Computer Aded Draftng, Desgn and Manufacturng Volume 5, Number, June 015, Page 14 CADDM Face Recognton Algorthm Fusng Monogenc Bnary Codng and Collaboratve Representaton FU Yu-xan, PENG Lang-yu College of Physcs and Informaton Scence, Hunan Normal Unversty, Changsha, 410081, Chna. Abstract: Monogenc bnary codng (MBC) have been known to be effectve for local feature extracton, whle sparse or collaboratve representaton based classfcaton (CRC) has shown nterestng results n robust face recognton. In ths paper, a novel face recognton algorthm of fusng MBC and CRC named M-CRC s proposed; n whch the dmensonalty problem s resolved by projecton matrx. The proposed algorthm s evaluated on benchmark face databases, ncludng AR, PolyU-NIR and CAS-PEAL. The results ndcate a sgnfcant ncrease n the performance when compared wth state-of-the-art face recognton methods. Key words: face recognton; monogenc bnary codng; collaboratve representaton 1 Introducton Face recognton, as one of the most typcal applcatons of mage analyss and understandng, has been extensvely studed n the past two decades [1]. However, t s stll dffcult for machnes to recognze human faces accurately under the uncontrolled crcumstances, ncludng occlusons and varatons n pose, llumnaton, expresson and agng, etc. Varous methods have been proposed for face feature extracton, such as Egenfaces [], Fsherfaces [3], Gabor Featutre based Classfcaton [4], LBP [5], LGBP [6] and MBC [7], etc. However, the performance of Egenfaces and Fsherfaces degrades when the lghtng condtons or expresson change. Lterature [4] demonstrated the promsng performance of Gabor feature, but wth sgnfcant tme and space complexty. LBP methods use local structural nformaton and hstogram of sub-regons to extract facal features. In addton to ts effcency, the smplcty of LBP allows for faster feature extracton than other methods. The advantage of MBC over the Gabor s that t has much lower tme and space complexty but wth better performance. The advantage of MBC over the LBP s that t has compettve performance. Ths s manly because monogenc sgnal analyss s a compact representaton of features wth lttle nformaton loss. The recognton of a query face mage s usually accomplshed by classfyng the features extracted from ths mage. The most popular classfer for FR may be the nearest neghbor (NN) classfer due to ts smplcty and effcency. SVM [8] can be also seen a classfer. Wrght et al. [9] reported a very nterestng work by usng sparse representaton for robust face recognton (FR). The testng mage s coded as a sparse lnear combnaton of the tranng samples, and the representaton fdelty s measured by the l 1 -norm or l -norm of the codng resdual. Such a sparse representaton based classfcaton (SRC) scheme acheves a great success n FR, and t boosts the research of sparsty based pattern classfcaton. But, the sparsty constrant on the codng coeffcents makes SRC s computatonal cost very hgh. In [10], Zhang et al. ndcated that the success of SRC actually comes from ts collaboratve representaton of query face mage over all classes of tranng samples and proposed a very smple yet much more effcent face classfcaton scheme, namely CR based classfcaton wth regularzed least square (CRC_RLS). The SRC and CRC_RLS scheme s a very powerful classfer. The method [11-1] ams to combne LBP and sparse representaton together, whch demonstrated the effectveness of fused algorthm. Motvated by the success of method [11-1], a new face recognton algorthm fusng monogenc bnary codng and collaboratve representaton s proposed n ths paper. Zhang et al. [13] proposed an unsupervsed learnng method for dmensonalty reducton n SRC, and t leads to hgher FR rates than PCA and random Correspondng author: FU Yu-xan, Male, E-mal: 363533517@qq.com.
