On-Line Density-Based Appearance Modeling for Object Tracking

Transcription

1 On-Line Densiy-Based Appearance Modeling for Objec Tracking Bohyung Han Larry Davis Dep. of Compuer Science Universiy of Maryland College Park, MD 2742, USA {bhhan, Absrac Objec racking is a challenging problems in real-ime compuer vision due o variaions of lighing condiion, pose, scale, and view-poin over ime. However, i is excepionally difficul o model appearance wih respec o all of hose variaions in advance; insead, on-line updae algorihms are employed o adap o hese changes. We presen a new on-line appearance modeling echnique which is based on sequenial densiy approximaion. This echnique provides accurae and compac represenaions using Gaussian mixures, in which he number of Gaussians is auomaically deermined. This procedure is performed in linear ime a each ime sep, which we prove by amorized analysis. Feaures for each pixel and recangular region are modeled ogeher by he proposed sequenial densiy approximaion algorihm, and he arge model is updaed in scale robusly. We show he performance of our mehod by simulaions and racking in naural videos. Inroducion One of he mos criical challenges in creaing robus visual rackers is he developmen of adapive appearance models ha can accommodae unsable lighing condiion, pose variaions, scale changes, view-poin changes, and camera noise. Many racking algorihms [4,, ] are based on a fixed arge model, and so are unable o rack over long ime inervals. Some effors have been made o overcome hese problems. In [], heurisics regarding he replacemen of he arge emplae are suggesed; Nummiaro e al. [4] updae he model by aking he weighed average of he curren and new hisograms. A view-based subspace model is implemened in EigenTracking [], bu i requires inensive offline learning before racking. Recenly, Ross e al. [7] propose an adapive racking algorihm ha updaes he models using an incremenal updae of eigenbasis. Insead of using a emplae or a hisogram for arge modeling, parameric densiy represenaions have been used in many racking algorihms. McKenna e al. [2] sugges Gaussian mixure models creaed by an EM algorihm for hisogram-based rackers, bu heir mehod requires knowledge of he number of componens, which may no be known in advance. Addiionally, i is no appropriae if here are a large number of modes in he underlying densiy funcion or he number of modes changes frequenly. In [7, 3], a pixelwise arge model based on Gaussian disribuion is proposed, and i is updaed during racking. However, his mehod canno model muli-modal densiy funcions accuraely. A more elaborae arge model is described in [9], where a 3- componen mixure for he sable process, he oulier daa and he wandering erm is designed o capure rapid emporal variaions in he model. The implemenaion of ha mehod allowed only a fixed number of componens, so, for example, i canno accommodae muliple sable componens since only one Gaussian is assigned o he sable componen. An imporan issue in arge model updae is he balance beween adapiveness o new observaions and resisance o noise. Since he arge model may drif away by undesirable updaes, only arge pixel observaions should be inegraed ino he model. From his poin of view, a probabiliy densiy funcion of visual feaures is a good soluion for arge modeling, because frequenly observed daa conribue he mos significan par while ouliers can have limied effecs on he inegriy of he model. We presen an on-line densiy-based appearance model for objec racking which is more flexible han previously published parameric mehods. The densiy funcion is composed of a mixure of Gaussians, where all of he parameers such as he number of modes, means, covariances, and weighs are deermined by a mean-shif algorihm [2, 3]. The mehod can represen he densiy funcion very accuraely wih a minimal amoun of memory. Whenever a new observaion is incorporaed ino he curren model, he densiy funcion is updaed in an on-line manner. This procedure is performed in linear ime; he ime complexiy is proved by amorized analysis. Color feaures a each pixel are modeled by a Gaussian mixure, and color recangular feaures are also inegraed in he densiy funcion o encode he local spaial informaion of a pixel. We also describe a model updae procedure in scale space using densiy approximaion echnique, so ha he racker can deal wih scale changes robusly. This paper is organized as follows. Secion 2 inroduces

