x-xi2P2),RBF;4)K(xi,x)=tanh(kxi.x+1SVMFig11Optimalseparatehyper2planeoftheSVMalgorithm86()()31),SigmoidRBF,SimplexCRBF[11]SVM,,Tobj,Tbkg,htwt,,max(ht,wt),,R,G,BSVM,SVM,,255,0,,,2,2(a),,,;2(b)SVM,;2(c);2(d)SVM,2Fig12Aprobabilitydistributionimage2Lindeberg,,[527],[5],,10%10%,,Lindeberg[8]Df:RDRD+1g:RDR+R,g(x;t)=1(2t)NP2e-x21++x2D2t,L:RDR+RfgL(;t)=g(;t)3f(),tL,:fff(x)=f(sx),LL,L(;t)=g(;t)3f(),L(;t)=g(;t)3f(),(5):x=sx,t=s2t,(6)L(x;t)=L(x;t)m9xmL(x;t)=sm9xmL(x;t)=xtP2,:9=tP29x,9=tP29x,(7)9mL(x;t)=sm(1-)9mL(x;t),(8)9mL(x;t)=1,9mL(x;t)=9mL(x;t),,f(x0;t0),,f(sx0;s2t0),,96pkuxbw2008012:3,,(x,y,t)Fig13Forblobswithdifferentsizes,(x,y,,t)assumeslocalmaximaatdifferentpositionswithdifferentscales,f,D=2,f:R2R=1,(t2L)2=(t2L)2=(t(Lxx+Lyy))2(blob)(x,y,t)=(t(Lxx(x,y)+Lyy(x,y)))2Laplacian,(x,y,t)3,,t=90,(x,y,t),t=391,(x,y,t),(x,y,t),31,,2(x,y,t),QP-TR(x,y,t)min(x,y,t)(x,y,t),(x,y,t)(x,y,t),:1),woho,wihi2)23),,11=wihohiwo,wihi4),25)x0=(xprev,yprev,tprev)T,(xprev,yprev),tprev0=9,end=011,MAXiter=10006)f(x)=-(x,y,t)QP-TR,xopt=(xopt,yopt,topt)T,(xopt,yopt),topt3)4,,4MeanShift[7]354320240MeanShift,,,,,5t,t,,607()()31,[7],3,217,3173494Fig14TrackingresultsofthePedestriansequence5tFig15ValuesoftforthePedestriansequence,[12],2,2053316Fig16TrackingresultsoftheCupsequence[13],333320240,,,,,5,SVMLindeberg,Laplacian,QP-TRLaplacian,,,LOG,,QP2TR,,,[1]ShiJ,TomasiC.GoodfeaturestotrackPPProceedingsoftheInternationalConferenceonCoputerVisionandPatternRecognition.Seattle,WA,1994:5932600[2]CollinsRT,LiuYanxi,LeordeanuM.Onlineselectionofdiscriminativetrackingfeatures.IEEETransactionson17pkuxbw2008012:PatternAnalysisandMachineIntelligence,2005,27(10):163121643[3]HanB,DavisL.ObjecttrackingbyadaptivefeatureextractionPPProceedingsofthe2004InternationalConferenceonImageProcessing.Singapore,2004,3:150121504[4]SternH,EfrosB.Adaptivecolorspaceswitchingforfacetrackinginmulti2coloredlightingenvironmentPPProceedingsoftheInternationalConferenceonAutomaticFaceandGesterRecognition.WashingtonDC,2002:2492254[5]ComaniciuD,RameshV,MeerP.Real2timetrackingofnon2rigidobjectsusingmeanshift.IEEEComputerVisionandPatternRecognition,2000,2:1422149[6]ComaniciuD,RameshV,MeerP.Kernel2basedobjecttracking.IEEETransactionsonPatternAnalysisandMachineIntelligence,2003,25(5):5642577[7]JiaJingping,ZhaoRongchun.TrackingofobjectsinimagesequencesusingbandwidthmatrixmeanshiftalgorithmPPProceedingsofthe7thInternationalConferenceonSignalProcessing.Beijing,2004,2:9182921[8]LindebergT.FeatureDetectionwithautomaticscaleselection.InternationalJournalofComputerVision,1998,30(2):792116[9]BerghenFV.Intermediatereportonthedevelopmentofanoptimizationcodeforsmooth,continuousobjectivefunctionswhenderivativesarenotavailable[EBPOL].(2003208)[2007208].http:PP[10]VapnikV,GolowichSE,SmolaA.Supportvectormethodforfunctionapproximation,regressionestimation,andsignalprocessing.AdvancesinNeuralInformationProcessingSystems,1997,9:2812287[11].[].:,2003[12]LjubomirJ,ButuroviC.PCP:Aprogramforsupervisedclassificationofgeneexpressionprofiles.Bioinformatics,2006,22(2):2452247[1