Fusion of Static and Dynamic Body Biometrics for Gait Recognition

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1 Fson of Statc and Dynamc Body Bometrcs for Gat Recognton Lang Wang, Hazhong Nng, Ten Tan, Wemng H Natonal Laboratory of Pattern Recognton (NLPR) Insttte of Atomaton, Chnese Academy of Scences, Bejng, P. R. Chna, 8 {lwang,hznng,tnt,wmh}@nlpr.a.ac.cn Abstract Hman dentfcaton at a dstance has recently ganed growng nterest from compter vson researchers. Ths paper ams to propose a vsal recognton algorthm based pon fson of statc and dynamc body bometrcs. For each seqence nvolvng a walkng fgre, pose changes of the segmented movng slhoettes are represented as an assocated seqence of complex vector confgratons, and are then analyzed sng the Procrstes shape analyss method to obtan a compact appearance representaton, called statc nformaton of body. Also, a model-based approach s presented nder a Condensaton framework to track the walker and to recover jont-angle trajectores of lower lmbs, called dynamc nformaton of gat. Both statc and dynamc ces are respectvely sed for recognton sng the nearest exemplar classfer. They are also effectvely fsed on decson level sng dfferent combnaton rles to mprove the performance of both dentfcaton and verfcaton. Expermental reslts on a dataset ncldng sbjects demonstrate the valdty of the proposed algorthm.. Introdcton Vson-based hman dentfcaton has recently attracted mch attenton, e.g., the Hman ID program of DARPA []. Ths strong nterest s drven by a varety of potental applcatons sch as vsal srvellance, covert secrty and access control. As a newly emergent bometrc featre, gat has the advantage of beng non-nvasve, and t s probably the only percevable modalty from a great dstance. Gat recognton ams essentally to dscrmnate ndvdals by the way they walk. Crrent gat recognton approaches may be explctly classfed nto two major categores, namely model-based methods [,4,] and moton-based methods [7,8,,]. As model-based examples, Johnson and Bobck [4] sed actvty-specfc statc body parameters for gat recognton wthot drectly analyzng gat dynamcs, and Yam et al. [] tred the rnnng acton of gat to recognze people as well as walkng and explored the relatonshp between walkng and rnnng that was expressed as a mappng based on the dea of phase modlaton. Most exstng approaches are moton-based. BenAbdelkader et al. [7] sed mage self-smlarty plots of a movng person to recognze people, and Phllps et al. [] descrbed a slhoette correlaton based algorthm for the gat dentfcaton problem. These approaches frther provde clear spports for the vew that t s feasble to recognze people by gat. For obtanng optmal performance, an atomatc person dentfcaton system shold ntegrate as many nformatve ces as avalable. There are varos propertes of gat that mght serve as recognton featres. We categorze them as statc featres and dynamc featres. The former sally reflects geometry-based measrements sch as body-heght, strde and bld, whle the latter means jont-angle trajectores of lower lmbs. Inttvely, recognzng people by gat depends greatly on how the statc slhoette shape changes over tme. So prevos work on gat recognton manly adopted low-level nformaton sch as slhoette [7,8,,]. De to the dffcltes of parameter recovery from vdeo, few methods except [,] sed hgher-level nformaton, e.g., temporal featres of jont angles reflectng the dynamcs of gat moton sffcently. Based on the dea that body bometrcs ncldes both the appearance of hman body and the dynamcs of gat moton measred drng walkng, here we attempt to fse the two completely dfferent sorces of nformaton avalable from walkng vdeo for personal recognton. The proposed method s shown n Fgre. For each mage seqence, backgrond sbtracton s sed to extract movng slhoettes of the walker. Statc pose changes of these slhoettes over tme are represented as an assocated seqence of complex vector confgratons n a common coordnate, and are then analyzed sng the Procrstes shape analyss method to obtan an egen-shape for reflectng the body appearance,.e., statc nformaton. Also, a model-based approach nder a Condensaton framework together wth hman body model, moton model and constrants s presented to track the walker n Proceedngs of the Nnth IEEE Internatonal Conference on Compter Vson (ICCV 3) -Volme Set /3 $7. 3 IEEE