2 he linear ime sequenial densiy approximaion echnique, and demonsraes is performance by simulaion. Secion 3 describes how o consruc he appearance model adapively, and experimens for objec racking in video are presened in secion 4. 2 On-line Densiy Approximaion Gaussian mixures are frequenly used o esimae densiy funcions, and several heurisics o deermine he number of componens have been proposed [, 6, 8]. However, i is exremely difficul o find he number of Gaussians in a principled way for on-line applicaions since previous daa are no ypically available a he curren sep due o memory consrain. In his secion, we presen an ieraive procedure for sequenial densiy approximaion o manage a Gaussian mixure densiy funcion adapively. Then, a more efficien algorihm is presened and is ime complexiy is discussed. Secion 2. presens he naive sequenial densiy approximaion mehod, while secion 2.2 presens a subsanially faser algorihm. In secion 2.3, he performance of our sequenial densiy approximaion echnique is invesigaed by various simulaions. 2. Sequenial Densiy Approximaion Assume ha a ime he underlying densiy is a mixure of Gaussians having n modes and ha for each mode we have allocaed a Gaussian N(κ i, x i, P i ), i =,...,n,where N( ) is Gaussian disribuion wih he parameer (weigh, mean, covariance). For he momen, selec a learning rae α and assume ha all incoming daa become par of he model. Le N(α, x n+, P n+ ) be a new measuremen. Wih he inegraion of he new measuremen, he densiy a ime +is iniially wrien as ˆf + (x) = ( α) (2π) d/2 α + (2π) d/2 P n+ where n i= exp /2 κ i P i ( ( exp /2 2 D2 ( x, x n+ ( 2 D2 x, x i, ) ) Pi, P n+ ) ) () D 2 ( x, x i, Pi ) (x x i ) (P i ) (x x i ) (2) is he Mahalanobis disance beween x and x i. To find he new mode locaions in ˆf + (x), we perform mean-shif ieraions unil convergence for each x i, i =...n +. The variable-bandwidh mean-shif vecor a locaion x is defined by m(x) = ( n+ i= ) ( n+ ω i (x)(pi ) i= ω i (x)(pi ) x i ) x (3) where he weighs ω i (x) = κ i P i /2 exp ( ( )) 2 D2 x, x i, P i n+ i= κi Pi /2 exp ( ( 2 D2 x, x i, )) Pi (4) saisfy n + i= ωi (x) =. We selec firs he convergence locaions a which more han one procedure or x n+ converged. Le y be a poin in his se and le x j, j =...m be he saring locaions for which he mean shif procedure converged o y. If he Hessian Ĥ(y) = ( ) ˆf + (y) is negaive definie, we associae wih he mode y a Gaussian componen defined by N(κ y, y, P(y)) where κ y is he sum of x j s weighs (j =...m) and he covariance marix P(y) is given by κ 2 d+2 y P(y) = 2π( Ĥ(y) ) ( Ĥ(y) ) () d+2 The basic idea of equaion () is o fi he covariance using he curvaure in he neighborhood of he mode. A ime +, he Gaussian componens locaed a x j (j =...m) will be subsiued for by he new Gaussian N(κ y, y, P(y)). If he Hessian Ĥ(y) is no negaive definie (i.e., he locaion y is eiher a saddle poin or a local minimum), all he componens associaed wih x j, j =...m are lef unchanged since he Gaussian approximaion in he neighborhood of y would yield oo high an error. For he convergence locaions a which only one procedure converged (excep he ), he weigh, mean and covariance of he associaed Gaussian componen are also lef unchanged. The new parameers in Gaussian mixure ˆf + (x) are deermined by a mode finding algorihm based on mean-shif and covariance esimaion mehod in equaion (), and he updaed densiy funcion is hen given by convergence locaion for x n+ ˆf + (x) = n + (2π) d/2 i= κ i + exp /2 ( ( 2 D2 x, x i +, ) ) Pi + P i + (6) where κ i +, x i +,andp i + are weigh, mean, and covariance of each componen a +, respecively. 2.2 Linear Time Algorihm for Sequenial Approximaion The sequenial densiy approximaion echnique described in he previous secion akes O(n 2 ) ime in each sep, where n is he number of modes a ime sep. Now, we relax he consrain ha he number of Gaussian componens is equal o he number of modes in he densiy funcion, and improve he ime complexiy o linear ime. As a resul, he number of Gaussian componens may be slighly more han he compac represenaion inroduced in secion 2., bu he sequenial densiy approximaion is performed much faser asympoically.

