Eigenface-Gabor Algorithm for Features Extraction in Face Recognition

Transcription

1 Issue, Volume 3, 009 Eigeface-Gabor Algorithm for Features Extractio i Face Recogitio Gualberto Aguilar-Torres, Karia Toscao-Media, Gabriel Sachez-Perez, Mariko akao-miyatake, Hector Perez-Meaa Abstract This paper provides a study o Face Recogitio Algorithms; several methods are used to extract image face features vector, which presets small iter-perso variatio. This feature vector is feed to a multilayer perceptro to carry out the face recogitio or idetity verificatio tasks. Proposed system cosists i a combiatio of Gabor ad Eigefaces to obtai the feature vector. Evaluatio results show that proposed system provides robustess agaist chages i illumiatio, wardrobe, facial expressios, scale, ad positio iside the captured image, as well as icliatio, oise cotamiatio ad filterig. Proposed scheme also provides some tolerace to chages o the age of the perso uder aalysis. Evaluatio results usig the proposed scheme with idetificatio ad verificatio cofiguratios are give ad compared with other feature extractio methods to show the desirable features of proposed algorithm. Keywords Gabor trasform, face recogitio, eigefaces, orthogoal trasforms, eural etworks, idetity verificatio, Walsh trasform. I. ITRODUCTIO EVERAL perso recogitio systems usig biometric S features such as figerprit, iris patter, voice ad face, etc. have bee proposed durig the last several years to provide alteratives to the growig ecessity for access cotrol i some strategic poits such as: airports, govermet ad military facilities, coutries borders, etc., as well to sesitive iformatio. These systems, depedig i their particular applicatio, ca be divided i perso idetificatio ad idetity verificatio, where the task of the first group is to determie who is the most probable perso, while the task of secod group is to determie if the perso is the whom he/she claims to be. Mauscript received May 6, 008: Revised versio received July, 008. This work was supported i part by the atioal Sciece ad Techology Coucil of Mexico. G Aguilar-Torres is a PhD degree studet of the atioal Polytechic Istitute of Mexico, gualberto@calmecac.esimecu.ip.mx. K. Toscao-Media is a Professor i the Graduate Departmet of the atioal Polytechic Istitute of Mexico. likatome@calmecac.esimecu.ip.mx. G Sachez-Perez is a Professor i the Graduate Departmet of the atioal Polytechic Istitute of Mexico. caaa@calmecac.esimecu.ip.mx. M akao-miyatake is with the Mechaical ad Electrical Egieerig School Culhuaca Campus of the atioal Polytechic Istitute mariko@calmecac.esimecu.ip.mx H Perez-Meaa is with the Mechaical ad Electrical Egieerig School Culhuaca Campus of the atioal Polytechic Istitute, Tel/Fax (+5) (Correspodig author). hmpm@prodigy.et.mx. The face image as biometric feature has bee widely used because its high acceptace betwee persos ad easy capture []-[5], however this feature has very high itra-perso variatios comparig with other features, such as iris patter ad figerprits []. The itra-perso variatios of the face image derive maily from chages i facial expressios, illumiatio coditios as well as because the use of some accessories such as eyeglasses ad muffler, etc. These variatios make the face recogitio a very difficult task [4]. However because its advatages are overcome the potetial disadvatages, several face recogitio algorithms have bee proposed to solve the still remaiig problems. Thus durig the last years have bee proposed template-based face recogitio methods [6], face recogitio usig eigefaces methods [7]-[9], Bayesia algorithms [4], geometric feature based methods [0]-[] ad Walsh trasform based algorithms []-[3], etc. Other related systems that also have bee applied are face regio locatig method proposed i [3], the deformable model proposed i [4] ad face recogitio methods usig the Karhue-Loeve trasform [5], etc. Recetly several authors have proposed the combiatio of differet features to improve the face recogitio rate [6]. O the other had, the discrete Gabor Trasform, that presets some relatio