2 mage seqences. From the trackng reslts, we can calclate jont-angle trajectores of man lower lmbs,.e., dynamcs of gat. Both statc and dynamc nformaton may be ndependently sed for recognton sng the nearest exemplar pattern classfer. They are also combned on decson level to mprove the fnal performance. Inpt Body model People trackng Moton model Moton constrants Jont angle recovery Trajectores Dynamc featre extracton Statc featre extracton Pattern classfer (R, S ) Combnaton classfer Dynamc template lbrary Reslt Slhoette extracton Shape representaton Egen-shapes Procrstes shape analyss (R, S ) Pattern classfer Statc template lbrary Fgre. Overvew of the proposed algorthm. Statc featre extracton.. Slhoette extracton and representaton A backgrond sbtracton procedre [9] s sed to extract a sngle-connectvty movng regon of the walker n each mage. An mportant ce n determnng nderlyng moton of a walkng fgre s hs or her slhoette shape changes over tme. For the sake of redcng redndancy, we only need to analyze spatal contors. The bondary can be obtaned sng a border followng algorthm based on connectvty. Then, we compte ts shape centrod (x c, y c ). Let the centrod be the orgn of a D shape space. We can nwrap the bondary as a set of pxel ponts (x, y ) along oter-contor antclockwse n a complex coordnate. That s, each shape can be descrbed as a vector consstng of complex nmbers wth N b bondary elements z=[z, z,,z, z Nb ] T, where z =x +j*y. Therefore, each gat seqence wll be transformed nto a seqence of sch D shape confgratons accordngly... Procrstes shape analyss We need one method that allows s to compare a set of statc pose shapes n gat pattern and s robst to poston, scale and slght rotaton changes. A mathematcally elegant way for algnng pont sets s Procrstes shape analyss. A good bref revew can be fond n []. Procrstes shape analyss s ntended to cope wth D shapes. A shape n D space can be descrbed by a vector of k complex nmbers z=[z, z,, z k ] T, called a confgraton. It s convenent to center shapes by defnng the centered confgraton =[,,, k ] T, = z z, z = k = z / k. The fll Procrstes dstance between two confgratons can be defned as * d F (, ) = () where the sperscrpt * represents the complex conjgaton transpose. Gven a set of n shapes, we can fnd ther mean by fndng that mnmzes the objectve fncton mn n α j k β j j () α,β j j j= To fnd, we compte the followng matrx S = n = ( ) /( ) (3) The Procrstes mean shape û s the domnant egenvector of S,.e., the egenvector that corresponds to the greatest egenvale of S []. *.3. Statc sgnatre acqston Or approach ses these sngle shape representatons from a gat seqence to fnd ther mean shape as statc sgnatres that can represent the appearance of body shape. The followng smmarzes the major steps n determnng the Procrstes mean shape of a gat pattern.. Select a set of k ponts from the bondary to represent a D shape as a vector confgraton z j as dscssed n Secton.;. Set the centered confgraton. When we represent the slhoette shape, we se the shape centrod as the orgn of D shape space to move all shapes to a common center. So we can drectly set j =z j, j=,,, n; 3. Compte the matrx S sng Eqn. (3). Then, compte the egenvales and the assocated egenvectors of S ; 4. Set the Procrstes mean shape û as the egenvector that corresponds to the maxmm egenvale, and ths mean shape s sed as statc sgnatres. * Proceedngs of the Nnth IEEE Internatonal Conference on Compter Vson (ICCV 3) -Volme Set /3 $7. 3 IEEE