3 Recall equaion (). The previous algorihm runs he meanshif procedure for all of n +componens, and finds convergence poins for all of hem. Then, i finds he mode associaed wih he new daa, and updaes ha mode. So, if we could idenify hose modes ha would merge wih he new daa efficienly, hen he execuion ime can be reduced. This echnique is explained nex Algorihm Descripion Given he n +modes in he +s sep, we firs search for he convergence poin c n+ of x n+ in he densiy ˆf + (x) of equaion (). Now, we have o find which oher modes converge o c n+ and should be merged wih x n+. The candidaes o converge o c n+ are deermined by meanshif, and his procedure is repeaed unil no candidae converges o c n+. The firs candidae mode is he convergence poin x i (i =...n ) from x n+ in he densiy funcion ˆf +(x) = ˆf + (x) N(α, x n+, P n+ ). Noe ha all he candidaes are one of he componens in he previous densiy funcion ˆf (x). The mean-shif procedure is performed for x i in ˆf + (x), and we check if he convergence poin of x i is equal o c n+. If hey are no equal, we conclude ha here are no furher merges wih x n+ and creae a Gaussian for he updaed mode; oherwise, we check he nex candidae, which is deermined by finding he nex convergence poin of x n+ in he densiy funcion ˆf + (x) = ˆf + (x) N(κi, xi, Pi ). The covariance marix and he weigh of he merged mode should be also updaed as proposed in secion 2.. The formal descripion of his algorihm is given in algorihm. In algorihm, MeanShifModeFinding is he funcion o deec he convergence locaion by he mean-shif algorihm from a poin (he second argumen) in he densiy (he firs argumen) Analysis of Algorihm The ime complexiy of his algorihm is O(n max ) by amorized analysis, where n max is he maximum number of modes in all ime seps, and a skech of he proof is as follows. Suppose ha each of new daa has n max + credis, which is defined o be he reserved number of operaions for he Gaussian componen corresponding o he new daa. For he search for he convergence poin (line 3 in algorihm ), a mos n max +operaions are performed and he new componen consumes n max +credis since he funcion MeanShif- ModeFinding akes linear ime. 2n max credis are required for wo mean-shif ieraions when he new componen fails o merge (he las ieraion of while loop). Also, we need 2n max operaions (line 6 and 7) whenever he new componen is merged wih he currenly exising mode, bu he exising mode is responsible for his cos. So, he remaining Rarely, some merges which do no include he new daa may happen. I hardly affecs he accuracy of he densiy funcions, bu leads o a difference in he number of componens beween he quadraic and he linear ime algorihm. Algorihm Linear-ime sequenial densiy approximaion : S = {x n+ }, κ = α 2: ˆf + (x) = ˆf + (x) 3: c n+ = MeanShifModeF inding( ˆf + (x), x n+ 4: ˆf + (x) = ˆf + (x) N(α, xn+, P n+ ) : while do 6: x i = MeanShifModeF inding( ˆf + 7: c = MeanShifModeF inding( ˆf + (x), x i ) 8: if c n+ c hen 9: break : end if ) (x), xn+ ) : S = S {x i }, κ = κ + κi 2: ˆf + (x) = ˆf +(x) N(κ i, x i, P i ) 3: end while 4: merge all he modes in he se S and creae N(κ, c, Pc) where Pc is derived by he same mehod in equaion () 2n max credis are supposed o be used when anoher mode is merged wih i laer. Afer losing all credis, he mode finally disappears. For K ime seps, K new Gaussian componens are enered and sequenial densiy approximaion is performed. Therefore, he number of operaions for all K ime seps is a mos O(Kn max ), and he average ime complexiy in each sep is O(n max ). The derived complexiy is bounded by O(n max ), bu pracically i is faser han his since he number of componens in each sep is less han n max in mos cases. The number of componens is slighly more han he previous quadraic algorihm, bu he improvemen of ime complexiy is he dominaing facor for he overall speed of algorihm. 