A Novel Biometric Feature Extraction Algorithm using Two Dimensional Fisherface in 2DPCA subspace for Face Recognition

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1 A Novel ometrc Feature Extracton Algorthm usng wo Dmensonal Fsherface n 2DPA subspace for Face Recognton R. M. MUELO, W.L. WOO, and S.S. DLAY School of Electrcal, Electronc and omputer Engneerng Unversty of Newcastle Newcastle upon yne, NE 7RU UNIED KINDOM Abstract: - hs paper descrbes a novel algorthm, 2D-FPA, for face feature extracton and representaton. he new algorthm fuses the two dmensonal Fsherface method wth the two dmensonal prncpal component analyss (2DPA). Our algorthm operates on the two dmensonal mage matrces. herefore a total mage covarance matrx can be constructed drectly usng the orgnal mage matrces and ts egenvectors are derved for feature extracton. Smlarly, the between and the wthn mage covarance matrces are constructed and transformed to a 2DPA subspace. he result s that 2D-FPA s faster and yelds greater recognton accuracy. he ORL database s used as a benchmark. he new algorthm acheves a recognton rate of 95.50% compared to the recognton rate of 90.00% for the Fsherface method. Key-Words: ometrcs, Recognton, Feature Extracton, Image Representaton, two dmensonal Fsherface, two dmensonal prncpal component analyss. Introducton he early strategy for face dentfcaton was based on geometrcal features such as nose wdth and length, mouth poston and chn shape [] almost all of the new approaches developed n recent years are based on holstc representatons known as templates. In [2] a comparson of geometrcal feature based matchng wth template (statstcal features) matchng s presented and the result favours the statstcal feature based matchng approach. he most commonly used statstcal representaton for face recognton s the Egenfaces [3], whch uses prncpal component analyss (PA) for dmensonalty reducton. he produced templates are not always good for dscrmnaton among classes. elhumeur et al. [4] proposed Fsherfaces method, whch s based on Fsher s Lnear Dscrmnant and produces well separated classes n a low-dmensonal subspace. Nonlnear PA-related methods such as ndependent component analyss (IA) and kernel prncpal component analyss (Kernel PA) have been proposed for feature extracton [5-6]. hese methods are superor to representatons based on PA. However, Kernel PA and IA are both computatonally more expensve than PA. In all the PA-based related technques above, the 2D face mage matrces must be transformed nto D mage vectors. he resultng mage vectors of faces usually lead to a hgh dmensonal mage vector space, where t s dffcult to evaluate the covarance matrx accurately due to ts large sze and the relatvely small number of tranng samples. Yang et al. [7] proposed a straghtforward mage proecton technque, called the mage prncpal component analyss, whch s drectly based on analyss of orgnal mage matrces. ased on the dea of the mage matrx L et al. [8] proposed the two dmensonal lnear dscrmnant analyss where the Fsher lnear proecton crteron s used to fnd a good proecton for better feature extracton. In ths paper, a straghtforward mage proecton technque called two dmensonal Fsherface Prncpal omponent Analyss, 2D-FPA, for feature extracton s presented. Our method uses Fsher lnear proecton crteron to fnd a good proecton n the 2DPA subspace. Performng 2DFLD n ths new subspace has three mportant advantages over Fsherface. Frstly, t s easer to evaluate the covarance matrces accurately. Secondly, less tme s requred to determne the correspondng egenvectors. Fnaly, the face recognton accuracy ncreases sgnfcantly. 2 2D-FPA 2. Idea and Algorthm Suppose that there are pattern classes n tranng set, {, where N denotes the sze of tranng set. A } N he th class has n samples, thus.he N n mean mage of all tranng set s

2 A and A,,..., denotes the mean mage of class. he th class and th tranng mage s denoted by A an m n mage matrx. denotes an n -dmensonal untary column vector. Our novel dea s to proect the th mage, A, onto to the 2DPA subspace by the followng lnear transformaton [7], [9]: Y A () We obtan a m dmensonal proected vector whch s the feature vector of the th mage A. We need to determne a good proecton vector. y defnton, PA fnds a proecton drecton, onto whch all samples are proected, so that the total scatter of the resultng proected samples s maxmzed. he total covarance (scatter) matrx of the proected samples s characterzed by the trace (tr) of the covarance matrx of the proected feature vectors as follows: J ) tr( S ) (2) ( t Where S E ( Y EY )( Y EY ) (3) t E [( A EA ) ][ A EA ) ] Hence J ( ) tr( S ) E[( A EA ) A EA )]. t ( We defne the total mage covarance matrx as: Gt E[( A EA ) ( A EA )] (4) herefore, (2) can be wrtten as, tr( St ) Gt (5) he untary proecton vector,, that maxmzes (5) s called the optmal proecton axs,( ) whch s opt the egenvector of G t. It s not enough to have only one optmal