PCA Based Gait Segmentation

Transcription

1 Honggu L, Cupng Sh & Xngguo L PCA Based Gat Segmentaton PCA Based Gat Segmentaton Honggu L, Cupng Sh, and Xngguo L 2 Electronc Department, Physcs College, Yangzhou Unversty, Yangzhou, Chna 2 Department of Electronc Engneerng, Nanng Unversty of Scence & echnology, Nanng, Chna hgl@yzu.edu.cn Abstract A PCA based gat segmentaton method s proposed. Background mages are used for PCA tranng. PCA reconstructon, recursve error compensaton and sngle threshold based method s put forward for gat segmentaton. Sngle threshold based method has the same gat segmentaton ablty as classcal adaptve threshold based method, and the former s faster n mplementaton than the later. Proposed method s better than classcal background subtracton based method, and can be compared wth Gaussan dervatve flter based method. Proposed method converges rapdly and has the excellent capablty of gat segmentaton for varant background. Keyword: PCA, Gat segmentaton, Gat recognton.. ntroducton Gat recognton s one of the man technologes for authentcatng a person at a long dstance. ther bometrcs technologes, such as fngerprnt recognton, rs recognton, face recognton, hand recognton and palmprnt recognton, can't work effectvely when person s far away. Gat segmentaton s the frst step for gat analyss and recognton. Gat segmentaton can be defned as extractng human body from background n gat mage. Usually the result of gat segmentaton s a slhouette mage. Classcal gat segmentaton method s background subtracton []. hs method can't work well when pxel of foreground mage has smlar gray level value as that of pxel of background mage n the same poston. Because there are new edges at human body contour n foreground mage, human body counter can be found through comparng the edge nformaton between foreground mage and background mage. We have provded a new gat segmentaton method, whch s based on comparng flterng results between foreground mage and background mage usng mult-scale and mult-drecton Gaussan dervatve flters [2]. Better gat segmentaton method s stll expected. Face recognton technology has been developed deeply, and a lot of algorthms have been proposed. Successful face recognton method can be used for other bometrcs. Some approaches have been * hs paper s sponsored by the proect (No. 04KJB5067) from educaton department of Jangsu, Chna. 36

2 nternatonal Journal of nformaton echnology Vol. 2 No proposed to extract and remove eyeglasses from facal mages. f we take person n gat mage as glasses n facal mage, glasses removal algorthm can be used for gat segmentaton. Sato reconstructed eyeglassless facal mages usng PCA [3]. Facal mages wth eyeglasses are proected nto the egenspace traned by eyeglassless facal mages, from whch correspondng eyeglassless facal mages are reconstructed. he representatonal capablty of PCA depends on the tranng mages. Because the tranng mages have no eyeglasses, the reconstructed mages don t have eyeglasses no matter the nput facal mages have eyeglasses or not. herefore, reconstructon errors caused by eyeglasses are spread out over the entre reconstructed mage. hs results n some degradaton of qualty and some traces of the eyeglasses frame remaned. Smple PCA method has some lmtatons n obtanng natural lookng glassless facal mages. Cheng Du and Guangda Su removed eyeglasses from facal mage usng PCA reconstructon, recursve error compensaton and adaptve threshold based method [4]. egons, whch are occluded by eyeglasses, are frstly detected by adaptve bnarzaton approach. hen natural lookng eyeglassless facal mage s obtaned by recursve error compensaton of PCA reconstructon. he reconstructed mages have nether trace of eyeglasses, nor the reflecton and shade caused by the eyeglasses. A PCA reconstructon, recursve error compensaton and sngle threshold based method s proposed n ths paper. he rest part of ths paper s arranged as follows. PCA and SVD algorthm are ntroduced n secton 2. Smple PCA reconstructon based gat segmentaton method and PCA reconstructon, recursve error compensaton and sngle threshold based gat segmentaton method wll be dscussed n secton 3. Experments and results are n secton 4. Secton 5 s conclusons.. PCA Algorthm and SVD Algorthm Proposed method s derved from PCA algorthm and SVD algorthm. PCA algorthm and SVD algorthm are descrbed as follows. A. SVD Algorthm SVD algorthm s gven frstly. Let A be a M N real matrx of a face mage, M > N, and rank A =, the sngular value decomposton ( SVD ) of A s, ( ) K where, Σ = dag( λ0, λ,..., λk,0,...,0), U = [ u0, u,..., uk, uk, uk +,..., um ], V = [ v0, v,..., v K, v K, v K +,..., v N ], Σ s a M N matrx, U s a M M matrx, V s a N N matrx, λ, = 0,,..., K are egenvalues of AA as well as λ, = 0,,..., K are sngular values of A, u, = 0,,..., M are column egenvectors of AA, v, = 0,,..., N are column egenvectors of A A. 2 A = UΣ V. () A A, and λ 0 > λ >... > λk, 37