FU Yu-xan et al., Face Recognton Algorthm Fusng Monogenc Bnary Codng and Collaboratve Representaton 15 projecton. Ths valdates that a well desgned dmensonalty reducton method can beneft the sparse classfcaton scheme. So the method [13] s used to reduce the dmensonalty of hstogram features n ths paper. The rest of the paper s organzed as follows. Secton brefly descrbes the MBC algorthm. Secton 3 presents n detal the CRC_RLS algorthm. Secton 4 detals the whole scheme of face recognton algorthm fusng monogenc bnary codng and collaboratve representaton. Secton 5 presents the expermental results, and Secton 6 concludes the paper. and vertcal frequences. Fg. 1 shows a face mage. Fg. shows the monogenc representaton of a face mage at one scale. We can see that the facal local structures are well captured n ts monogenc components. Fg. 1. A face mage. Monogenc Bnary Codng (MBC) Monogenc sgnal was ntroduced by Felsberg and Sommer n 001 [14] to generalze the analytc sgnal from 1D to D. The monogenc representaton of D sgnals s accomplshed va the Resz transform [15]. Monogenc sgnal representaton decomposes a face mage sgnal nto three complementary components: ampltude, phase and orentaton. The local ampltude a, the local orentaton o and the local phase p can be computed by Eq. 1. a g hx hy hx h y p sgn hx arctan (1) g hy o arctan hx wth 1 g I* F Gw 1 1w h F H, x, y wx w y Here, I denotes the nput mage, and * denotes the convoluton operator, G(w) denotes the Log-Gabor flter n Fourer doman, F -1 represents the D nverse Fourer transform, H=F(g), The frequency response of log-gabor flters can be descrbed as w ln w0 Gwexp ln ln w 0 where w 0 s the center frequency and σ s the scalng factor of the bandwdth. w x and w y are the horzontal (a) (b) (c) Fg.. Monogenc representaton of a face mage at one scale: (a) ampltude component, (b) orentaton component (c) phase component. Monogenc bnary codng contans two parts. The frst part encodes the varaton between the central pxel and ts surroundng pxels n a local patch, whle the second part encodes the value of central pxel tself. Lke LBP [5], the local varaton of monogenc ampltude could be coded by comparng the ampltude value of central locaton wth those of ts neghbors. The nformaton of central pxel tself can have dscrmnatve nformaton whch may not be carred out by the local varaton. For nstance, the two pxels havng the same local varaton pattern may have very dfferent ntenstes. Yang [7] proposed to use the magery part of monogenc sgnal representaton to encode the local feature ntensty nformaton of the central pxel. Gven the sgnfcant tme complexty of the proposed algorthm, the monogenc orentaton and phase nformaton s not used n ths artcle. Fg. 3 shows the MBC of a face mage at three scales. Fg. 3. MBC of a face mage at three scales. The statstcal nformaton of mage local areas can
16 Computer Aded Draftng, Desgn and Manufacturng (CADDM), Vol.5, No., Jun. 015 be descrbed by local hstograms, whch are robust to the mage occluson and varatons of pose, expresson, and nose, etc. For each knd of pattern map on each scale, t s parttoned nto multple non-overlappng regons, and then the local hstogram s bult for each sub-regon. Fnally, all the local hstograms across dfferent scales and dfferent regons are concatenated nto a sngle hstogram vector to represent the face mage. 3 Collaboratve Representaton Usng Regularzed Least Square (CRC-RLS) CRC-RLS proposed by Zhang et al. [10] s a very smple yet very effectve face recognton method that explots the role of collaboraton between classes n mn representng the query sample. Denote by A the dataset of the th class, and each column of A s a sample of class. Suppose that we have K classes of subjects, and let A=[A 1, A,,A K ]. The query sample m s