proecton axs. We need to select a set of proecton axes,, n such a way that not,.... d much dscrmnant nformaton s lost whle nose s reduced. he selected egenvectors,,,.... d contan prncpal components (Ps) whch retan both the wthn varatons (unwanted nformaton) and between varatons (mportant dscrmnant nformaton). Once the 2DPA subspace has been created we use the Fsher s lnear proecton crteron n ths new space to fnd a good proecton that maxmzes the rato of the scatter among the face classes to the scatter wthn the face of the same class. he between mage class covarance (scatter) matrx and the wthn mage class covarance (scatter) matrx the nput space can be transformed to the 2DPA subspace as S and S by, S S W WW SWW SW (6) n S S (7) We derve S and S as follows: WW S n ( Y Y ) ( Y Y ) (8) n[( A A) ] [( A A) ] n ( A A) ( A A) Where S n ( A A) ( A A) (9) herefore S S (0) n ( ) ( ) Smlarly S ( Y Y ) ( Y Y ) () ww ( ) ( ) n ( ) ( ) ( ) ( ) [( A A ) ] [( A A ) ] n ( ) ( ) ( ) ( ) ( A A ) ( A A ) n ( ) ( A A ) WW SW Where ( ) ( ) (2) Sw ( ) ( A A ) Smlarly, S (3) We refer to S and SWW as the between feature and wthn feature class covarance (scatter) matrces wth dmensons of d d, where d s the number of egenvectors of G t that we choose. he man dea at ths stage s to proect onto the untary column vector Z as follows: Y R Y Z (4) o measure the class separablty of the proected samples, R,,2,... N, we determne the trace of the between S and SWWW wthn matrx of the proected samples as follows: tr( S ) J ( Z) (5) tr( SWWW ) Usng a smlar dea as n (2), tr ( S ) and tr( S WWW ) s expressed as: Z S Z J ( Z) Z SWW Z hs s the Fsher lnear proecton crteron. he untary vector Z that maxmzes (5) s called the Fsher optmal proecton axs ( ). It means that Z opt the proected mage samples on the drecton Z has the mnmal wthn mage class scatter and the

3 maxmal between mage class scatter n the subspace spanned by Z. If SWW s nonsngular, the soluton to above optmzaton problem s to solve the generalzed egenvalue problem [3-4]: S Z λs Z (6) opt WW opt SWW SZopt λzopt In (6), λ s the egenvalue of SWW S. In the tradtonal LDA, we were faced wth the sngularty problem. However, 2D-FPA overcomes ths problem successfully. L et al. [8] showed that the wthn mage class covarance (scatter) matrx s non-sngular n real stuaton. In general, t s not enough to have only one Fsher optmal proecton axs. We usually need to select a set of proecton axs, Z,...Z g S W, subect to the orthonormal constrants. 2.2 Feature Extracton he optmal proecton vectors of 2DPA,, are used for the frst feature extracton.,.... d For a gven mage sample, A Y A k, k,... d. (7) he prncpal component vectors obtaned are used to form an m d matrx Y [,... ], whch s called the feature matrx or feature mage of the th mage sample A. We refer to as the prncpal component (vectors) of the th sample A. Here we can thnk of Y as a smaller mage matrx wth less nose from th sample mage A. he Fsher feature vectors k, form a,.... g g d m Fsher feature matrx R [,... g ] for the th mage sample A as follows: R Y Z, p,... g. (8) p It should be noted that each Fsher feature of Fsherface s a scalar, whereas the Fsher feature of 2D-FPA s a vector. 2.3 lassfcaton Method After a transformaton by Z, a Fsher feature matrx s obtaned for each mage. hen, a nearest neghbour classfer s used for classfcaton. Here, the dstance between two feature matrces, R [,,... ] and R [ 2, 2, g ] s defned as D R, R2 ) g p p 2 p 2 g ( (9) Where 2 denotes the Eucldean dstance p p between the two prncpal component vectors p and. Gven a test sample R, f 2 p and R, we decde that R. D ( R, R7 ) mn D( R, R ) 7 k k Fg. Fve sample mages of one subect n the ORL database 3 Image Reconstructon Image reconstructon for the 2D-FPA can be performed n the followng way. he orgnal mage can be reconstructed usng (7) and (8). From (7), Y A, k,... d. Let k U [,... d ] Y A U, then (7) can be wrtten as (20) Snce,.... d are orthonormal, t s easy to obtan the reconstructed mage of the th sample A : d A Y U k k k (2) ut Y needs to be obtaned from (8), let V Z,... Z ]. We can rewrte (8) as: g Y R V A R p p Z p [ g (22) Hence, V U, whch s the same sze as the th mage sample A and represents the reconstructed sub mages A. hat s, the th mage A can be approxmately reconstructed by addng up the frst g and frst d sub mages. In partcular, when the selected number of prncpal component vectors A g d and d n, we have A,.e., the mage s completely reconstructed by ts prncpal component vectors wthout any loss of nformaton. Otherwse, f ether g < d or d < n, the reconstructed mage A s an approxmaton for A. 4 Analyss he new 2D-FPA method was used for face recognton. he performance of our proposed algorthm was tested on a well-known face mage database from the Olvett Research Laboratory (ORL database). he ORL database [0] was used to evaluate the performance of the 2D-FPA under condtons where the pose and number of 2DPA egenvectors vared.