3 Honggu L, Cupng Sh & Xngguo L PCA Based Gat Segmentaton he relatonshp of U and V s 2 U = AVΣ. (2) B. PCA Algorthm PCA ( prncpal component analyss ) algorthm s dscussed as follows. Let, = 0,,..., M be N N face mages for tranng, and t can be represented as N 2 vectors Γ, = 0,,..., M. he dfference vector Φ s defned as Φ = Γ Ψ, where M Ψ = Γ. M Ψ s the average vector of where A [ Φ Φ Φ ] = 0,,..., M dffcult, so egenvectors v of SVD, AA and A A u = Av. λ mage Γ. he 2 2 N N covarance matrx C s defned as, M C = ΦΦ M = 0 = AA M. Drectly computng egenvectors u of M M matrx A A s computed ( = 0. (3) 2 2 N N matrx AA s 2 M << N ). Accordng to have same egenvalue λ, and the relatonshp of u and N N can be represented as vector N 2 v s Γ, and related dfference vector s Φ = Γ Ψ. he feature of N N s F = U Φ. he reconstructed Φˆ s Φ ˆ = UF. he reconstructed mage vector Γˆ s Γ ˆ = Φ ˆ + Ψ. (4). Gat Segmentaton Method Smple PCA reconstructon based method, and recursve error compensaton and sngle threshold based method, are depcted as follows. A. Smple PCA econstructon Based Method Frstly background mages are used to tran PCA algorthm [3]. Secondly foreground mage s proected to the egenspace traned by background mages. hen reconstructed mage of foreground mage can be computed from egenspace usng PCA reconstructon algorthm. Because tranng mages have no person, the reconstructed mage has no person yet. Fnally, reconstructed mage s subtracted from orgnal foreground mage, and segmented bnary mage can be ganed by threshold, where H s threshold operator. ( ) = H. (5) 38

4 nternatonal Journal of nformaton echnology Vol. 2 No B. ecursve Error Compensaton and Sngle hreshold Based Method PCA reconstructon, recursve error compensaton and sngle threshold based gat segmentaton method s gven as follows. t s followed by a postprocessng, n order to obtan good gat segmentaton results. he qualty of from smple PCA reconstructon based method s not very good. ecursve error compensaton and sngle threshold based method should be used [4]. he man dfference between proposed method and method n [4] s, usng sngle threshold to take the place of adaptve threshold. he proposed method s depcted as follows. where, s the number of teraton, s orgnal foreground mage, C s error compensaton mage, s PCA reconstructed mage, ( W ), =,2 J. (6) C = W +,..., ( ) PCA _ EC, = =. (7) C PCA _ EC( ), = 2,3,..., J ( m, n) ( m, n), = W ( m, n) =. (8) 0, = 0 ( ) = H. (9) s the segmented bnary mage, PCA _ EC s PCA reconstructon algorthm, W s weght matrx, H s sngle threshold operator, whch s take the place of adaptve threshold. C C f < ε, where ε s a small threshold, the algorthm s termnated. J s the ultmate segmented slhouette mage. Dstance between PCA reconstructed mage and orgnal mage s defned as ( ) = SUM ( ), =,2 J D,...,. (0) Because there are small regons and holes n J, a postprocessng s needed. Frstly a morphologcal close operator s used to merge small and near regons n J. hen bnary mage are labeled and small regons are removed. Fnally a hole-fllng operator s used to fll the hole n bnary mage. V. Experments and esults Gat mages come from CMU MB database [5]. hs database has 25 persons, sx dfferent vew angles, and four types of walk: slow walk, fast walk, slow nclne walk and slow walk holdng a ball. 39