denoted y. In order to collaboratvely represent the query sample usng A wth low computatonal burden, Zhang [8] proposed to use the regularzed least square method. There s arg mn ya () where λ s the regularzaton parameter. The soluton of CR wth regularzed least square n Eq. can be easly and analytcally derved as T 1 T AA I Ay (3) Let P=(A T A+λI) -1 A T. Clearly, P s ndependent of y so that t can be pre-calculated as a projecton matrx. Once a query sample y comes, we can just smply project y onto P va Py. Ths makes CR very fast. 4 Face Recognton Algorthm Fusng Monogenc Bnary Codng and Collaboratve Representaton It can be seen that when the 8 closest neghbors of a pxel are nvolved n local varaton codng, each MBC pattern wll have 10 bts. Then the number of possble patterns for each MBC s 104, whch s larger than that of prevous bnary codng methods such as LBP, LGBP. It s easy to see that mult-scale monogenc sgnal representatons are redundant. We adopt the SDR (Sparse Dmensonalty Reducton) [16] scheme to reduce the hstogram feature dmenson whle enhancng ts dscrmnaton. In [16], Denote by z R m 1 the -th tranng sample of A and by A = [z 1, z -1, z +1, z n ]R m (n-1) the collecton of tranng samples wthout the -th sample, an orthogonal DR matrx P was learnt under the framework of sparse representaton, and t acheves better performance than Egenfaces and Randomfaces n the CRC scheme. Specfcally, the matrx P s learnt va the followng objectve functon based on Leave-One-Out scheme: P N arg mn, 1 1 1 F J Pz PA s.t. PP T A I T P PA F where β s the CR coeffcent vector of z over A, λ 1 and λ are scalar parameters. The whole algorthm of the proposed fusng monogenc bnary codng and collaboratve representaton s summarzed as follows: (1) When a face mage comes, the MBC hstogram s computed. Denote by X and y the dmensonalty reduced features of MBC hstogram of a tranng mage and a testng mage. The dctonary s denoted by X=[X 1, X,,X ]. () The projecton matrx s computed as P=(X T X +λi) -1 X T. y s coded over dctonary X by ρ=py. (3) The regularzed resduals s computed as r y X (4) The dentfy of y s output as Identty(y)=arg mn {r }. 5 Expermental Results and Analyss In order to evaluate the effectveness of the proposed method, extensve experments were carred out on 3 standard databases: AR [17] PolyU-NIR [18] and CAS-PEAL [19]. All the experments were carred out usng Matlab verson R01a on a 3.30 GHz machne wth 3.49 GB RAM. In AR, as n [10], a subset (wth only llumnaton and expresson changes) that contans 50 male subjects and 50 female subjects was chosen from the AR dataset n our experments. For each subject, the seven mages from Sesson 1 were used for tranng, wth the other seven mages from Sesson for testng. The mages were cropped to 60 43. The comparson of competng methods s gven n Table 1. In order to be consstent wth other methods and provde a far comparson, we used SDR reduce the dmenson of
FU Yu-xan et al., Face Recognton Algorthm Fusng Monogenc Bnary Codng and Collaboratve Representaton 17 each mage to 300. In our test, 8 samplng ponts on a crcle of radus of 8 are adopted, and a LBP or MBC mage s dvded nto 5 5 sub-blocks. In the DR learnng process, λ 1 =0.03 and λ =1.5. LBP uses a nearest neghbor classfer and ts smlarty measure s based on the Ch-square dstance. Whle cosne dstance s used n MBC. The parameter λ n CRC s set as 0.01. Consderng the accuracy and effcency, we chose l1_ls [0] to solve the l1-regularzed mnmzaton n SRC. Table 1. Recognton Rate and Speed on AR Database Recognton rate /% Tme /s NN 71.30 - SVM 68.44 - SRC 84.17 1.9633 CRC 84.69 0.0031 L-SRC [11] 93.9.0064 M-CRC 98.06 0.0579 In PolyU-NIR., The PolyU-NIR face database s a large scale near-nfrared face database, consstng of 350 subjects, each subject provdng