3 Seqence Seqence Seqence 3 Seqence 4 Exemplar Sbject 6, degree Sbject 5,8,4,6 and, degree Exemplar Exemplar Exemplar 3 Exemplar 4 Exemplar (a) (b) Fgre. Plots of mean shapes and the exemplars For mltple mean shapes from mltple seqences of the same sbject, we may acqre an exemplar by averagng them as a statc template for that class to avod selectng a random reference sample. Fgre (a) shows plots of mean shapes of for seqences of a sbject and ther exemplar, and Fgre (b) shows plots of mltple exemplars from dfferent sbjects. From Fgre we can see that the ntra-sbject changes n egenshapes are very small, whle the nter-sbject changes are more sgnfcant. Sch reslt mples that the mean shapes have consderable dscrmnatng power. Frther detals on statc featre extracton may be fond n [9]. 3. Dynamc featre extracton For extractng dynamc featres of gat moton, we present a new model-based approach to trackng the walkng fgre nder the Condensaton framework [6]. 3.. Pror knowledge Or model knowledge ncldes three parts: hman body model, moton model and moton constrants [8]. The hman body model sed n ths paper, smlar to [5], s composed of 4 rgd body parts, each of whch s represented by a trncated cone except for the head represented by a sphere. Wth the constrant that people are walkng parallel to the mage plane, the state space can be natrally descrbed by a -dmensonal vector P = { x, y, θ, θ, L, θ}, where (x, y) s the global poston of hman body and θ (=~) s jont angles. Or moton model s emprcally descrbed wth Gassan fnctons Gk, t ( k, t, σ k, t ) for each jont k (k = ) at any phase t (t = T) n the walkng cycle. We also se condtonal dstrbtons to model the moton constrants of the dependences of neghborng jont angles. Gven the above consderatons, we frst predct the global poston from the centrod of the detected movng hman and then refne t by searchng the neghborhood of the predcted poston. Each lmb s tracked nder the Condensaton framework that ses learnt dynamcal models, together wth vsal observatons, to propagate the random sample set. The dynamc model needs to be desgned careflly to mprove the effcency of factored samplng. Here, the learnt moton model servng as pror s ntegrated nto the dynamc model. Wth the assmpton that the Gassan dstrbtons at dfferent phases n the moton model are ndependent, at tme nstant t the th moton parameter θ satsfes the dynamc model,t ( ( )) ( θ θ ) G α + β + γ θ λ ( α σ ) ( β σ ) p, t, t =, t, t, t,, t +, t where α + β + γ = makes the drftng of θ, t not only from the trackng hstory θ, t bt also from the moton model, and λ s a scalar that s often set to. Ths dynamc model s generally sffcent for all moton parameters, bt moton constrants can frther concentrate the samples for parameters of elbow, knee and ankle jonts. For nstance, after the sholder jont θ s, t s sampled, sample postons generated from the condtonal dstrbton p ( θ e, t θ s, t ) for the elbow jont θ e, t also contan mch nformaton. So a mxed-state Condensaton [7] can be nclded n the factored samplng scheme by choosng wth a probablty q to generate samples from the dynamc model and wth a probablty -q to generate samples from the condtonal dstrbton,.e., θ satsfes ( θ θ, θ ) qgα + β + γθ, λ( ασ ) + ( βσ ) e, t ( ( )) + ( q ) p( θ ) p e, t et, st, = et, et, et,, t, t et, θst, where α, β, γ, λ are defned as above. 3.. Trackng Trackng s eqvalent to relate the mage data to the pose vector P. Snce the artclated body model may be natrally formlated as a tree-lke strctre, a herarchcal estmaton,.e., locatng the global poston and trackng each lmb separately, s stable here. Fgre 3. Parts of the trackng reslts Proceedngs of the Nnth IEEE Internatonal Conference on Compter Vson (ICCV 3) -Volme Set /3 $7. 3 IEEE

4 The PEF (Pose Evalaton Fncton) reveals the observaton densty p ( z t x t ) of an mage z t gven that the hman model has the postre x t at tme t. In general, bondary nformaton mproves the localzaton, whereas regon nformaton stablzes the trackng. Therefore, we combne both of them n the PEF by comptng the bondary matchng error E b and the regon matchng error E r to acheve both accracy and robstness. Here the trackng reslts of seqences are showed n Fgre 3. De to space constrant, only the hman areas clpped from the orgnal mages are gven. More detals on trackng may be fond n [8] Dynamc sgnatre acqston Estmatng an nderlyng skeleton from the trackng reslts enables s to measre jont-angle trajectores. Fgre 4 shows sgnals of for jonts: left and rght hps, left and rght knees from a walkng nstance, where the smoothed crves are the reslts after the medan flterng. It s varatons n