5 Honggu L, Cupng Sh & Xngguo L PCA Based Gat Segmentaton A. PCA ranng wth Smlar Background mages 8 smlar background mages of vew angle are used for PCA tranng. Fg. s the result of proposed method. Fg. (a) s the background mage. Fg. (b) s the foreground mage. Fg. (c) s J. Fg. (d) s the result mage of morphologcal close operator. Fg. (e) s the result mage of removng small regons. Fg. (f) s the result mage of hole fllng. Fg. (f) shows that proposed method has perfect ablty of gat segmentaton. Fg. (g) s the result mage of background subtracton based method. Comparng Fg. (g) and Fg. (f), t shows proposed method s better than background subtracton based method. Fg. (h) s the result mage of Gaussan dervatve flter based method. Comparng Fg. (h) and Fg. (f), t shows proposed method s as good as Gaussan dervatve flter based method. Fg. () s the result mage of PCA reconstructon, recursve error compensaton and adaptve threshold based method. Comparng Fg. () and Fg. (f), t shows proposed method has the same ablty as PCA reconstructon, recursve error compensaton and adaptve threshold based method. Because proposed method uses sngle threshold and need not compute adaptve threshold, whose computaton load s large, t s faster n mplementaton than adaptve threshold based method. Fg. 2 and Fg. 3 further study the ablty of sngle threshold based method and adaptve threshold base method. Fg. 2(a)~2(d) are ~ 4 of sngle threshold based method. Fg. 2(e)~2(h) are ~ 4 of adaptve threshold based method. t shows the bggest dfference s n the frst teraton. hs s because, sngle threshold based method uses a unquely small threshold and adaptve threshold based method uses varant threshold, whch s n drect proporton to the mean of. Fg. 3 s the relatonshp curve of dstance D ( ) and the number of teraton. he sold lne s the curve of sngle threshold based method, and the dashed s the curve of adaptve threshold based method. t shows the bggest dfference s n second teraton. hs because s same n both methods of the frst teraton. Fg. 2 and Fg. 3 show sngle threshold based method has the same ablty for gat segmentaton as adaptve threshold based method. Fg. 3 also shows proposed method wll termnate at the ffth teraton. So proposed method converges rapdly. hs s very mportant for realtme gat recognton system. Fg. 4 has more examples of proposed method. B. PCA ranng wth Four Knds of Background mages 25 background mages of vew angle are used for PCA tranng. hese back-ground mages can be dvded nto four knds. Fg. 5 shows four knds of background and ts gat segmentaton examples. Fg. 5 shows that proposed method can be used for varant background. hs s very mportant for practcal gat recognton system. V. Concluson A PCA based gat segmentaton method s proposed. Frstly background mages are used for PCA tranng. hen PCA reconstructon, recursve error compensaton and sngle threshold based method s brought forward for gat segmentaton. Fnally a postprocessng s adopted for obtanng well segmented mage. Sngle threshold based method has the same ablty as classcal adaptve threshold 40