with the huma visual system, has bee successfully used i several applicatios such as figerprit ehacemet [7], sigature recogitio [8], image compressio [9] etc. This paper proposes a robust ad reliable automatic face recogitio system i which the feature extractio is performed usig D Gabor Trasform, Eigefaces, discrete Walsh trasform ad discrete cosie trasform, which presets eough small itra-perso variatio ad cosiderably large iter-perso variatio, a desirable feature i ay recogitio system. ext after the feature vectors are estimated, they are itroduced to the multilayer eural etworks for face image idetificatio or idetity verificatio. Computer simulatio shows that proposed system is robust agaist variatios i the illumiatio coditio, wardrobe, facial expressios, chages of image size, cotamiatio by oise ad image shiftig, as well as to age variatio of the perso uder aalysis. Evaluatio results are also givig to compare the performace of proposed algorithm with other previously proposed feature extractio methods. II. FACE RECOGITIO ALGORITHMS The proposed face recogitio system ca perform either, face idetificatio ad idetity verificatio tasks. I the first case 0

2 Issue, Volume 3, 009 the system output provides the idetity of the perso with highest probability, while i the secod case the system determies is the perso is whom he/she claims to be. I both cases cosists of a features vector extractio stage, a artificial eural etwork, A, ad a decisio stage that takes the acceptatio or rejectio decisio. ext sectio describes the proposed face idetificatio ad idetity verificatio systems. ω deotes the umber of ormalized radial frequecies ad φ the umber of agle phases as follows ' ' w( x, y, ω m, φ ) = g( x, y ) ' ' ' ' ( cos ω ( x + y ) + j si ω ( x + y )) m where m=,,, ω ad =,,3,.., φ, ω m is the m-th ormalized radial frequecy, m () ( x ' / λ) + ' ' ' y g ( x, y ) = exp () πλσ σ Fig. Proposed face idetificatio system is the Gaussia fuctio, σ is the radial badwidth, λ λ is ' ' Gaussia shape factor ad ( x, y ) is the positio of the pixel (x,y) rotated by a agle φ as follows ( x cosφ + y si φ )(, x si φ y cosφ ) ( x', y' ) = + (3) Table Procedure used to segmet the face regio Fig. Block diagram of proposed idetity verificatio system, Fig. 3 Face segmetatio method A. GABOR EXPASIO To estimate the features vector, firstly the regio of the picture cotaiig the face uder aalysis is segmeted as show i Fig. 3, usig the procedure described i Table. ext M captured image is divided i M x M y receptive fields each oe of size ( x +)( y +) (Fig. 4), where x =(-M x )/M x, y =(M- M y )/M y. This fact allows that the features vector size be idepedet of the captured image size. ext, the cetral poit of each receptive field whose coordiates are give by (c i,d k ), where i=,,.., x ; k=,,3,, y, are estimated. Subsequetly the first poit of the cross-correlatio betwee each receptive field ad the ω φ Gabor fuctios is estimated usig eqs. ()-(4), where P=K/v, R=L/v J= For m=; R- Do d r =X(jv,mv)-X((j-)v,mv) IF abs(d r )<ε ad j<p The j=j+ Goto ELSE X r (m)=j j=p d l =X(jv,mv)-X((j-)v,mv) IF abs(d r )<ε ad j>the j=j- Goto ELSE X l (m)=j Ed m= For j=; P- Do 3 d u =X(jv,mv)-X(jv,(m-)v) IF abs(d r )<ε ad j<r The m=m+ Goto 3 ELSE Y u (j)=m j=r 4 d l =X(jv,mv)-X(jv,(m-)v) IF abs(d l )<ε ad j>the m=m- Goto 4 ELSE Y l (j)=m ed d =max(x r (m))-v, m=,,..,r- d =max(x l (m))+v, m=,,..,r- d 3 =max(y u (j))-v, j=,,.,p- d 4 =max(y l (j))+v, j=,,.,p-

3 Issue, Volume 3, 009 Fig. 4 (a) Origial image (b) 08 receptive fields ad cetral poits estimatio (x,y). Thus the cross-correlatio betwee the Gabor fuctios, give by eqs. ()-(3), with each receptive field ca be estimated as, B. EIGEFACES The objective of the recogitio by the Eigefaces method is to extract relevat iformatio from face image, ecode this iformatio as efficietly as possible ad compare them with each model stored i a database. I mathematical terms, we wish to fid the pricipal compoets of the distributio of faces, or the eigevectors of the covariace matrix of the set of face images [0]. The idea of usig eigefaces