Gait Tracking and Recognition Using Person-Dependent Dynamic Shape Model

Transcription

1 Ga Trackng and Recognon Usng Person-Dependen Dynamc Shape Model Chan-Su Lee and Ahmed Elgammal Rugers Unversy Pscaaway, NJ 8854 USA Compuer Scence Deparmen Absrac Characerscs of he D shape deformaon n human moon conan rch nformaon for human denfcaon and pose esmaon. In hs paper, we nroduce a framework for smulaneous ga rackng and recognon usng person-dependen global shape deformaon model. Person-dependen global shape deformaons are modeled usng a nonlnear generave model wh knemac manfold embeddng and kernel mappng. The knemac manfold s used as a common represenaon of body pose dynamcs n dfferen people n a low dmensonal space. Shape syle as well as geomerc ransformaon and body pose are esmaed whn a Bayesan framework usng he generave model of global shape deformaon. Expermenal resuls show person-dependen synhess of global shape deformaon, ga recognon from exraced slhouees usng syle parameers, and smulaneous ga rackng and recognon from mage edges. Inroducon Characerscs of he shape deformaon n a person moon conan rch nformaon such as body confguraon, person deny, gender nformaon, and even emoonal saes of he person. Ga recognon has become aracve for survellance and for secury n publc areas [4, 8, ] as s easly observable and dffcul o dsguse han oher bomercs. Ga nvolves spaoemporal deformaons n shape and appearance. Such spaoemporal shape deformaon are nvesgaed n many appearance-based ga recognon sysems [, 4,,, 3,, ]. Mos of he ga recognon sysems rely on slhouees exraced usng background subracon algorhms. Recognon performance n many sysems depends on he accuracy of exraced slhouees. On he oher hand, here have been a lo of work on conour rackng from cluered envronmen, whou he need for background subracon, such as acve shape models (ASM) [3], acve conours [9], and exemplar-based rackng []. Spaoemporal models are also used for conour rackng [] However, s dffcul o acheve rackng of dynamc conour ha s accurae enough o dsngush ndvdual dfferences from arculaed human moon. There are no spaoemporal models for conour rackng o descrbe person-specfc varaons of shape for ga recognon. Our objecve s o model person-specfc dfferences of shape deformaon n addon o he global deformaon of he shape n order o acheve adapve rackng and person denfcaon from ga. For ceran classes of moon lke ga and facal expressons, he global shape deformaon mgh le on a low dmensonal manfold, f we consder a sngle person. In [7], a framework o separae he moon from he syle n a generave fashon was nroduced where he moon s represened n a low dmensonal nonlnear manfold. Indvdual dfferences n he shape deformaon can be dscovered n he nonlnear mappng space beween embedded represenaon of he confguraon space and he observaon. Nonlnear manfold learnng can be used o fnd nrnsc body confguraon space [3, 7]. However, when appled o mage sequences, nonlnear manfold learnng yelds manfolds ha are wsed dfferenly accordng o person syle, vew, and oher facors lke clohes [6]. I s hard o acheve unfed represenaon from hese varan manfolds. In addon, he ndvdual dfference n shape conour wll exs no only n he nonlnear mappng space bu also n he embeddng space (.e., separaon s no opmal). We propose o use knemacs manfold embeddng, whch represens body confguraon n low dmensonal space and nvaran o dfferen people, o model dynamcs of shape deformaon n body confguraon space. The enre nrnsc confguraon can have one-o-one correspondence wh knemacs manfolds. Usng hs knemac manfold embeddng, ndvdual dfference of shape deformaon can be solely conaned n he nonlnear mappng. Even hough he dynamcs of global shape deformaon are