the jont sgnals that we wsh to consder as dynamc nformaton of body bometrcs,.e., dynamcs of gat. Rotaton Angle Rotaton Angle 4 Left Hp Rght Hp Rotaton Angle Rotaton Angle 5-5 Left Leg Rght Leg Fgre 4. Jont-angle trajectores of lower lmbs Dfferences n body strctre and dynamcs natrally case jont-angle trajectores to vary n both magntde and tme. To analyze these sgnals for dentty recognton, we need to normalze them. We select only one walkng cycle from each seqence. Wthot drectly sng the jont-angle trajectores, we carry ot varance normalzaton by sbtractng the mean of each sgnal and then dvdng by the estmated standard devaton to redce the effect of nose. DTW (Dynamc Tme Warpng) s appled to temporally algn the sgnals to a fxed reference phase. Fgre 5 shows the reslts of tme-normalzed sgnals of thgh rotaton, from whch we fnd that there are lttle varatons among seqences from the same sbject, whereas there are apparent varatons among dfferent sbjects. We choose for normalzed sgnals from left and rght hps and knees to consttte a dynamc featre vector. Smlarly, we also se mltple vectors from the same sbject to obtan the exemplar by averagng them, whch s regarded as a dynamc template for that class. Angle (deg) Left Thgh Rotaton After Tme Normalzaton and Algnment Sbject 4-5 Seqence Seqence - Seqence 3 Seqence Gat Cycle (%) Angle (deg) Thgh Rotaton from For Dfferent Sbjects Sbject Sbject Sbject 3 Sbject Gat Cycle (%) (a) (b) Fgre 5. Tme-normalzed sgnals of jont angles 4. Pattern classfers and fson rles Gat recognton s a tradtonal pattern classfcaton problem. Here we try the nearest neghbor classfer wth class exemplar (ENN). No dobt, a more sophstcated classfer cold be employed, bt the nterest here s to evalate the dscrmnatory ablty of the extracted featres. To measre smlarty, we se both the Procrstes mean shape dstance defned n Eqn. () for statc featres and the Ecldean dstance for dynamc featres respectvely. The smaller the above dstance measres are, the more smlar the two gats are. Man reasons for combnng classfers are effcency and accracy. A varety of fson approaches for bometrc recognton are avalable, a few of whch are mentoned here [3-6]. Here, we nvestgate several dfferent approaches to classfer combnaton. It shold be noted that havng obtaned the score for each modalty gven the observaton, one generally cannot drectly combne these scores n a statstcally meanngfl way becase they are not drect estmates of the posteror, bt rather measres of the dstance between the test example and the reference example [3]. These scores, wth qte dfferent ranges and dstrbtons, mst therefore be transformed to be comparable before fson (the logstc ( α + βx ) ( α + βx ) fncton e /( + e ) s sed n ths paper). Frst, we respectvely nvestgate rank-smmaton-based and score-smmaton-based approaches descrbed n [6]. Followng the theoretcal framework presented n [5], we also compare the max, mn, mean, and prodct rles for combnng classfer otpts. To statstcally jstfy the above rles, a monotonc transformaton fncton over scores S needs to be appled to reflect the posteror probablty. We se the smlar approach proposed n [3]. That s, we may estmate a probablty dstrbton over the scores assgned to the correct labels by a mappng fncton T from scores to the emprcal dstrbton and treat T(S) as the estmate of the posteror. Proceedngs of the Nnth IEEE Internatonal Conference on Compter Vson (ICCV 3) -Volme Set /3 $7. 3 IEEE

5 5. Experments We collected 8 seqences from sbjects and for seqences per sbject for or experments. Each seqence ncldes a walkng fgre and the walker moves natrally n the feld of vew wthot occlson laterally wth respect to the mage plane. All mage seqences are captred by a statonary dgtal camera at a rate of 5 frames per second. 