Online EM Algorithm for Background Subtraction

Transcription

1 Avalable onlne a Proceda Engneerng 9 (0) Inernaonal Workhop on Informaon and Elecronc Engneerng (IWIEE) Onlne E Algorhm for Background Subracon Peng Chen a*, Xang Chen b,bebe Jn a,xangbng Zhu a a College of Phyc and Elecronc Informaon, Anhu Normal Unvery, WuHu 4000, P.R. Chna b Guangzhou eeorologcal Saelle Saon, Guangzhou 50640, P.R.Chna. Abrac Gauan mure model a popular model n background ubracon and effcen equaon have been derved o updae G parameer prevouly. In order o compue parameer more accuraely whle manan conan compung me per frame, we apply onlne E algorhm o updae he parameer of Gauan mure model. o avod compung he nvere of covarance mar, we ue oropc mar and he correpondng ncremenal E equaon are derved. Epermen demonrae ha onlne E algorhm can gve more accurae egmen reul han prevou updae equaon. 0 Publhed by Elever Ld. Open acce under CC BY-NC-ND lcene. Keyword: Gauan mure model; on-lne E; background ubracon. Inroducon Background ubracon o deec all he movng obec (foreground) n a vdeo ream by buldng a repreenaon of he cene called he background model. Once learned, h background model compared agan he ncomng frame and any gnfcan change n an mage regon from he background model gnfy a movng obec. Over he year, numerou algorhm have been propoed for background ubracon uch a Gauan ure odel (G)[] and he Kernel Deny Emaor(KDE) []. In he cae of pel-level background model, he background can be decrbed by a probably deny funcon (PDF) for each pel eparaely. Sngle Gauan model one of uch model and wa propoed by Wren e al.[3]. Alhough ngle Gauan model ha been ued uccefully for ndoor cene, for more comple oudoor cene, no a good model [4] and elaborae model are needed. A ubanal mprovemen n background modelng acheved by ung mulmodal model uch * Peng Chen. el.: E-mal addre: ahnuchp@mal.ahnu.edu.cn Publhed by Elever Ld. do:0.06/.proeng Open acce under CC BY-NC-ND lcene.

2 Peng Chen e al. / Proceda Engneerng 9 (0) a G o decrbe per-pel background color. In G, each pel value modeled a a mure of Gauan. A pel from a new mage condered o be a background pel f new value well decrbed by background deny funcon. Oherwe, he pel clafed a foreground. Effcen updae equaon n G are gven n [] wh a fed number of Gauan componen. Zoran and Ferdnand propoed an adapve mehod whch can auomacally elec he rgh number of componen [5]. In h paper, we decrbe he G mehod n on-lne Epecaon amzaon (E) framework and how ha he foreground obec can be deeced more accuraely f he parameer of G are calculaed by onlne E mehod. he paper organzed a follow. In he ne econ, we revew G background ubracon approach and decrbe algorhm n he E framework. In Secon 3, wo knd of onlne E algorhm are nroduced. Epermenal reul for a mple Gauan mure model and vdeo baed background ubracon are preened n Secon 4 before concluon n Secon 5.. Gauan ure odel and E Algorhm For oudoor cene, mulple color can be oberved a a ceran locaon due o complcaed oudoor cene and llumnaon varaon. In h cae, mulnomal PDF uch a G have been nroduced o model he background. In more deal, G model each pel wh a mure of Gauan. hu, a me $$, he probably of occurrence of a pel value repreened a p( ) = w N( μ, Σ ) θ () = where w 0 and w =. he parameer vecor θ con of he mng proporon w, he mean vecor μ and he covarance marce. For a gven pel locaon, we aume ha N pel value X = {,,3 N} ndependen dencally drbued. We can oban emaon of θ by mamzng log lkelhood funcon wh andard E algorhm (Algorhm ) [6]. For every pel locaon, we ue he andard E algorhm o deermne he correpondng G parameer vecor. o clafy he new pel, we ue he followng rule [5]: B () { p ( BG ) = w N ( μ, Σ )} > chr = where c hr a conan hreh. If () afed, he new pel hould be clafed a a background pel. he componen are ored n decendng order by proporon w. p( BG) he background model whch repreened by B large Gauan componen of all componen n (). B can be deermned by b B = arg mn w > c (3) b b = where c b a meaure of he mnmum poron of he pel ha can appromae background. he aracvene of he andard E algorhm (Algorhm ) ha eay o mplemen and guaraneed o converge o a local mamum of he log-lkelhood funcon. However, h algorhm need o collec all he mage frame o compue he G parameer, whch demand huge amoun of memory and make unuable o be ued n real me applcaon. o overcome h dffculy whle mananng he advanage of E algorhm, we brng forh an onlne E approach n he ne econ.

