Mean Shift Tracking.pdf

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1、MeanShiftTrackingCS4243ComputerVisionandPatternRecognitionLeowWeeKhengDepartmentofComputerScienceSchoolofComputingNationalUniversityofSingapore(CS4243)MeanShiftTracking1/28MeanShiftMeanShiftMeanShift[Che98,FH75,Sil86]Analgorithmthatiterativelyshiftsada

2、tapointtotheaverageofdatapointsinitsneighborhood.Similartoclustering.Usefulforclustering,modeseeking,probabilitydensityestimation,tracking,etc.(CS4243)MeanShiftTracking2/28MeanShiftConsiderasetSofndatapointsxiind-DEuclideanspaceX.LetK(x)denoteakernelfu

3、nctionthatindicateshowmuchxcontributestotheestimationofthemean.Then,thesamplemeanmatxwithkernelKisgivenbyXnK(x−xi)xii=1m(x)=(1)XnK(x−xi)i=1Thedifferencem(x)−xiscalledmeanshift.Meanshiftalgorithm:iterativelymovedatepointtoitsmean.Ineachiteration,x←m(x).T

4、healgorithmstopswhenm(x)=x.(CS4243)MeanShiftTracking3/28MeanShiftThesequencex,m(x),m(m(x)),...iscalledthetrajectoryofx.Ifsamplemeansarecomputedatmultiplepoints,thenateachiteration,updateisdonesimultaneouslytoallthesepoints.(CS4243)MeanShiftTracking4/28

5、MeanShiftKernelKernelTypically,kernelKisafunctionofkxk2:K(x)=k(kxk2)(2)kiscalledtheprofileofK.PropertiesofProfile:1kisnonnegative.2kisnonincreasing:k(x)≥k(y)ifx

6、sofkernels[Che98]:Flatkernel:1ifkxk≤1K(x)=(4)0otherwiseGaussiankernel:K(x)=exp(−kxk2)(5)(a)Flatkernel(b)Gaussiankernel(CS4243)MeanShiftTracking6/28MeanShiftDensityEstimationDensityEstimationKerneldensityestimation(Parzenwindowtechnique)isapopularmetho

7、dforestimatingprobabilitydensity[CRM00,CRM02,DH73].Forasetofndatapointsxiind-Dspace,thekerneldensityestimatewithkernelK(x)(profilek(x))andradiushisnf˜1Xx−xiK(x)=Knhdhi=1!(6)Xn2=1kx−xinhdhi=1Thequalityofkerneldensityestimatorismeasuredbythemeansquarede

8、rrorbetweentheactualdensityandtheestimate.(CS4243)MeanShiftTracking7/28MeanShiftDensityEstimationMeansquarederrorisminimizedbytheEpanechnikovkernel:12(d+2)(1−kxk)ifkxk≤1KE(x)=2Cd(7)0otherwisewhereCdisthevolumeoftheunitd-Dsphere,withp