4 4. Analyss usng the ORL benchmark Database hs publcly avalable database comprses of 40 ndvduals, each provdng 0 dfferent mages. For some subects, the mages were taken at dfferent tmes. Furthermore, other wthn class varatons such as facal expresson e.g. eyes open, eyes closed, smlng, not smlng vared. Occluson due to other accessores e.g. glasses was used for some subects. All the mages were taken aganst a dark background wth the subects n an uprght, frontal poston wth tolerance for some sde movement. he mages were taken wth a tolerance for tltng and rotaton of the face of up to 20 degrees. he sze of each mage s 2 92 pxels, wth 256 grey levels per pxel. Fve samples from the ORL database are shown n Fg. Frst, a face recognton experment was performed usng fve mage samples per class for tranng, and the remanng mages for testng. he mages were normalzed to pxels. A total number of tranng samples and testng samples were both 200. he 2D-FPA algorthm was used for feature extracton. Here, the sze of the total mage covarance G, wthn mage covarance S, and between mage covarance S s n n matrx, so t was relatvely easy to evaluate the egenvectors of G t. We chose the egenvectors correspondng to the nne ( d 9) largest egenvalues,., as proecton axs. After the proecton of the th mage sample onto these axes usng (7), we obtan nne prncpal component vectors. We then transformed SW and S t,.... d,... wth the same egenvectors usng (6) and (7) to obtan S and S n the 2DPA subspace. W hese new d d covarance matrces are called the wthn feature and between feature class covarance matrces, SWW and S. It s therefore relatvely easer to calculate the egenvectors of S WW and compared to S and S. hs results n faster S W and more accurate evaluaton of S and SWW. he evaluaton of G t does not have to be as accurate as the evaluaton of S and SWW, rather t s mportant to be able to keep a set of egenvectors,, that wll optmze the evaluaton of (6) wthout a loss of much nformaton. he egenvectors of (6) contan dscrmnant nformaton whch s essental n face classfcaton. In ths analyss we kept only d W A,.... d fve egenvectors, Z,...Z g, from (6) correspondng to the fve ( g 5) largest egenvalues. Fnally, the Fsher features vectors are extracted usng (8) and are used to form a m g matrx R. he magntude of the egenvalues obtaned for the 2DPA and for the 2DFLD n the subspace s plotted n decreasng order n Fg. 2 and Fg. 3. Magntude of egenvalues No. of egenvalues Fg. 2 he magntude of the egenvalues of 2DPA n descendng order Fg. 2 shows that the magntude of the egenvalues quckly converges to zero, whch s exactly consstent wth the results n [3, 4, and 7]. Fg. 3 shows smlar characterstcs although t does not converge to zero n ths case. herefore, we can conclude that the energy of an mage s concentrated on ts frst small number of component vectors. It s reasonable to use these component vectors to represent the mage for dentty recognton purposes. Magntude of egenvalues No. of egenvalues Fg. 3 he magntude of the egenvalues for 2DFLD n descendng order We evaluated the performance of 2D-FPA under condtons where the number of egenvectors for 2DPA ( ) s vared e.g. 5, 7, 9,, 3.,.... d d he recognton results are shown n Fg. 4. he graphs ndcates that the performance of 2D-FPA s optmzed when d 9. he accuracy decreases for values of d > 9 and d < 9. 2D-FPA acheves a top recognton of % at t s optmum value ( d 9) usng fve Fsher feature vectors. he lowest top recognton accuracy of % was obtaned when d 5 usng fve Fsher feature vectors.