2.3 Performance of Approximaion The linear ime sequenial densiy approximaion algorihm, which we will refer o as he fas approximaion algorihm,is a varian of he quadraic ime algorihm. The performance of he fas approximaion algorihm was esed hrough simulaion, and compared wih he quadraic algorihm as well as a sequenial version of kernel densiy esimaion. Saring from he iniial densiy funcion, a new daa elemen is incorporaed a each sep, and Mean Inegraed Squared Error (MISE) wih sequenial kernel densiy esimaion is employed as a basis of comparison. The weighed Gaussian mixure N(., 8, 2 ), N(.4, 22, 2 ),and N(.4, 22, 2 ) is used as he iniial densiy funcion, and he new daa is sampled from anoher Gaussian mixure N(.2, 2, 2 ), N(.,, 2 ),andn(., 7, 2 ) plus a uniform disribuion in [, 2] wih weigh.. In his experimen, we expec he iniial densiy funcion o morph o he new densiy funcion from which daa samples are drawn. As seen in figure, he fas approximaion algorihm accuraely simulaes he sequenial kernel densiy esimaion; he final densiy funcion has hree major modes which closely

4 correspond o he Gaussian ceners in he sampling funcion. The simulaed densiy funcion using he quadraic algorihm is very similar o ha of he fas approximaion algorihm in mos seps, so i is no presened separaely in his figure. Noe ha he sequenial kernel densiy esimaion has more han 3 Gaussian componens a he 3h ime sep, bu he fas approximaion algorihm has only 7 modes. 8 x MISE by fas approximaion algorihm 8 x Num. of modes by fas approximaion algorihm MISE by quadraic approximaion algorihm (a) MISE Num. of modes by quadraic approximaion algorihm (b) Number of componens Figure 2: Comparison of MISE and number of componens in each sep of D simulaion beween fas approximaion algorihm (op) and quadraic ime algorihm (boom) (a) = (b) = (c) = 2 (d) = 8.4 (a) = (e) = 24 (f) = 3 Figure : Simulaion of fas approximaion algorihm and comparison wih sequenial kernel densiy esimaion. (a)- (f) Fas sequenial densiy approximaion (op) vs. sequenial kernel densiy esimaion (boom) Figure 2 shows ha he MISE of he fas approximaion algorihm is comparable o he quadraic algorihm (and in repeaed experimens, he new algorihm is ofen beer) while he increase in he number of componens using he fas algorihm is moderae. Muli-dimensional simulaions were also performed, and similar resuls were observed. Figures 3 and 4 presen he simulaion resuls, showing he comparisons of MISE and number of componens, respecively. To compare he speed beween he linear and quadraic ime algorihms, he CPU ime for he one-sep sequenial densiy approximaion procedure was measured for densiy funcions wih differen numbers of componens. Since sequenial densiy esimaion involves marix operaions, i is also worh- (b) = Figure 3: Simulaion of fas sequenial densiy approximaion (lef) and comparison wih sequenial kernel densiy esimaion (righ) while o check he performance wih respec o dimensionaliy. So, our experimens are performed by varying he number of modes and he dimensionaliy. We performed comparisons for wo differen dimensionaliies (2D and 6D), and he resuls are presened in figure. We observe ha he running ime of he fas approximaion algorihm is significanly less han he quadraic algorihm. Finally, we performed -sep sequenial densiy esimaions in various dimensions, and compued he average CPU ime and MISE 2. Figure 6 illusraes ha he fas approximaion algorihm is faser and comparable in accuracy. 2 The MISE is compued only a sample locaions in his case o handle high dimensional examples.