3 66 Peng Chen e al. / Proceda Engneerng 9 (0) Onlne E Algorhm 3.. Suffcen Sac Baed Algorhm A andard E algorhm a bach algorhm, applyng E o background ubracon applcaon me and memory conumng. For he ake of h, he E algorhm can only work offlne. o overcome h lmaon, we ue an ncremenal veron of E algorhm (onlne E). Compared wh E algorhm, he onlne E change he parameer mmedaely afer each daa arrved. I need no ore all he daa and hu olve he problem confroned by E algorhm. he fr one uded n h paper he algorhm preened by [7], whch baed on uffcen ac. Algorhm (onlne E): E-ep Calculae he poeror probably ha -h componen reponble for generang (ame a algorhm )[6].Afer each new daa arrved, updae uffcen ac vecor for each componen: new =< ε, ε, ε = = = >= + < ε, ε, ε -ep amze he lkelhood funcon wh repec o parameer θ: w = /( + + L + ) μ = / Σ = / /( ) 3 = ε = ε, 3 = = = =, ε >, = K where, and 3 are he correpondng elemen of uffcen ac vecor for he -h componen repecvely. he dfference beween Algorhm and Algorhm ha n Algorhm, he parameer are emaed by uffcen ac vecor whch accumulaed a new daa arrved. Furhermore, Algorhm can only emae parameer vecor θ afer all daa are proceed n E ep, wherea Algorhm can emae θ mmedaely afer each daa arrved. Noe ha n background ubracon applcaon, daa em a 3 dmenonal vecor whch compre hree color value (RGB), a calar, a 3 dmenonal vecor and 3 a 3 by 3 ymmerc mar. A a full 3 by 3 covarance mar, we need o compuer nvere and deermnan n E ep. In order o mplfy calculaon, we can keep covarance marce oropc by makng =σ I 3 3. Now he parameer vecor θ con of he mng proporon w, he mean vecor μ and he covarance value σ. By mamzng log-lkelhood, we can derve mlar erave equaon for oropc covarance marce baed onlne E algorhm. Algorhm 3(mplfed onlne E): E-ep Calculae he poeror probably ha -h componen reponble for generang :

4 Peng Chen e al. / Proceda Engneerng 9 (0) w N ( μ, σ Ι 3 3 ε = p( ; θ ) = w N ( μ, σ Ι 3 3 ) = Calculae he uffcen ac vecor for each componen: new = + < ε, ε, ε >, = K -ep amze he lkelhood funcon wh repec o parameer θ: w = μ = σ = 3 /( / ( / /( )) L+ ) Noe ha now 3 a calar, wherea n Algorhm, 3 a ymmerc mar. Noe alo ha he deermnae and nvere of σ I 3 3 very eay o calculae, whch ave a lo of compung me. 3.. Eponenally Decay Facor Baed Algorhm Anoher ncremenal varan of he E algorhm wa preened by Nowlan [8]. I ue ac compued a an eponenally decayng average of recenly-ved daa pon. Algorhm 4(decay onlne E): E-ep Calculae he poeror probably ha -h componen reponble for generang [6]. Calculae he uffcen ac vecor for each componen: new = + γ < ε, ε, ε >, = K where γ he decayng facor. -ep Same a he ep n Algorhm. Smlarly, we can alo derve eponenally decay onlne E algorhm for oropc covarance marce. 4. Reul 4.. ure model reul In order o demonrae ha he ncremenal E algorhm can fnd he correc parameer of G model, we have appled o a 3 componen dmenonal G model. We ynhecally generaed daa pon from h G model and hen appled he andard E and he ncremenal E o emae he model' parameer. For andard E, we ue 000 daa em a npu and erae E ep 00 me. A each daa em wll be ved only once n ncremenal E, we ue daa em for o make onlne and andard E go hrough he ame number of E ep. Fg how he reul. We can ee from Fg ha he onlne E a good appromaon o he andard E. If he covarance no mporan, hen he mplfed onlne E wh oropc covarance marce can alo be condered. )