5 Recognton Accuracy (%) Dmenson of the 2DFLD Feature Vector Fg. 4 he plot of the recognton accuracy (%) versus the dmenson of the feature vector usng n classfcaton for varyng d. We further compared the performance of Fsherface and 2D-FPA for d 9. 2D-FPA and the Fsherface method were used for feature extracton. Fnally, a nearest neghbour classfer was employed for classfcaton. For 2D-FPA, (9) was used to calculate the dstance between two feature matrces. In Fsherface, the common Eucldean dstance measure s adopted. Fg. 5 presents the recognton accuracy plotted aganst the dmensons of the feature matrx used n classfcaton for 2D-FPA and for the Fsherface approach. 2D-FPA performed better than the Fsherface method. A top recognton accuracy of % for the 2D-FPA was acheved and % for the Fsherface. he 2D-FPA method s also superor to Fsherface n terms of computatonal effcency for feature extracton snce n the Fsherface approach Gt s a mn mn matrx compared to a n n matrx for the 2D-FPA. It s hard work to calculate the egenvectors of a mn mn matrx where mn 2576 and n 46 n ths case. Recognton Accuracy (%) d5 d7 d9 d d3 fsherface 2D-FPA Dmenson Fg. 5 Perfomance of 2D-FPA and Fsherface. Furthermore, the Fsherface approach selects d N egenvectors ( N s the number of tranng mages and s the number of classes) from to make S W non-sngular whereas n 2D-FPA we seek a value of d that optmzes the recognton accuracy whle mantanng a faster speed. In the Fsherface approach S and SWW are of the order d N whch can stll be a large number dependng on the sze of the tranng sample compared to the optmal value of d for 2D-FPA. In ths analyss the former was a matrx compared to a 9 9 matrx for 2D-FPA. When compared to recently publshed results [7-3], 2D-FPA has superor performance. 4 oncluson A novel technque for mage feature extracton and representaton was developed usng the two dmensonal Fsher s Lnear Dscrmnant (2DFLD) combned wth 2DPA subspace. 2D-FPA has many advantages over Fsherface. Frstly, snce 2D-FPA s based on the mage matrx, t s smpler and more straghtforward to use for mage feature extracton. Secondly, 2D-FPA outperforms Fsherface n terms of recognton accuracy as t acheves a hgh recognton accuracy of 95.50% compared to 90.00% for Fsherface. hrdly, 2D-FPA selects a smaller set of 2DPA s egenvectors that optmzes the accuracy and speed. Fnally, 2D-FPA s computatonally more effcent than the Fsherface and t mproves the speed of mage feature generaton sgnfcantly. References: [] W. Zhao, R. hellappa, A. Rosenfeld, and P.J. Phllps, Face recognton: A lterature survey, VL echncal Report, Unversty of Maryland, Oct.2000, [2] R runell and Pogo, Face Recognton through Geometrcal Features, Proc. European onference on omputer Vson, pp , 992 [3] M. A. urk and A. P. Pentland, Egenfaces for recognton, J. ogntve Neurosc., vol. 3, pp. 7 86, 99. [4] P. N. elhumeur, J. P. Hespanha, and D. J. Kregman, Egenfaces versus fsherfaces: Recognton usng class specfc lnear proecton, IEEE rans. Pattern Anal. Machne Intell., vol. 9, pp , 997. [5] S. artlett, J. R. Movellan,. J. senowsk, Face Recognton by Independent omponent Analyss, IEEE rans. On Neural Networks, Vol. 3, No. 6, Nov G t

6 [6] Mng-Hsuan Yang, Kernel egenfaces vs. kernel fsherfaces: Face recognton usng kernel methods, n Proc. IEEE Internatonal onference on Automatc Face and Gesture Recognton, Washngton D.., May 2002, pp [7] J. Yang, D. Zhang, A. F. Frang, J. Y. Yang, wo dmensonal PA: A new approach to appearance-based face representaton and recognton. IEEE rans. Pattern Anal. Machne Intell. Vol. 26, no., pp. 3 37, [8] Mng L and aozong Yuan, 2D-LDA: A statstcal lnear dscrmnant analyss for mage matrx, Pattern Recognton Letters, Vol. 26, no. 5, pp , [9] J. Yang, J.Y. Yang, From Image Vector to Matrx: A Straghtforward Image Proecton echnque IMPA vs. PA, Pattern Recognton, Vol. 35, no. 9, pp , [0] he Olvett Research Laboratory (ORL), Olvett database, 994 < [] Q. Lu, H. Lu, S.Ma, Improvng Kernel Fsherface Dscrmnant Analyss for Face Recognton, IEEE rans. Pattern Anal. Machne Intell. Vol. 4, no., pp , [2] J. Yang, A. F. Frang, J. Y. Yang, D. Zhang, Z. Jn, KPA Plus LDA: A omplete Kernel Fsher Dscrmnant Framework for Feature Extracton and Recognton, IEEE rans. Pattern Anal. Machne Intell. Vol. 27, no. 2, pp , [3] J. Lu, K. N. Platanots, A.N. Venetsanopoulos, Face Recognton Usng Kernel Drect Dscrmnant Analyss Algorthms, IEEE rans. Neural Networks, Vol. 4, no., pp. 7-26, 2003.