5 2 x 8. Speed comparison quadraic linear MISE comparison MISE by fas approximaion algorihm 2 x Num. of modes by fas approximaion algorihm CPU ime MISE raio MISE by quadraic approximaion algorihm (a) MISE Num. of modes by quadraic approximaion algorihm (b) Number of componens Dimension (a) Dimension (b) Figure 4: Comparison of MISE and number of componens in each sep of 2D simulaion beween fas approximaion algorihm (op) and quadraic ime algorihm (boom). Figure 6: CPU ime and MISE wih respec o dimensionaliy in sequenial densiy approximaion. (MISE raio is error raio of fas approximaion algorihm o quadraic ime algorihm.) CPU ime Comparison in 2D quadraic linear Num. of componens (a) 2D CPU ime Comparison in 6D quadraic linear Num. of componens (b) 6D Figure : CPU ime of fas approximaion algorihm and quadraic ime algorihm. 3 On-line Appearance Model On-line appearance models are imporan for real-ime objec racking, since he arge model can change due o many facors. In his secion, we presen a densiy based arge modeling and on-line model updae algorihm o deal wih changes in arge appearance and size. 3. Targe Modeling We consruc he model of feaures for each pixel in he arge objec wih a mixure of Gaussians, so he arge model is represened as a se of densiy funcions. Our represenaion can include an arbirary number of Gaussian componens in he densiy funcion, and describes he underlying densiy accuraely. Using pixel-wise color densiy modeling has he advanage of describing he deails of arge region, bu does no capure any srucural aspecs of an objec s appearance. So, we also incorporae recangular feaures ino our arge model. These feaures are obained by averaging he inensiies of neighbors (e.g., 3 3 or ) in each color channel (r, g, b) and are compued efficienly wih inegral images [9]. Since recangular feaures encode he spaial informaion around a pixel, hey ameliorae some problems caused by non-rigid moions of objecs and pixel mis-regisraions. The performance of such feaures have previously been invesigaed in objec racking [6] and deecion [9]. Iniially, a ime, he densiy funcion for each pixel (i, j) wihin a seleced arge region has a single Gaussian componen N(, x (i, j), P (i, j)) whose mean x (i, j) is he combinaion of color a (i, j) and average color of is neighborhood. In each ime sep, he new daa x (i, j) a he pixel locaion (i, j) is denoed as x (i, j) =(r, g, b, r, ḡ, b) (7) where ( r, ḡ, b) denoes he average inensiy of he neighborhood cenered a (i, j) for each color channel. Noe ha x (i, j) would be a 2D vecor composed of inensiy and average inensiy for gray scale images. Whenever a new observaion is inegraed ino he curren densiy, he densiy funcion is updaed as explained in secion 2.2. As ime progresses, highly weighed Gaussian componens are consruced around frequenly observed daa, and several minor modes may also develop. Using exponenial updaing, old informaion is removed gradually if no furher observaions are around i. So, he represenaion mainains a hisory of feaure observaions for any given pixel. 3.2 Updae in Scale Space The arge model so consruced is robus o changes of feaure values, bu is no inended o handle scale change. Tracking may fail in sequences conaining large scale changes of arge objecs, since he observaions are severely affeced by drasic up- or down-sampling. So, we updae he size of he arge model a every β% scale change as follows: he pixel locaion in he new arge window is projeced ino he old arge window, and he densiy funcion is compued by a weighed sum of neighborhood densiy funcions as ˆf x (i, j) = (u,v) N(i,j) w(u, v) ˆfx(u, v) (8) where N(i, j) is a se of pixels adjacen o (i, j) s projecion ono he old arge window, ˆfx(u, v) is an esimaed densiy funcion for feaure vecor x a (u, v), andw(u, v) is