5 68 Peng Chen e al. / Proceda Engneerng 9 (0) Background ubracon reul o demonrae he effecvene of he propoed mehod for background ubracon, we compare onlne E baed background ubracon reul wh ha of Adapve Deny Emae (ADE) [5]. Epermenal reul reveal ha our mehod can reduce he noe around egmened foreground obec (Fg ). a b c d e f Fg.. G model reul. (a) Daa generaed. (b)rue PDF. (c) Sandard E (d) Smplfed onlne E (e) Onlne E (f) Decay onlne E a b c d e f Fg.. Background ubracon reul. Algorhm 3 ued for onlne E. (a) frame 96; (b) ADE for Frame 96; (c) Onlne E for Frame 96;(d)frame 76;(e) ADE for Frame 76;(f)onlne E for Frame 76.

6 Peng Chen e al. / Proceda Engneerng 9 (0) Concluon Gven background ubracon n a broad range of applcaon, adopon of he new echnque provde gnfcan benef n a number of area. In h paper, we propoe a novel approach by ung onlne E algorhm. Our mehod can recognze foreground obec more accuraely compared o he ADE. Fuure reearch nclude eplorng cohevene of adacen pel nead of relyng olely on each pel n olaon. Alo, how o eplo emanc of obec from hgh level module o feedback he deecon needed o focu on. A more robu model for dynamc background anoher ue. 6. Acknowledgemen h work wa uppored by Naural Scence Foundaon of Anhu Provnce, Chna (No ), Key Program of Naural Scence Foundaon of Anhu Provnce, Chna and Docor Reearch Foundaon of Anhu Normal Unvery. Reference [] C. Sauffer and W.E.L. Grmon, Adapve background mure model for real-me rackng, n IEEE Compuer Socey Conference on Compuer Von and Paern Recognon., 999, vol., pp [] Ahmed Elgammal, Davd Harwood, and Larry Dav, Non-paramerc model for background ubracon, n Compuer Von-ECCV 000, pp [3] Chropher Rchard Wren, Al Azarbayean, revor Darrell, and Ale Penland, Pfnder: Real-me rackng of he human body, IEEE ranacon on Paern Analy and achne Inellgence, vol. 9, no. 7, pp , 997. [4] X. Gao,. E. Boul, F. Coezee, and V. Rameh, Error analy of background adapon, n CVPR, 000, pp. I: [5] Zoran Zvkovc and Ferdnand van der Heden, Effcen adapve deny emaon per mage pel for he ak of background ubracon, Paern Recognon Leer, vol. 7, no. 7, pp , 006. [6] Bhop C. Paern Recognon and achne Learnng[]. ed. Cambrdge:Sprnger, 008. [7] R.. Neal and G. E. Hnon, A new vew of he E algorhm ha ufe ncremenal, pare and oher varan, n Learnng n Graphcal odel,. I. Jordan, Ed., pp Kluwer Academc Publher, 998. [8] S. J. Nowlan, Sof Compeve Adapaon: Neural Nework Learnng Algorhm baed on Fng Sacal ure, Ph.D. he, School of Compuer Scence, Carnege ellon Unvery, Pburgh, PA, Apr. 99.