6 nternatonal Journal of nformaton echnology Vol. 2 No based method, and the former s faster n mplementaton than the later, because sngle threshold based method uses a unquely small threshold and adaptve threshold based method uses varant threshold. Proposed method s better than classcal background subtracton based method, and can be compared wth Gaussan dervatve flter based method. Proposed method converges rapdly and can be used for varant background. he man drawback of proposed method s that shade removng s not ncluded. n future work shade removng wll be studed. (a) (b) (c) (d) (e) (f) (g) (h) () Fg.. (a) Background mage, (b) foreground mage, (c) J, (d) result mage of morphologcal close operator, (e) result mage of removng small regons, (f) result mage of hole fllng operator, (g) result mage of background subtracton based method, (h) result mage of Gaussan dervatve flter based method, () result mage of PCA reconstructon, recursve error compensaton and adaptve threshold based method. 4

7 Honggu L, Cupng Sh & Xngguo L PCA Based Gat Segmentaton (a) (b) (c) (d) Fg. 2. (a) sngle threshold, (e) (e) (f) (g) (h) of sngle threshold, (b) 2 of sngle threshold, (c) of adaptve threshold, (f) threshold, (h) 3 of sngle threshold, (d) 2 of adaptve threshold, (g) 4 of adaptve threshold.. 4 of 3 of adaptve Fg. 3. he relatonshp curve of dstance and the number of teraton. Sold lne s the curve of sngle threshold, and dashed s the curve of adaptve threshold. 42

8 nternatonal Journal of nformaton echnology Vol. 2 No Fg. 4. More examples for foreground mages and related segmented mages. 43

9 Honggu L, Cupng Sh & Xngguo L PCA Based Gat Segmentaton (a) (b) (c) (d) Fg. 5. Four knds of background and ts gat segmentaton examples. (a) background and ts gat segmentaton example, (b) background 2 and ts gat segmentaton example, (c) background 3 and ts gat segmentaton example, (d) background 4 and ts gat segmentaton example. 44

10 nternatonal Journal of nformaton echnology Vol. 2 No eferences [] obert. Collns, alph Gross and Janbo Sh, Slhouette-based human dentfcaton from body shape and gat, Proc. of nt. Conf. n Automatc Face and Gesture ecognton, 2002, pp [2] Honggu L, Xngguo L, LLE based gat analyss and recognton, Stan Z. L (eds.), Advances n Bometrc Person Authentcaton, Lecture Notes n Computer Scence, Vol Sprnger-Verlag, Berln Hedelberg New York, 2004, pp [3] Sato, Y. Kenmoch, Y. and Kotan, K., Estmaton of eyeglassless facal mages usng prncpal component analyss, Proc. of nt. Conf. on mage Processng, Vol.4, 999, pp [4] Cheng Du, Guangda Su, Eyeglasses removal from facal mages, Manuscrpt Draft (PAEC-D pdf), Pattern ecognton Letters. [5].Gross, J. Sh, he CMU Moton of Body (MoBo) Database, echncal eport CMU , obotcs nsttute, Carnege Mellon Unversty, 200. Honggu L born n 97, receved B.S. degree of appled electroncs from physcs department of Yangzhou Unversty, Chna, n 994, and Ph.D. degree of mechancal-electronc engneerng from electronc engneerng department of Nanng Unversty of Scence & echnology, Chna, n 999. He was a tutor of Yangzhou Unversty n 994. He read for PhD degree n Nanng Unversty of scence and technology from 995 to 999. He s an assocate professor n Yangzhou Unversty snce Hs research area ncludes computer vson, pattern recognton and machne learnng. Cupng Sh born n 98, receved B.S. degree from Daqng Petroleum Unversty, Chna, n 2004, and M.S. degree from Yangzhou Unversty, Chna, n She s a tutor n Qqhaer Unversty n Chna. Her research area ncludes computer vson and pattern recognton. Xngguo L born n 940, receved B.S. degree from Chengdu Unversty of Electronc Scence & echnology n Chna. He s a professor and a doctoral supervsor n Nanng Unversty of Scence & echnology. Hs research area s MMW sgnal processng. 45