about 100 samples. Varous varatons of face mages, such as expresson, pose, scale, focus, tme, are nvolved n the capturng. In our experments, a subset of 18 subjects (each subject provdng about 50 samples) was chosen from the PolyU-NIR dataset. We randomly chose 5 samples per subject as tranng set, wth the remanng as the testng set. The face mages are normalzed to 64 64 pxels. We used SDR reduce the dmenson of each mage to 300. In the DR learnng process, λ 1 =0.005 and λ =.0. Other settngs of the experments are n accord wth the testng on AR. The maxmal recognton rate of each method s lsted n Table. Table. Recognton Rate and Speed on PolyU-NIR Database Recognton Tme /s rate /% NN 6.1 - SVM 76.00 - SRC 93.30 1.7878 CRC 93.70 0.004 L-SRC [11] 94.75 1.8031 M-CRC 97.4 0.0401 In CAS-PEAL, the CAS-PEAL s a large-scale database of face photographs, whch s constructed by the Jont R&D Laboratory for Advanced Computer and Communcaton Technologes (JDL) of Chnese Academy of Scences (CAS). The CAS-PEAL face database contans 99,594 mages of 1040 ndvduals (595 males and 445 females) wth varyng Pose, Expresson, Accessory, and Lghtng (PEAL). In ths paper, we do three tests followng the experment settng n [1]. These three subsets are Expresson (100 tranng samples, 1040 gallery samples and 1884 testng samples), Accessory (100 tranng samples, 1040 gallery samples and 616 testng samples), and Dstance (100 tranng samples, 1040 gallery samples and 34 testng samples). The mage s cropped to 100 100 by placng the two eyes at fxed locatons. We used SDR reduce the dmenson of each mage to 300. In the DR learnng process, λ 1 =0.005 and λ =1.5. Other settngs of the experments are n accord wth the testng on AR. The maxmal recognton rate of each method s lsted n Table 3. Table 3. Recognton Rate and Speed on CAS-PEAL Database Recognton rate /% Expresson Accessory Dstance Tme /s NN 53.70 37.10 74.0 - SVM 57.3 38.98 69.83 - SRC 65.66 55.73 93.06.3347 CRC 66.41 56.58 93.83 0.0051 L-SRC [11] 87.10 63.18 96.67.8648 M-CRC 91.51 68.90 98.46 0.5973 We can see that the proposed M-CRC outperforms other methods. However, t should be notced that the computatonal burden of M-CRC s hgher than the CRC. The performance of MBC s more compettve and even better than the state-of-art local feature such as Gabor, LBP, LGBP. The CRC can be seen a very powerful classfer. We can conclude that the proposed M-CRC could not only ncrease the dscrmnaton of local features but also has powerful classfcaton ablty due to the use of CRC. 6 Conclusons In ths paper, we proposed a new approach based on Monogenc bnary codng and collaboratve representaton based classfcaton. When the MBC feature s extracted, the dmensonalty problem s resolved by applyng Sparse Dmensonalty Reducton. And the CRC scheme s used to varous pattern classfcaton. The expermental results demonstrated that the proposed M-CRC s superor to
18 Computer Aded Draftng, Desgn and Manufacturng (CADDM), Vol.5, No., Jun. 015 other methods and has some potental to be appled n practcal face recognton systems. The future works nclude: (1) Explorng other new and effcent local feature extracton scheme for the potental performance ncrease. () Selectng more effcent scheme to reduce the feature dmenson whle enhancng ts dscrmnaton. (3) Explorng more robust fuson scheme, whch not only have sgnfcantly lower tme and space complexty, but also have better recognton rates. References [1] Zhao W, Chellappa R, Phllps P J, et al. Face recognton: a lterature survey [J]. ACM Computng Survey, 003, 35(4): 399-458. [] Turk M, Pentland A. Egenfaces for recognton [J]. Cogntve Neuroscence, 1991, 13(1):71-86. [3] Belhumeur P N, Hespanha J P, Kregman D J. Egenfaces vs. fsherfaces: recognton usng class specfc lnear projecton [J]. IEEE Transactons