2 complcaed and nonlnear, we can successfully model he dynamcs by smple one dmensonal lnear model usng hs knemacs manfold. We develop a generave model for person-dependen dynamc shape conour for rackng and recognon usng he knemacs manfold. The generave model s represened by a confguraon sae and a shape syle sae. The shape syle sae s a compac represenaon of varaons n shape conours ndependen of body pose (he confguraon sae). We use he esmaed syle for ga recognon. When he exraced slhouee s provded (e.g. usng background subracon), we can drecly esmae he conour syle sae and recognze ga based on he esmaed conour syle parameers. On he oher hand, f slhouee exracon s no possble, we use conour rackng where he rackng problem s formulaed as esmaon of body confguraon sae as well as conour syle sae usng Bayesan framework ulzng he generave model. We can recognze person ga durng rackng usng parcle flerng as we esmae sae of person syle, global shape deformaon characerscs, as well as body confguraon, whch s mpossble n parcle model usng knemac models whou global shape deformaons [5]. Syle esmaon gradually ges dscrmnave usng deermnsc annealng lke procedure n order o esmae conour syle sae, whch can be hgh dmensonal, robusly whou rappng o local mnma. Expermenal resuls usng Unversy of Souhampon ga daabase [8] shows poenal for smulaneous ga recognon and conour rackng. Decomposable Generave Models usng Knemacs Manfold Embeddng We can hnk of he shape of a dynamc objec as nsances drven from a generave model. Le z R d be he shape of he objec a me nsance represened as a pon n a d-dmensonal space. Ths nsance of he shape s drven from a model n he form z = T α γ(b ;s ), () where he γ( ) s a nonlnear mappng funcon ha maps from a represenaon of he body confguraon b no he observaon space gven a mappng parameer s ha characerzes he person shape n a way ndependen from he confguraon and specfc o he person beng racked. T α represens a geomerc ransformaon on he shape nsance. Gven hs generave model, we can fully descrbe observaon nsance z by sae parameers α,b,ands. Fgure shows a graphcal model llusrang he relaon beween hese varables where y s a conour nsance generaed from model gven body confguraon b and shape syle s. The observed shape conour z s formed by geomercally ransformng he conour nsance y n he mage b α s y z Fgure. A graphcal model for decomposable generave models b α s y z Fgure. Knemacs manfold embeddng and s mean manfold: wo dfferen vews n 3D space space. Knemacs manfold embeddng s used for nrnsc manfold represenaon of confguraon b.. Knemacs Manfold Embeddng We fnd low dmensonal represenaon of knemacs manfold by applyng nonlnear dmensonaly reducon echnques for moon capure daa. We frs conver jon angles of moon capure daa no jon locaons n 3 dmensonal spaces. We algned global ransformaon n advance n order o coun moon only due o body confguraon change. In order o fnd low dmensonal nrnsc represenaon from he hgh dmensonal daa (collecon of jon locaon) we appled nonlnear dmensonaly reducon procedure lke Locally lnear embeddng (LLE) [6]. Fgure shows knemacs manfold based on hree walkng cycles of moon capure daa and her mean manfold represenaon. The manfold s one-dmensonal wsed crcular manfold n hree-dmensonal spaces. The manfold s represened usng a one-dmensonal parameer by splne fng. For one-dmensonal represenaon of he mulple cycles, we use mean-manfold represenaon n he parameerzaon. The mean-manfold s parameerzed by splne fng by a one-dmensonal parame-