was motivated by a techique developed by Sirovich ad Kirby [5] for efficietly represetig pictures of faces usig pricipal compoet aalysis. They argued that a collectio of face images ca be approximately recostructed by storig a small collectio of weights for each face ad a small set of stadard pictures. h ( u, v) = x y I ( x ci, y d k ) w( x, y, ω m, φ ) (4) x= x y= y where u=m y *(i-)+k ad v= ω (m-)+. ext, to avoid complex valued data i the features vector we ca use the fact that the magitude of h(u,v) presets a great similarity with the behavior of the complex cells of the huma visual system [8]-[]. Thus the magitude of h(u,v) could be used istead of its complex value. However, as show i eq.(4) the umber of elemets i the features vector is still so large eve for small values of M x, M y, φ y ω. Thus to reduce the umber of elemets i the features vector, we ca average h(u,v) to obtai the proposed features vector M(u) which is give by v M ( u) = h( u, v) (5) v v= where v = φ ω. Figure 5 illustrate this procedure. (a) (b) Fig. 5 a) Features extracted from each receptive field h(u,v). b) Estimated feature vector M(u). a) b) Fig. 6. a) Average face. b) Eigefaces. The Eigefaces computatio is as follows: Let the traiig set of face images be Γ, Γ, Γ3,... ΓM. The average face of M the set is defied by Ψ = Γ. Each face differs from de average by the vector φ M = = Γ Ψ. A example traiig set is show i Figures 9 ad 0, with the average face show i figure 6a. This set of very large vectors is the subject to pricipal compoet aalysis, which seeks a set of M orthoormal vectors µ ad their associated eigevalues λ k which best describes the distributio of the data. The vectors µ k ad scalars λ k are the eigevectors ad eigevalues, respectively, of the covariace matrix M T T C = φφ = AA (6) M = T where the matrix A = [ φ φ... φ M ], A is a trasposed matrix. The matrix C, however, is by, ad determiig the eigevectors ad eigevalues is a itractable task for typical image sizes. We eed a computatioally feasible method to fid these eigevectors. Fortuately we ca

4 Issue, Volume 3, 009 determie the eigevectors by first solvig a much smaller M by M matrix problem, ad takig liear combiatios of the resultig vectors. Cosider the eigevectors v of A T A such that A T Av Premultiplyig both sides by A, we have AA T Av = λ v (7) = λ Av (8) from which we see that Av are the eigevectors of C = AA T. Followig this aalysis, we costruct the M by M matrix L = A T T A, where Lm, = φmφ, ad fid the M eigevectors v of L. These vectors determie liear combiatios of the M traiig set face images to form the eigefaces u = M k= k k u v φ = Av, =,..., M (9) With this aalysis the calculatios are greatly reduced, from the order of the umber of pixels i the images ( ) to the order of the umber of images i the traiig set (M). I practice, the traiig set of face images will be relatively small (M<< ), ad the calculatios become quite maageable. The associated eigevalues allow us to rak the eigevectors accordig to their usefuless i characterizig the variatio amog the images. Oce the Eigefaces have bee calculated, the image is projected oto "face space" by a simple operatio, = u ( Γ Ψ) ω (0) for =,.,M. This describes a set of poit-by-poit image multiplicatios ad summatios. Some Eigefaces are show i figure 6b. T The weights form a vector Ω = [ ω, ω,..., ωm ] that describes the cotributio of each eigeface i represetig the iput face image, treatig the eigefaces as a basis set for face images. Fially, the simplest method for determiig which face class provides the best descriptio of a iput face image is to fid the face class k that miimizes the Euclidia distace where k Ω k ε = Ω () Ω k is a vector describig the kth face class. C. DISCRETE WALSH TRASFORM The discrete Walsh trasform (DWT) is oe of the most importat techiques as well as the discrete Fourier trasform i the field of sigal processig []-[3]. The DWT works well for digital sigals due to the fudametal fuctio called the Walsh fuctio. The Walsh fuctio has oly +/-, ad is the system of orthogoal fuctios. I geeral, the