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11520065JournalofImageandGraphicsVol.11,No.5May,2006:(02153073):2005203217;:2005209212:(1978),2004,E2mail:rocsovsky@163.comMeanShift(,710072)MeanShift,,,MeanShift,,,,;,,,,:TP391.41:A:100628961(2006)0520707207RobustTrackingofObjectsinImageSequencesUsingMultipleDegreesofFreedomMeanShiftAlgorithmJIAJing2ping,CHAIYan2mei,ZHAORong2chun(SchoolofComputer,NorthwesternPolytechnicalUniv.,Xian710072)AbstractCurrentMeanShifttrackingalgorithmusesasingleradiusparametertodescribethescaleofthetarget,andEachtargethasthepositionandsizefreenessonly,whichisnotsuitableforcomplexmovementsoftheobjects.Inthispaperweprovideanewalgorithminwhichabandwidthmatrixisemployedtodescribetheobjectswithtwodirectionsdeterminedindependently.Target2angleisalsointroducedtoaccommodatetherotationofobjects.Furthermorewebringforwardanefficientsearchstrategytocopewithatemporalocclusionoftheobjects.Experimentalresultsshowthatthenewalgorithmisabletoadapttoanykindofobjectsmovementsandthereforehasbettertrackingprecision.KeywordsMeanShift,trackingofobjectsinimagesequences,target2angle,bandwidthmatrix,adaptability1,,,,,,[1]MeanShift,,,,,,©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[2]DOG2Epanichnikov,,,MeanShift,[1][2],h,,,,2MeanShiftMeanShift,[3],MeanShift,2nXiR2,i=1,,n22H,K(X)[3]f^H,K(X)=1nH1/2ni=1K(H-1/2(X-Xi))(1)K(X),R2K(X)dX=1limXX2K(X)=0R2XK(X)dX=0R2XXTK(X)dX=cKIcKK(X),Hdiag[h2H,h2V],K(X),K(X)=ckk(X2),k(x)x0k(x)K(X)(profile),ckk(x)f^H,k(X)=cknH1/2ni=1k(H-1/2(X-Xi)2)(2)k(x)[0,),g(x)=-k(x)g(x)G(X)=cgg(X2),cgg(x),f^H,g(X)=cgnH1/2ni=1g(H-1/2(X-Xi)2)(3)ý^fH,k(X)ýf^H,k(X)=cknH1/2ni=1ýk(H-1/2(X-Xi)2)=2cknH1/2H-1ni=1(X-Xi)k(H-1/2(X-Xi)2)(4)mH,G(X)=ni=1Xig(H-1/2(X-Xi)2)ni=1g(H-1/2(X-Xi)2)-X(5)MeanShift(3)ý^fH,k(X)=2ckcgH-1f^H,g(X)mH,G(X)(6)mH,G(X)=cgHý^fH,k(X)2ckf^H,g(X)(7)Epanechnikov:KE(X)=2V(1-X2)X10,V,kE(x)=1-x0x10,gE(x)=10x10[1],,MeanShift,K(X)=KE(X),mH,G(X)MeanShift,ý^fH,k(X)=0,(1):MeanShift,G(X){Yj}j=1,2,,(7),Y1,G(X)YjYj+1=ni=1Xig(H-1/2(X-Xi)2)ni=1g(H-1/2(X-Xi)2)(8)K(X){f^H,K(j)}j=1,2,,f^H,K(j)=f^H,K(Yj)j=1,2,,MeanShift{mH,G(j)}j=1,2,,mH,G(j)=Yj+1-YjK(X)=KE(X)(kE(x),),{mH,G(j)}j=1,2,{f^H,K(j)}j=1,2,[4][1]{Yj}j=1,2,,Yj+1-Yj,{Yj}j=1,2,,,([5]){mH,G(j)}j=1,2,©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:,hHhVx(xc,yc),(xt,yt)(1),,xy1Fig.1Targetrectangle{Xi