3 er β R and a splne fng funcon f : R R 3 ha sasfes b = f (β ) s used o map from he parameer space no he hree dmensonal embeddng space as shown n Fg... Decomposng and Modelng Shape Syle Space Indvdual varaons of he shape deformaon can be dscovered n he nonlnear mappng space beween he knemac manfold embeddng and he observaon for dfferen people. We employ nonlnear mappng based on emprcal kernel map [7] o capure nonlnear deformaon n dfference body pose. There are hree seps o model ndvdual shape deformaons usng nonlnear mappng. Frs, for a gven shape deformaon sequence, we deec ga cycles and embed colleced shape deformaon daa o he nrnsc manfold. In our case, knemac manfold are used for ga embeddng n each deeced cycle. As he knemac manfold comes from consan speed walkng moon capured daa, we can embed he shape sequence n equally spaced pons along he manfold. Second, we learn nonlnear mappng beween he knemac embeddng space and shape sequences usng Generalzed Radal Bass Funcon (GRBF) [5] smlar o [7]. The mappng has he form y k = γ k (b )=C k ψ(b ),wherec k s he mappng coeffcens whch depend on parcular person shapes, ψ( ) s a nonlnear mappng wh N RBF kernel funcons o model he manfold n he embeddng space, y k s person k shape a me, andb s a correspondng pon on he knemac manfold. Thrd, gven learned nonlnear mappng coeffcens C,C,,C K, for ranng people,,k,heshape syle parameers are decomposed by fng an asymmerc blnear [9] o he coeffcen space: c k = As k, () where c k s a vecor represenaon of marx C k usng column sackng. As a resul, we can generae conour nsance y k for parcular person k a any body confguraon b as y k = A s k ψ(b ), (3) where A s a hrd order ensor, s k s a shape syle vecor for person k. The syle marx, collecon of syle vecors, S =[s s s k ] T, s orhonormal marx as a resul of asymmerc blnear model analyss. For a gven cycle of walkng sequence, we can esmae syle vecor analycally. We can fnd mappng coeffcens C new for he gven new sequence based on knemacs embeddng and nonlnear mappng descrbed above. Usng Eq., we can fnd syle represenaon n closed-form for new sequence s new = A + c new,wherec new s vecor represenaon of marx C new and A + s pseudo nverse of he marx A. Usng hs closed form soluon, we can perform ga recognon from exraced slhouee shape sequences as wll be shown n Sec. 4.. Ulmaely he syle parameer s should be ndependen of he confguraon and herefore should be me nvaran and can be esmaed a nalzaon. However, we don know accurae shape and body confguraon nally and we canno esmae correc shape syle a he begnnng. Therefore, he syle needs o f o he correc person syle gradually durng he rackng. So, we formulaed shape syle as me varan facor ha should be sablzed as more observaons become avalable. The dmenson of he syle vecor depends on he number of people (or number of cycles) used for ranng and can be hgh dmensonal. We pursue lower dmensonal represenaon and mpose consrans as explaned n Sec. 3.. The overall generave model can be expressed as z = T α (A s ψ(b )). (4) The rackng problem usng hs generave model s he esmaon of parameer α, b,ands a each new frame gven observaons Z. 3 Bayesan Trackng and Syle Esmaon Gven he nonlnear shape generave model nroduced above, he rackng problem s an nference problem where a me we need o nfer he body confguraon b and he shape syle s and he geomerc ransformaon T α gven he observaon Z. The Bayesan rackng framework enables a recursve updae of he poseror P(X Z ) over he objec sae X gven all observaons Z = Z,Z,..,Z up o me : P(X Z ) P(Z X ) P(X X )P(X Z ) (5) X In our generave model, he sae X s (α,b,s ),whch unquely descrbes he sae of he racked objec. Observaon Z s he capured mage nsance a me. 3. Parcle Fler wh Decomposable Models The sae X s decomposed no hree sub-saes α,b,s. These hree random varables are concepually ndependen snce we can combne any body confguraon wh any shape syle wh any geomercal ransformaon o synhesze a new shape. However, hey are dependen gven he observaon Z. I s hard o esmae jon poseror dsrbuon P(α,b,s Z ) for s hgh dmensonaly. The objecve of he densy esmaon s o esmae mos lkely saes α,b,s for gven observaons. The decomposable feaure of our generave model enables us o esmae each sae by a margnal densy dsrbuon P(α Z ), P(b Z ),andp(s Z ).