Walsh fuctio ca be geerated by the Kroecker s product of the Hadamard matrix H s. First, the -by- Hadamard matrix H is defied by + + H = () + where the symbols + ad mea + ad -, respectively. Furthermore, calculatig the Kroecker s product betwee two H s, the 4-by-4 Hadamard matrix H 4 is easily give as follow: H + H + + H 4 = H H = = (3) + H + + H + + where the symbol idicates the Kroecker s product. The frequecy characteristics ca be give by the Hadamard matrix. Alog each row of the Hadamard matrix, the frequecy is expressed by the umber of chages i sig. The umber of chages is called sequece. The sequece has the characteristics similar to the frequecy. The Walsh fuctio ca be expressed as each row of H, where is order o Hadamard matrix. Therefore, DWT is kow as a kid of the Hadamard trasform, where H has some useful followig characteristics. Thus, the DWT ad the iverse DWT are defied as follows: (4) V = H B B = H V (5) where B is the sampled data vector, H is the Hadamard matrix, i.e. Hadamard-ordered Walsh fuctios. V is the DWT of B. V is called Walsh spectrum. The D-DWT does the DWT toward the images of m-by- pixels. The D-DWT ad the D-IDWT are defied as follows: F = H fh M M (6) f = H M FH (7) where f is the sample data matrix ad F is the D-DWT of f. F is called -dimesioal Walsh spectrum. I case of orthogoal 3

5 Issue, Volume 3, 009 trasform of the image, the D-DWT is more efficiet tha the DWT. However, to use D-DWT, the row ad colum umbers of sample data, matrix must be ( is a atural umber) respectively, because Hadamard matrix ca be geerated by the Kroecker s product of Hadamard matrix H. Figure 7 shows a example: B (x + ) uπ (y + ) vπ (0) ( x, y, u, v) = cos cos To esure adequate represetatio of the image, each block overlaps its horizotally ad vertically eighborig blocks by 50%, thus for a image which has Y rows ad X colums, there are D blocks foud by followig formula: ( ( / ) ) x(( / ) ) () D = Y P X P a) b) Compared to other trasforms, DCT has the advatages of havig bee implemeted i a sigle itegrated circuit because of iput idepedecy, packig the most iformatio ito the fewest coefficiets for most atural images, ad miimizig block like appearace [][]. A additioal advatage of DCT is that most DCT coefficiets o real world images tur out to be very small i magitude []. Figure 8 shows a example: c) Fig. 7. a) Origial image, b) Image with reduced pixel, c) DWT spectrum i a group of 8 x 8 pixels. D. DISCRETE COSIE TRASFORM The DCT is used i may stadard image compressio ad statioary video as the JPEG ad MPEG, because it presets excellet properties i codifyig the outlies of the images that, i fact, has bee oe of the mai reasos to be selected ito almost all the codig stadards. The cosie trasform, like the Fourier trasform, uses siusoidal basis fuctios. The differece is that the cosie trasform basis fuctios are ot complex; they use oly cosie fuctios ad ot sie fuctios [4]. D DCT based features are sesitive to chages i the illumiatio directio [5]. The idea of usig the trasform for facial features extractio is summarized as follows: the give face image is aalyzed o block by block basis give a image block I(x, y), where x,y = 0,,..., p, ad result is a p x p matrix C(u,v) cotaiig D DCT coefficiets. The DCT equatios are give by formulas (8), (9), (0) [4][5][6][7] [8][9] below: for p p (, v) = ( u) α( v) I( x, y) B( x, y, u, v) C u α (8) x= 0 y= 0 u, v = 0,,,..,p where α α ( u) () v = = for for for for u = 0 u =,, v = 0 v =,, (9) a) b) c) d) Fig. 8. a) Origial image. b) Image with reduced pixel, c) DCT spectrum i a group of 8 x 8 pixels, d) Feature vector. E. FACE IDETIFICATIO STAGE Whe the proposed system is required to perform a face idetificatio task, after the feature vector is estimated as metioed, it is feed ito a multilayer perceptro eural etwork with x y euros i the iput layer ad M euros i the output layer traied usig the backpropagatio algorithm [30], where x y is the umber of receptive fields ad M is the umber of faces to be idetified. After the traiig, i.e. durig ormal operatio, to carry out the idetificatio task, the eural etwork output vector is feed ito a wier takes all (WTA) circuit whose output is the idex related to the most probable face. F. IDETITY VERIFICATIO STAGE This A is traied usig the backpropagatio algorithm [30to provide a output closed to oe whe the people is who he/she claims to be ad closed to cero or mius oe otherwise. Fially oes the A is traied, i.e. durig ormal operatio, the eural etwork output is passed through a threshold to take the fial decisio. Here if the output is larger tha the threshold, the idetificatio is cosidered positive. Otherwise 4