on Pattern Analyss and Machne Intellgence, 1997, 19(7): 711-70. [4] Lu C, Wechsler H. Gabor feature based classfcaton usng the enhanced Fsher lnear dscrmnant model for face recognton [J]. IEEE TPAMI, 00, 11(4): 467-476. [5] Ahonen T, Hadd A, Petkanen M. Face recognton wth local bnary patterns [C]// Proceedngs of the 8th European Conference on Computer Vson, Prague, 004, LNCS301: 469-481. [6] Zhang W, Shan S, Gao W, et al. Local Gabor bnary pattern hstogram sequence (LGBPHS): a novel non-statstcal model for face representaton and recognton [C]// Proceedngs of IEEE Internatonal Conference on Computer Vson, 005, 1: 786-791. [7] Yang M, Zhang L, Shu S C K, et al. Monogenc bnary codng: an effcent local feature extracton approach to face recognton [J]. IEEE Trans. on Informaton Forenscs and Securty, 01, 7(6): 1738-1751. [8] Hesele B, Ho P, Poggo T. Face recognton wth support vector machne: global versus component-based approach [C]// Proc. of IEEE Int l Conf. Computer Vson, 001. [9] Wrght J, Yang A, Ganesh A, et al. Robust face recognton va sparse representaton [J]. IEEE Trans. Pattern Analyss and Machne Intellgence, 009, 31(): 10-7. [10] Zhang L, Yang M, Feng X. C. Sparse representaton or collaboratve representaton: whch helps face recognton? [C]// In ICCV(011), 471-478. [11] Mn R, Dugelay J. L. Improved combnaton of LBP and sparse representaton based classfcaton (SRC) for face recognton [C]// Proceedngs of IEEE Int l Conf. Multmeda and Expo, 011. [1] Kang C C, Lao S C, Xang S.M, et al. Kernel sparse representaton wth local patterns for face recognton [C]// Proceedngs of IEEE Int l Conf. Image Processng, 011. [13] Zhang L, Yang M, Feng Z, et al. On the dmensonalty reducton for sparse representaton based face recognton [C]// Proceedng of the ICPR, 010. [14] Felsberg M, Sommer G. The monogenc sgnal [J]. IEEE TSP, 001, 49(1): 3136-3144. [15] Sten E M, Wess G. Introducton to Fourer Analyss on Eucldean Spaces. Prceton [M]. NJ: Prnceton Unv. Press, 1971. [16] Zhang L, Yang M, Feng Z, et al. On the dmensonalty reducton for sparse representaton based face recognton [C]// Proceedng of the ICPR, 010. [17] Martnez A, Benavente R. The AR Face Database [R]. CVC Tech. Report No. 4, 1998. [18] Zhang B C, Zhang L, Zhang D, et al. Drectonal bnary code wth applcaton to PolyU near-nfrared face database [J]. Pattern Recognton Letters, 010, 31(14): 337-344. [19] Gao W, Cao B, Shan S, et al. The CAS-PEAL Larege-Scale Chnese Face Database and Evaluaton Protocols [R]. Techncal Report JDL-TR-04-FR-001, Jont Research & Development Laboratory, CAS, 004. [0] Km S J, Koh K, Lustg M, et al. A nteror-pont method for large-scale l1-regularzed least squares [J]. IEEE Journal on Selected Topcs n Sgnal Processng, 007,1(4): 606-617. [1] Shan S. G, Yang P, Chen X. L, et al. AdaBoost gabor fsher classfer for face recognton [C]// Proceedng of IEEE Internatonal Workshop on Analyss and Modelng of Faces and Gestures (AMFG005), Bejng, Chna, LNCS 373, 005, 78-91. FU Yu-xan s currently a M.S. degree canddate n College of Physcs and Informaton Scence from Hunan Normal Unversty, Changsha, Chna. Hs research nterests nclude mage processng, pattern recognton, and especally focus on face recognton. He can be reached by 363533517@qq.com. PENG Lang-yu s currently a Ph.D. and professor at College of Physcs and Informaton Scence from Hunan Normal Unversty, Changsha, Chna. She receved her B.S. degree at Xangtan Unversty, Chna, n 1986, and her M.S. and Ph.D. degree from Hunan Unversty, n Chna, n 1995 and 003 respectvely. She was a postdoctor of Bejng Unversty of Aeronautcs and Astronautcs. Her research nterests nclude mage processng and actve flter desgn. She has authored over 100 papers n journals and conferences. She can be reached by langyu_peng@163.com.