4 We approxmae he margnal densy of each sub-sae usng maxmum a poseror (MAP) of he oher sub-saes,.e., P(α Z ) P(α b,s,z ), P(b Z ) P(b α,s,z ), where α, b,ands are maxmum a poseror esmae of each approxmaed margnal densy. We represen sae denses usng parcle flers snce such denses can be non-gaussan and he observaon s nonlnear. We can represen hree dmensonal body confguraon parameers b as a one-dmensonal parameer β as explaned n Sec... The shape syle s also parameerzed by syle class weghng parameers λ as n Sec. 3.. In case of global ransformaon, we esmae geomerc ransformaon parameers α n he mage space. So, usng he generave model n Eq. 4, he rackng problem s o esmae α, λ,andβ for gven observaons Z.Themargnalzed poseror denses for α, β,andλ are approxmaed by hree parcle sysems. {α (), α π () } N α ( j) =,{β, b π ( j) } N b (k) j=,{λ, s π (k) } N s k=, (6) where N α,n b,andn s are parcle numbers used for each sub-saes. 3. Syle Esmaon wh Consrans and Annealng Procedure There are wo facors o be consdered n he shape syle esmaon: One s hgh dmensonaly n he syle represenaon and he oher s dscrmnave power for ga recognon. The decomposon of syle vecor from he collecon of mappng coeffcen usng blnear model gves syle vecor whose dmenson s he same as he number of cycle used for he ranng. We need o keep he hgh dmensonal erms o ge accurae synhess of shape deformaon as shown n Fg. 3 (b). We esmae syle usng deermnsc annealng procedure wh addonal consrans n he parcle samplng o acheve gradually dscrmnave esmaon of hgh dmensonal shape syle vecor. Frs, we represen a new shape syle as a lnear combnaon of shape syle classes whn convex hull of gven syle classes. A new syle vecor s new s represened by lnear weghng of each of he syle classes s k, k =,,K usng lnear wegh λ k wh consrans: s new = K k= λ k s k, K λ (k) = =, λ (k) for all k (7) where K s he number of represenave syle classes. In acual syle esmaon usng parcle flerng, we force he In acual mplemenaon, we allow small exrapolaon n sampled parcles for fas convergence of mean parcle weghs o he arge syle negave λ (k) o be zero afer mporan-samplng wh resamplng for he syle parcles. We normalze agan for hs modfed parcle values accordng o Eq. 7. In acual syle esmaon, hese consrans help no o dverge no unusual dynamc shape deformaon. Second, he syle esmaon needs o become more dscrmnave as rackng progresses. If we ry o be dscrmnave from he begnnng and selec a specfc syle for ga recognon, he esmaed syle nclnes o be rapped n local mnma. Therefore, we sar from he mean syle, whch s he syle wh unform weghs for all he represenave shape syle classes. When addonal frames become avalable, he esmaed syle vecor can gradually be more dscrmnave snce weghng parcles become more sensve o observaons. To acheve hs progressve dscrmnaon, we use a deermnsc annealng lke procedure: esmaed syle weghs are forced o be close o unform weghs a he begnnng o avod hard decsons abou syle classes and gradually become dscrmnave hereafer. We assume he syle dsrbuon gven observaon Z, global ransformaon T α and body confguraon b, can be approxmaed by a Gaussan dsrbuon. ( ) s φ (k) P(Z α,b,s(k) ) exp d(z,z (k) ) = exp ( d(z,t α A s (k) ) ψ(b )), s he conour from he generave model usng α,b,s(k). For geomerc ransformaon esmaon, we use weghed Chamfer dsance as dsance measure o gve more wegh o upper body par. For body pose esmaon, we use orened Chamfer dsance measure o be more sensve o leg orenaon. When he where d( ) s dsance measure, z (k) varance Σ s very bg (Σ >> d(z,z ) ), he wegh s φ (k) wll be assgned smlar value regardless o d( ). When he varance s small (Σ < d(z,z ) ), he lkelhood s sensve o he dsance value and correspondng weghs n he parcle updae wll be dscrmnave. To acheve annealng-lke procedure, we use syle class varances, whch are unform o all classes and are defned by Σ s = T s σ s I + λ I respecvely as me varan parameers. The parameers T s sar wh large values a he frs frame and are gradually reduced and n each sep and a new body confguraon esmae s compued. 3.3 Trackng Algorhm We perform rackng of ga syle by sequenal updae of he margnalzed sub-denses ulzng he predced denses of he oher sub-saes. These denses are Σ Σ

5 updaed wh curren observaon Z by updang weghng values of each sub-sae parcle approxmaons gven observaons. We esmae global ransformaon α usng predced densy ŝ, ˆb. Then body confguraon b s esmaed usng esmae global ransformaon α, and predced syle densy ŝ. Fnally syle s s esmaed wh gven esmaon α, and b. The followng able summarzes he sae esmaon procedure usng me esmaon.. Imporance-samplng wh re-samplng a : For gven sae densy esmaon: {α (), α π () }N α =, {β ( j), b π ( j) }N b (k) j=, {λ, s π (k) }N s k=. Re-samplng: {ὰ (),/N ( j) α}, { `β,/n b}, and {`λ (k),/n s}.. Predc curren sae denses usng dynamc models: α () = Hὰ () + N(,σ α ) β ( j) ( j) = `β + ṽ + N(,σ b ), b ( j) = f (β ( j) ) λ (k) (k) = `λ + N(,σ s ), λ (k) = λ (k), Ns = λ (k) 3. Force syle parcle o sasfy consrans of Eq. 7: If λ (k) hen, λ (k) = forall,k, λ (k) = λ (k) Ns = λ (k) 4. Sequenal updae of sae weghs usng curren observaon: Global ransformaon α wh ˆb, ŝ : P(α () α π () ˆb,ŝ,Z ) P(Z α (), ˆb,ŝ )P(α () = P(Z α (), ˆb,ŝ ), α π () ) = α π () Nα j= α π ( j) Body pose b wh α, ŝ : α = α ( ),where = argmax α π () b π ( j) P(b ( j) α,ŝ,z ) P(Z α,b ( j),ŝ )P(b ( j) ) = P(Z α j),b(,ŝ ), b π ( j) = b π ( j) N b = b π () Syle s wh α, b : b = b ( j ),wherej = argmax b j π ( j) P(s (k) s π (k) α,b,z ) P(Z α = P(Z α,b,s(k) ), s π (k) 5. Reducng syle varance: 4 Expermenal Resuls )P(s (k),b,s(k) ) = s π (k) Ns = s π () We demonsrae he performance of he proposed algorhms on Unversy of Souhampon (UoS) ga daabase [8]. The daabase provdes well-exraced slhouee mages under conrolled envronmens for walkng sequence of more han people. We used provded slhouee sequences o learn our nonlnear generave model n Sec.. We colleced subjecs o learn he global shape deformaons dependen on ndvdual syle and embeddngs. Four cycles from each person are used o learn,. he syle varaons n each person. Toal 4 cycles are used o learn he generave model (N s = 4) afer knemacs manfold embeddng. Represenaon: We represen shape by an mplc funcon smlar o [6] where he conour s he zero level of such funcon. From each frame, we exraced edge usng Canny edge deecor algorhm. 4. Synhess of New Dynamc Shapes We esed he performance of synhess of shape deformaon accordng o shape syle vecor n our nonlnear generave model by changng syle parameer and s dmenson. Fg. 3 (a) shows colleced orgnal sequence of hree dfferen people. When we use reduced number of syle bass, we los deals of he person. However, we sll be able o generae sequences showng body pose change even wh one bass as shown n he frs row of Fg. 3 (b). When we used correspondng person syle vecors wh full dmenson, he new sequence preserves deal dfference of ndvdual shape deformaon. Fg. 3 (c) shows lnear nerpolaon of syle vecor and correspondng shape nerpolaon. Ths capably allows rackng of new person adapvely as shown n he followng expermens. 