6 he normalized weigh associaed wih each densiy funcion ˆfx(u, v). The new densiy funcion ˆf x(i, j) is also a mixure of Gaussians, and he bach version of our densiy approximaion echnique [8] is applied o reduce he number of componens for a compac represenaion. The modeling error in scale change is fairly small because of he spaial coherence of he arge. Also, since he recangular feaures for adjacen pixels are based on highly overlapping areas, hey are robus o updaes in scale space. This appearance model updae in scale space is simple, bu performs well in experimens; he sraegy plays an imporan role in he examples displaying significan scale change. (a) = (b) = 9 4 Objec Tracking In his secion, he crierion o deermine he opimal parameers for objec racking is described, and we presen various racking examples showing he effeciveness of on-line densiy-based appearance modeling. Comparisons wih oher appearance modeling mehods are also performed. 4. Maximum Likelihood Parameer Opimizaion Le M(x; p) denoe he parameerized moion of locaion x, where p =(v x,v y,s) is a vecor for ranslaions and scaling. Denoe by d(m(x; p)) he observaion a he image of x under moion p. Now, he racking problem involves finding he opimal parameer using he maximum likelihood mehod. p =argmax log(p(d(m(x (i,j) ; p)) p p,a (i,j) )) (9) (i,j) R where (i, j) is he relaive locaion in he arge region R, and A (i,j) he curren appearance model a (i, j). A simple gradien-based racking mehod is employed o find he opimal p, and he arge model is updaed as explained in secion Experimens Various sequences are esed o illusrae he performance of our on-line appearance modeling echnique. New daa is inegraed wih he weigh of α =.. Also, he arge model is updaed in scale space a every β =% change of size, and a slighly higher learning rae α =. is used a his ime. For he recangular feaures, neighborhood pixels are used. Figure 7 shows he resuls on he ank sequence, in which he arge has low conras and changes is orienaion during racking. Our racking algorihm succeeds in racking for 94 frames even wih ransien severe noise levels due o dus (e.g., figure 7 (b) and (d)). The resuls on a person sequence are presened nex. In his sequence, a human face is racked wih a large change of face (c) = 94 (d) Targe appearance changes Figure 7: Tracking resul of ank sequence orienaion and lighing condiion; he resuls are shown in figure 8. Figure 8 (e) illusraes how he appearance of he face changes over ime; figure 8 (f) shows he average inensiy of he arge region over ime. In figure 9, he racking resuls for he head of a fooball player are shown. In his sequence, he arge objec moves fas in high cluer and is blurred frequenly. Also, he changes in orienaion and exure of he head make racking difficul, so he densiy funcion for he arge model mus be able o accommodae hose variaions for accurae racking. As shown in figure 9 (f), he average number of modes per pixel (blue solid line) and he sandard deviaion (black doed line) varies up o around 6, which suggess ha a densiy funcion wih a fixed number of componens may produce a high racking error compared wih our mehod. In figure, a gray scale image sequence involving a large scale and illuminaion change is presened, and our appearance model updae sraegy adaps o his well. In he las sequence, he appearance of he car changes frequenly because of he shadow and is red lighs. Also, a person passes in fron of he car and he image is severely shaken several imes by camera movemen. Figure shows ha our on-line densiy-based modeling is successful in spie of occlusion and appearance change. 4.3 Comparison wih Oher Mehods Two differen appearance modeling mehods are implemened for comparison; one is fixed modeling wih a Gaussian disribuion and he oher is 3-componen mixure model based on [9]. For each algorihm, wo differen feaure ses color only and color wih recangular feaure for each pixel are employed. Using he same gradien-based racking, six differen cases including wo for our algorihm are esed, and he

7 (a) = (b) =36 (a) = (b) =22 (c) = (d) = 2 (e) Targe appearance changes Inensiy Frame (f) Inensiy changes Figure 8: Tracking resuls of person sequence (c) =47 (d) =67 (e) Targe appearance changes Frame (f) Num. of componens Figure 9: Tracking resul of fooball sequence resuls are summarized in able. Also, some examples of failures are illusraed in figure 2. As able illusraes, our on-line densiy approximaion shows good performance compared wih oher parameric echniques. The only algorihm able o successfully rack hrough boh sequences was our mehod using boh pixel-wise and recangular feaures. Conclusion We described a sequenial densiy approximaion algorihm in which he densiy funcion is represened wih a mixure of Gaussians whose number, mean, covariance and weigh are auomaically