}i=1,,n,(xc,yc)b:R2{1,,m},Xi,b(Xi)Epanechnikov,u=1,,mpu(Y)=CHnhi=1k(H-1(Y-Xi)2)[b(Xi)-u](9)Kronecker,CHH,mu=1pu=1,CH=1nhi=1k(H-1(Y-Xi)2)(nh)h,H=diag[h2H,h2V],hH,hVXidHdV,,H-1(Y-Xi)2=4(xt-xc)2h2H+(yt-yc)2h2V4d2Hh2H+d2Vh2V[1]{Xi}i=1,,n,0,(hH,hV)Epanechnikov,u=1,,mqu=Cni=1k(Xi2)[b(Xi)-u](10)Bhattacharyya[6](Y)[p(Y),q]=mu=1pu(Y)qu(11)d(Y)=1-[p(Y),q](12),,,,,Y,Y0,[p(Y),q]Y0,[p(Y),q]:[p(Y),q]12mu=1pu(Y0)qu+12mu=1pu(Y)qupu(Y0)(13)(9)(13)[p(Y),q]12mu=1pu(Y0)qu+CH2nhi=1wik(H-1(Y-Xi)2)(14)wi=mu=1[b(Xi)-u]qupu(Y0)(15),(12)d(Y),(14)2,Yk(x),wiMean2Shift,Y0Y1:Y1=nhi=1Xiwig(H-1(Y-Xi)2)nhi=1wig(H-1(Y-Xi)2)=nhi=1Xiwinhi=1wi(16)'1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(14),k+1,MeanShift,,,[7],,(2)2Fig.2Searchstrategy2k0(2),,k+1A,,Mean2Shift,1,Bhattacharyya,1,,0,1,2,,([8]),,,,,,81,20(48)5(TrackOnce):{qu}u=1,,m,Y0,Y1:(1)Y0{pu(Y0)}u=1,,m,[p(Y0),q]=mu=1pu(Y0)qu;(2){wi}i=1,,m;(3)MeanShift,Y1=nhi=1Xiwig(H-1(Y-Xi)2)nhi=1wig(H-1(Y-Xi)2)=nhi=1Xiwinhi=1wi(4){pu(Y1)}u=1,,m,[p(Y1),q]=mu=1pu(Y1)qu(5)[p(Y1,q],Y112(Y0+Y1),[p(Y1),q][p(Y0),q];(6)Y1-Y0,,Y0Y1,(2)Y0Y1(TrackOnce),(TrackNormal):(1)3,,10,3Bhattacharyya,;(2)3,hH,hH10%,3Bhattacharyya,hH;(3)3,hV,hV10%,3Bhattacharyya,hV,3,,,hHhVIIR:(1)(TrackNormal),BhattacharyyaTG(G),,,(2);©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(2)1,BhattacharyyaTP(P),(TrackOnce),BhattacharyyaTG,,(3);(3),1,2,BhattacharyyaTP,(TrackOnce),BhattacharyyaTG,,6,,3143320320,RGB161616,,104,3,105,,,143,,,4[1],,,5,376320240,,(),,204,,,,6,,7[1]7,154162,,,168,,[1]MeanShift,TG=015,TP=013©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.[1][2],,,13Tab.1Thecomparisonofthethreealgorithms2520(ms)[1]4080,[2]120200,50180,,©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(References)1ComaniciuDorin,RameshVisvanathan,MeerPeter.Real2timetrackingofnon2rigidobjectsusingmeanshift[A].In:ProceedingsoftheIEEEConforenceonComputerVisionandPatternRecognition[C],HiltonHeadIsland,SouthCarolina,USA,2000,2:142149.2CollinsRobertT.Mean2shiftblobtrackingthroughscalespace[A].In:Proceedingsofthe2003IEEEComputerSocietyConferenceonComputerVisionandPatternRecognition[C],Madison,Wisconsin,USA,2003,2:234240.3ComaniciuDorin,MeerPeter.MeanShift:Arobustapproachtowardfeaturespaceanalysis[J].IEEETransactionsonPatternAnalysisandMachineIntelligence,2002,24(5):603619.4JiaJing2ping,ZhaoRong2chun.Track