4. Ga Recognon Usng Shape Syle We esed he performance of ga recognon n wo suaons. Frs, we perform ga recognon durng rackng usng edge nformaon whou any background subracon. Ga recognon s performed by selecng hghes weghs n esmaed syle weghs represened by parcles. We esed he ga recognon performance for ndoor sequences. The ndoor sequences have relavely smple background. However, when we use jus edge nformaon, s no easy o esmae he whole shape and denfy he person as has many mssed edge n he correspondng conours and addonal edge nsde desred conour, whch causes confuson n he esmaon of shape usng edge-based dsance ransformaon (DT). Fg. 4 shows change of syle weghs for wo people ga sequences. Boh of he case, he weghs begn from equal weghs and gradually f o one of shape. In case of person, he person syle ge domnan quckly. In he case of person 4, he correc person syle fals o fnd correc syle when he geomerc ransformaon msalgned conours around 3 h frame. Table shows ga recognon resuls from each person sequence. We dd no coun syle weghs of he nal frames as syle weghs are no relable a he begnnng. Second, we esed he ga recognon when exraced slhouee sequences are gven. We seleced 4 cycles from 37 people and learn he generave model. In hs case, he syle dmenson becomes 48 (37 4) dmenson. We

6 Table. Ga recognon confuson marx Person Id P P P3 P4 P5 P6 P7 P8 P9 P P (3.3%) 5 (83.3%) 3(%) (3.3%) P 3(%) P3 3(%) P4 3(76.7%) 3(%) (6.7%) (6.7%) P5 (3.3%) 8(93.3%) (3.3%) P6 (3.3%) (3.3%) 4(46.7%) 3(%) P7 4(8.%) 5(6.7%) (3.3%) P8 (3.3%) (3.3%) 8(93.3%) P9 (3.3%) 5(83.3%) (3.3%) (6.7%) (3.3%) P (36.7%) (3.3%) 3(%) 5(5%) (a) Orgnal slhouees (b) Synhess n dfferen syle dmenson (c) Syle combned synhess Fgure 3. Syle dependen dynamc shape synhess: (a) Row : P, Row : P, Row 3: P3 orgnal slhouee, (b) Synhess of P slhouees usng Row : syle bass, Row : 5% syle bass, Row 3: full syle bass, (c) Synhess by syle combnaon: Row :.5P+.5P, Row :.5P+.5P3, Row 3: combnaons of all syle vecors equally (mean syle vecor) colleced anoher 3 cycles whch are no used for model learnng from he same daabase and esmaed syle vecor n closed form usng pseudo nverse as explaned n Sec... For each esmaed 48 dmensonal vecor, we compue smlary by nner produc S s es, whch gves cosne value of wo vecor snce he syle bass are orhonomal. We classfed ga by maxmum smlary value and we ge 83.8% recognon rae from 37 subjecs by recognzng 93 sequence correcly a rank among (3 37) sequences. Furher expermen shows cumulave machng characerscs(cmc) as n Fg. 5. Idenfcaon Rae Cummulave Mach Score Rank Fgure 5. Performance of ga recognon usng syle vecor 5 Conclusons We presened a ga rackng and recognon sysem usng nonlnear generave model for person-dependen conour deformaon. Usng knemac manfold represenaon, we can perform rackng body pose on a one-dmensonal manfold. By represenng varaons n spaoemporal conour deformaon among dfferen people usng syle vecors, we can acheve person denfcaon usng ga smulaneously wh person-adapve conour rackng. For accurae esmaon of hgh dmensonal syle vecor, we added consrans n he shape syle parcles and employed annealng-lke gradual ncrease of dscrmnaon. We performed ga recognon wh smple smlary measuremen and relavely small daase ha showed promsng resuls. More advanced classfcaon algorhms can be performed usng syle vecors as feaure vecors. Expermens wh larger dae se of subjec and oudoor sequences wll be performed n he fuure. In case of vew varan suaon, we may be able o exend curren blear decomposon of mappng no mullnear model wh vew facor n addon o syle facor. We may be able o acheve smlar resul usng concepual manfold embeddng [] nsead of knemac manfold embeddng. Acknowledgemen Ths research s parally funded by