deermined. This algorihm has linear ime complexiy, and can be used in many real-ime applicaions. We apply his echnique o he adapive arge appearance modeling using pixel-wise and recangular feaures for objec racking. The effeciveness of he fas approximaion algorihm and combined feaure is presened by various simulaions and racking resuls in naural videos. Acknowledgmen We hank Dorin Comaniciu and Ying Zhu in Siemens Corporae Research (SCR) and Yoo-Ah Kim in Univ. of Connecicu for he valuable commen and discussion. This work is suppored by ARDA projec (DOD24H842) and SCR. References [] M. J. Black and A. Jepson, Eigenracking: Robus maching and racking of ariculaed objecs using a view-based represenaion, in Proc. European Conf. on Compuer Vision, Cambridge, UK, 996, pp [2] D. Comaniciu and P. Meer, Mean shif analysis and applicaions, in Proc. 7h Inl. Conf. on Compuer Vision, Kerkyra, Greece, Sepember 999, pp [3] D. Comaniciu and P. Meer, Mean shif: A robus approach oward feaure space analysis, IEEE Trans. Paern Anal. Machine Inell., vol. 24, no., pp , 22. [4] D. Comaniciu, V. Ramesh, and P. Meer, Real-ime racking of non-rigid objecs using mean shif, in Proc. IEEE Conf. on Compuer Vision and Paern Recogniion, Hilon Head, SC, volume II, June 2, pp [] A. Elgammal, R. Duraiswami, and L. Davis, Probabiliy racking in join feaure-spaial spaces, in Proc. IEEE Conf. on Compuer Vision and Paern Recogniion, Madison, WI, June 23. [6] P. Fieguh and D. Teropoulos, Color-based racking of heads and oher mobile objecs a video frame raes, in Proc. IEEE Conf. on Compuer Vision and Paern Recogniion, San Juan, Puero Rico, 997, pp

8 (a) = (b) = 27 (a) = (b) =8 (c) = (d) Targe appearance changes (c) = 92 (d) Targe appearance changes Figure : Tracking resul of car sequence Figure : Tracking resul of car2 sequence Table : Comparison of racking resuls Modeling mehod person fooball (2 frames) (8 frames) Fixed C a fail fail Gaussian C+R b fail fail 3-componen C succeed fail mixure [9] C+R succeed fail Our C succeed fail mehod C+R succeed succeed a color feaure b color recangular feaure [7] B. Frey, Filling in scenes by propagaing probabiliies hrough layers ino appearance models, in Proc. IEEE Conf. on Compuer Vision and Paern Recogniion, Hilon Head, SC, volume I, 2, pp [8] B. Han, Y. Zhu, D. Comaniciu, and L. Davis, Kernel-based bayesian filering for objec racking, in Proc. IEEE Conf. on Compuer Vision and Paern Recogniion, San Diego, CA, volume I, June 2, pp [9] A. Jepson, D. Flee, and T. El-Maraghi, Robus online appearance models for visual racking, in Proc. IEEE Conf. on Compuer Vision and Paern Recogniion, Hawaii, volume I, 2, pp [] J. Li and A. Barron, Mixure densiy esimaion, in Advances in Neural Informaion Processing Sysems 2, MIT Press, 2. [] I. Mahews, T. Ishikawa, and S. Baker, The emplae updae problem, IEEE Trans. Paern Anal. Machine Inell., vol. 26, no. 6, pp. 8 8, 24. [2] S. McKenna, Y. Raja, and S. Gong, Tracking colour objecs using adapive mixure models, Image and Vision Compuing Journal, vol. 7, pp , 999. Figure 2: Examples of racking failure. Tracking for person sequence wih he fixed Gaussian modeling (C+R, = 2) (lef) and for fooball sequence wih he 3-componen mixure modeling (C, =9) (righ) [3] H. T. Nguyen, M. Worring, and R. van den Boomgaard, Occlusion robus adapive emplae racking, in Proc. 8h Inl. Conf. on Compuer Vision, Vancouver, Canada, Ocober 2. [4] K. Nummiaro, E. Koller-Meier, and L. V. Gool, An adapive color-based paricle filer, Image and Vision Compuing, vol. 2, no., pp. 99, 23. [] P. Perez, C. Hue, J. Vermaak, and M. Gangne, Color-based probabilisic racking, in Proc. European Conf. on Compuer Vision, Copenhagen, Denmark, volume I, 22, pp [6] C. Priebe and D. Marchee, Adapive mixure densiy esimaion, Paern Recog., vol. 26, no., pp , 993. [7] D. Ross, J. Lim, and M. Yang, Adapive probabilisic visual racking wih incremenal subspace updae, in Proc. European Conf. on Compuer Vision, Prague, Czech, volume II, May 24, pp [8] J. J. Verbeek, N. Vlassis, and B. Kröse, Efficien greedy learning of gaussian mixure models, Neural Compu., vol., no. 2, pp , 23. [9] P. Viola and M. Jones, Rapid objec deecion using a boosed cascade of simple feaures, in Proc. IEEE Conf. on Compuer Vision and Paern Recogniion, Kauai, Hawaii, 2, pp. 8.