5.. Expermental reslts For each mage seqence, we frst extract statc featres n the manner descrbed n Secton. Frther, we perform model-based trackng and recover dynamc featres n the manner descrbed n Secton 3. It shold be noted that self-occlson of body parts, shadow nder the feet, the arm and the torso havng the same color, and low qalty of the mages all brng challenges to or trackng method. For a small porton of faled trackng seqences, we manally obtan the moton parameters as the focs of ths paper s not on trackng per se bt on gat recognton sng the trackng data as dynamc featres. De to a small nmber of examples, we hope to compte an nbased estmate of the tre recognton rate sng a leave-one-ot cross-valdaton method. That s, we frst leave one example ot, tran on the rest, and then classfy or verfy the omtted element accordng to ts dfferences wth respect to the rest examples. Cmlatve Match Scores The CMS Crves of Indvdal Featres Rank FAR The ROC Crves of Indvdal Featres EER FRR (a) Identfcaton (b) Verfcaton Fgre 6. The reslts sng a sngle modalty Frst, we separately se statc featres and dynamc featres obtaned from walkng vdeo for recognton. In dentfcaton mode, the classfer determnes whch class a gven measrement belongs to. One sefl measre of classfcaton performance that s more general than classfcaton error s CMS (Cmlatve Match Scores) [9] whch s frstly ntrodced n the FETET protocol for the evalatons of face recognton algorthms. It ndcates the probablty that the correct match s nclded n the top n matches. For completeness, we also se the ROC (Recever Operatng Characterstc) crves to report verfcaton reslts. In verfcaton mode, the classfer s asked to verfy whether a new measrement really belongs to certan clamed class. ROC crves gve plots of varos pars of FAR (False Acceptance Rate) and FRR (False Rejecton Rate) nder dfferent decson threshold vales for the acceptance. Fgre 6 (a) and (b) respectvely show performance of dentfcaton (for ranks p to ) and verfcaton sng a sngle modalty. It shold be mentoned that the CCR (Correct Classfcaton Rate) s eqvalent to p () (.e., rank=). Cmlatve Match Scores Cmlatve Match Scores.95.9 The CMS Crves.85 Fson Based on Rank Smmaton Fson Based on Score Smmaton Rank.95.9 FAR The ROC Crves Fson Based on Rank Smmaton Fson Based on Score Smmaton EER FRR (a) Identfcaton (b) Verfcaton Fgre 7. Fson reslts of rank and score based smmaton rles CMS Crves.85 Fson Usng Prodct Rle Fson Usng Sm Rle Fson Usng Max Rle Fson Usng Mn Rle Rank FAR The ROC Crves EER Fson Usng the Prodct Rle Fson Usng the Sm Rle Fson Usng the Max Rle Fson Usng the Mn Rle FRR (a) Identfcaton (b) Verfcaton Fgre 8. Fson reslts sng the prodct, sm, max and mn combnaton rles Based on the combnaton rles descrbed n Secton 4, we examne the reslts after fsng both statc featres and dynamc featres. Fgre 7 (a) and (b) show the reslts of dentfcaton and verfcaton sng rank-smmaton-based and score-smmaton-based combnaton rles respectvely, and Fgre 8 (a) and (b) gve the reslts of dentfcaton and verfcaton sng the prodct, sm, max and mn combnaton rles respectvely. For comparson, we also plot the reslts sng a sngle modalty n Fgre 7 and Fgre Analyss of reslts From Fgre 6, we can see that there s ndeed dentty nformaton n both statc and dynamc featres derved from walkng vdeo that can be explored for the recognton task. The reslts sng dynamc nformaton are somewhat better than those sng statc nformaton. Ths s lkely de to the fact that the dynamcs reflect more essental nformaton of gat moton. Fgre 7 and Fgre 8 demonstrate the mproved performance of both dentfcaton and verfcaton for the ntegraton step than that sng any sngle modalty. A smmary of CCRs and EERs (Eqal Error Rate) s gven n Table for clarty. Another nterestng observaton from Proceedngs of the Nnth IEEE Internatonal Conference on Compter Vson (ICCV 3) -Volme Set /3 $7. 3 IEEE

6 the comparatve reslts s that the score-smmaton-based rle otperforms other combnatons schemes as a whole. Of the last 4 statstcal combnaton rles, the sm rle s the best for dentfcaton, whch has also been shown n [5] sng the senstvty analyss to demonstrate that the sm rle s the most reslent to estmaton errors. However, the prodct rle s best for verfcaton. The man reason for the poor performance of the mn rle s probably becase that t sffers more from the nose n score assgnment than the relatvely robst mean and prodct rles. Also, t s beleved that there wll be better reslts f there are sffcent data to precsely model the probablty dstrbtons of scores for the two pattern classfers. In all, these stdes hghlght the mportance of a carefl choce of the whole combnaton strategy. Table. Smmary of CCRs and EERs CCR (rank=) CCR (rank=3) EER Statc featres 83.75% 9.5%.