7 Syle Syle Syle 3 Syle 4 Syle 5 Syle 6 Syle 7 Syle 8 Syle 9 Syle Person Syle Syle Syle 3 Syle 4 Syle 5 Syle 6 Syle 7 Syle 8 Syle 9 Syle Person 4 Syle weghs.4.3 Syle weghs Frame number Frame number Fgure 4. Smulaneous ga recognon and rackng:lef: person syle weghs and conour rackng a 5h, h, h, 3h, and 4h frames. Rgh: person 4 syle weghs and conour rackng a 5,,, 3, 4h frame NSF award IIS-3899 References [] A. Baumberg and D. Hogg. Generang spaoemporal models from examples. Image and Vson Compung, 4(8):55 53, 996. [] C. BenAdbelkader, R. Culer, and L. Davs. Moon-based recognon of people n egenga space. In Proc. of FGR, pages 54 59,. [3] T. F. Cooes, C. J. Taylor, D. H. Cooper, and J. Graham. Acve shape models: Ther ranng and applcaons. CVIU, 6():38 59, 995. [4] D. Cunado, M. S. Nxon, and J. Carer. Auomac exracon and descrpon of human ga models for recognon purposes. CVIU, 9: 4, 3. [5] J. Deuscher, A. Blake, and I. Red. Arculaed body moon capure by annealed parcle flerng. In Proc. of CVPR, volume, pages 6 33,. [6] A. Elgammal and C.-S. Lee. Inferrng 3d body pose from slhouees usng acvy manfold learnng. In Proc. CVPR, volume, pages , 4. [7] A. Elgammal and C.-S. Lee. Separang syle and conen on a nonlnear manfold. In Proc. CVPR, volume, pages , 4. [8] P. Huang, C. Hars, and M. Nxon. Recogsng humans by ga va paramerc canoncal space. Arfcal Inellgence n Engneerng, 3: , 999. [9] M. Isard and A. Blake. Condensaon condonal densy propagaon for vsual rackng. In.J.Compuer Vson, 9():5 8, 998. [] A. Kale, A. Sundaresan, A. N. Rajagopalan, N. P. Cunoor, A. K. Roy-Chowdhury, V. Kruger, and R. Chellappa. Idenfcaon of human usng ga. IEEE Trans. Image Processng, 3(9):63 73, 4. [] C.-S. Lee and A. Elgammal. Ga syle and ga conen: Blnear model for ga recognon usng ga re-samplng. In Proc. of FGR, pages 47 5, 4. [] C.-S. Lee and A. Elgammal. Syle adapve bayesan rackng usng explc manfold learnng. In Proc. of Brsh Machne Vson Conference, 5. [3] L. Lee, G. Dalley, and K. Teu. Learnng pedesran models for slhouee refnemen. In Proc. of ICCV, pages , 3. [4] Z. Lu and S. Sarkar. Smples represenaon ye for ga recognon: Averaged slhouee. In Proc. ICPR, pages 4, 4. [5] T. Poggo and F. Gros. Neworks for approxmaon and learnng. Proceedngs of he IEEE, 78(9):48 497, 99. [6] S. Rowes and L. Saul. Nonlnear dmensonaly reducon by locally lnar embeddng. Scence, 9(55):33 36,. [7] B. Schlkopf and A. Smola. Learnng wh Kernels: Suppor Vecor Machnes, Regularzaon, Opmzaon and Beyond. MIT Press,. [8] J. D. Shuler, M. G. Gran, M. S. Nxon, and J. N. Carer. On a large sequence-based human ga daabase. In Proc. In. Conf. on Recen Advances n Sof Compung, pages 66 7,. [9] J. B. Tenenbaum and W. T. Freeman. Separang syle and conen wh blear models. Neural Compuaon, :47 83,. [] D. Tollver and R. T. Collns. Ga shape esmaon for denfcaon. In Proc. AVBPA, pages , 3. [] K. Toyama and A. Blake. Probablsc rackng n a merc space. In ICCV, pages 5 59,. [] L. Wang, T. Tan, H. Nng, and W. Hu. Slhouee analyssbased ga recognon for human denfcaon. IEEE Trans. PAMI, 5():55 58, 3. [3] Q. Wang, G. Xu, and H. A. Learnng objec nrnsc srucure for robus vsual rackng. In CVPR, volume, pages 7 33, 3.