% Dynamc featres 87.5% 97.5% 8.4% Rank-smmaton 87.5% % 3.75% Score-smmaton 97.5% % 3.75% Prodct 9.5% 97.5% 3.54% Sm 96.5% % 5.% Max 95.% % 4.7% Mn 9.5% 97.5% 5.% Althogh as a whole the reslts are very encoragng, more experments on a larger and more realstc database stll need to be nvestgated n ftre work n order to be more conclsve. 6. Conclsons Ths paper has proposed a method based on fson of statc and dynamc body bometrcs for gat recognton. A statstcal approach based on Procrstes shape analyss s sed to obtan a compact representaton of the appearance of body shape from spatotemporal pattern of walkng. A model-based approach s employed to track the walker and to recover jont-angle trajectores of lower lmbs that reflect the dynamcs of gat. Both statc and dynamc ces of body bometrcs may be ndependently sed for recognton. Also, they have been combned on decson level for mprovng the performance. Expermental reslts have demonstrated the feasblty of the proposed method. Acknowledgements Ths work s spported by NSFC (Grant and 65), Natral Scence Fondaton of Bejng (Grant 434), the Natonal 863 Hgh-Tech R&D Program of Chna (Grant AA7), and Insttte of Atomaton, the Chnese Academy of Scences. [] J. Boyd, Vdeo Phase-locked Loops n Gat Recognton, Proc. of Intl. Conf. on Compter Vson, I: ,. [] R. Tanawongswan and A. Bobck, Gat Recognton from Tme-normalzed Jont-angle Trajectores n the Walkng Plane, Proc. of Intl. Conf. on Compter Vson and Pattern Recognton,. [3] G. Shakhnarovch, L. Lee, and T. Darrell, On Probablstc Combnaton of Face and Gat Ces for Identfcaton, Proc. of Intl. Conf. on Atomatc Face and Gestre Recognton, pp. 76-8,. [4] A. Bobck and A. Johnson, Gat Recognton Usng Statc, Actvty-specfc Parameters, Proc. of Intl. Conf. on Compter Vson and Pattern Recognton,. [5] S. Wachter and H. Nagel, Trackng Persons n Monoclar Image Seqences, CVIU, 74(3): 74-9, 999. [6] M. Isard and A. Blake, Condensaton Condtonal Densty Propagaton for Vsal Trackng, IJCV, 9(): 5-8, 998. [7] C. BenAbdelkader, R. Clter, H. Nanda, and L. Davs, EgenGat: Moton-based Recognton of People Usng Image Self-smlarty, Proc. of Intl. Conf. on Ado- and Vdeo-based Person Athentcaton, pp ,. [8] R. Collns, R. Gross, and J. Sh, Slhoette-based Hman Identfcaton from Body Shape and Gat, Proc. of Intl. Conf. on Atomatc Face and Gestre Recognton, pp ,. [9] J. Phllps, H. Moon, S. Rzv, and P. Rase, The FERET Evalaton Methodology for Face Recognton Algorthms, PAMI, (): 9-4,. [] C. Y. Yam, M. S. Nxon, and J. N. Carter, On the Relatonshp of Hman Walkng and Rnnng: Atomatc Person Identfcaton by Gat, Proc. of Intl. Conf. on Pattern Recognton,. [] P. Phllps, S. Sarkar, I. Robledo, P. Grother, and K. Bowyer, The Gat Identfcaton Challenge Problem: Data Sets and Baselne Algorthm, Proc. of Intl. Conf. on Pattern Recognton,. [] L. Lee and W. Grmson, Gat Analyss for Recognton and Classfcaton, Proc. of Intl. Conf. on Atomatc Face and Gestre Recognton, pp. 55-6,. [3] R. Brnell and D. Falavgna, Person Identfcaton Usng Mltple Ces, PAMI, 7(): , 995. [4] L. Hong and A. Jan, Integratng Faces and Fngerprnts for Personal Identfcaton, PAMI, (): 95 37, 998. [5] J. Kttler, M. Hatef, R. Dn, and J. Matas, On Combnng Classfers, PAMI, (3): 6 39, 998. [6] B. Achermann and H. Bnke, Combnaton of Classfers on the Decson Level for Face Recognton, Techncal Report IAM-96-, Unversty Bern, 996. [7] M. Isard and A. Blake, A Mxed-state Condensaton Tracker wth Atomatc Modal Swtchng, Proc. of Intl. Conf. on Compter Vson, pp. 7-, 998. [8] H. Nng, L. Wang, W. H, and T. Tan, Artclated Model Based People Trackng Usng Moton Models, Proc. of Intl. Conf. on Mlt-modal Interface, pp ,. [9] L. Wang, T. Tan, W. H, and H. Nng, Atomatc Gat Recognton Based on Statstcal Shape Analyss, IEEE Trans. Image Processng, Agst 3 (to appear). [] Avalable: References Proceedngs of the Nnth IEEE Internatonal Conference on Compter Vson (ICCV 3) -Volme Set /3 $7. 3 IEEE