6 Issue, Volume 3, 009 the idetificatio is cosidered to be egative. This threshold is a compromise betwee the false acceptace ad false rejectio because to miimize the false acceptace the threshold must be closed to oe although this will icrease the false rejectio rate. Fig. 9. Examples of face images provided i the AR database. III. EVALUATIO RESULTS To evaluate the proposed system two differet databases were used. The AR Face Database, which has a total 5,670 face images that icludes face images with several differet illumiatios, facial expressio ad partial occluded face images with trasparet eyeglasses, dark eyeglasses ad scarf, etc. ad the ORL database, created by Olivetti Research Laboratories i Cambridge UK. The ORL database cosists of 300 face images of 30 differet peoples. Here there are 0 differet images of each people, each oe with differet illumiatio, rotatio agle, icliatio, hair stile, etc. Some examples of the face image iclude i these databases are show i Figs. 9 ad 0. As metioed, to features extract by Gabor method the face image is divided i 08 receptive fields (9 x blocks) cetered at poit ( x0, y 0), (Fig. 4), doig the umber of receptive fields is idepedet of the face image size. ext to estimate the feature vector, i each receptive field, six differet ormalized spatial frequecies, f =π/, f =π/4, f 3 =π/8, f 4 =π/6, f 5 =π/3, f 6 =π/64, together with 9 differet phases φ =0, φ =π/9, φ 3 =π/9, φ 4 =π/3, φ 5 =4π/9, φ 6 =5π/9, φ 7 =π/3, φ 8 =7π/9, φ 9 =8π/9 where used. Fig. 0. Examples of face images provided i the ORL database. Other possibility is to iclude a upper ad lower thresholds such that is the A output is larger tha the upper threshold the idetificatio is cosidered to be positive, if the A output is smaller tha the lower threshold the idetificatio is cosidered egative, ad otherwise the idetificatio process is repeated usig a ew iput picture. This choice reduces the positive idetificatio ad rejectios errors, although the computatioal complexity is also icreased. Fig.. Features vectors of the same face with differet illumiatio. 5

7 Issue, Volume 3, 009 Fig.. Features vectors of three differet faces. Figure shows the features vector extracted from the same face with three differet illumiatio coditios ad Fig. shows the feature vector extracted from three differet faces. These figures show that the Gabor fuctios provide feature vectors with small eough itra-perso variatio ad cosiderably large iter-perso variatio that allows a accurate idetificatio ad idetity verificatio, as show i table. Figure 3 shows the features vector extracted from the same people with differet ages from 8 to 57 years old. As show i this figure, the extracted feature vectors are quite similar whe differet ages are ot so large, allowig a accurate idetificatio. However whe the age differece becomes larger the feature vectors extracted may presets large variatios that difficult a correctly idetificatio. This fact is illustrated i Fig. 3. Fially, the figure 4 shows the features vector extracted from the same face with differet size image. To evaluate the robustess of proposed system from the itra-perso variatio poit of view ad the iter-perso variatio discrimiatio capacity poit of view, several tests were carried out usig face images with several variatios icludig: illumiatio, level variatios, facial expressio, etc., as metioed, addig to the origial variatios i the AR Database, several other alteratios such as filterig usig Gaussias ad Medium filters, cotamiatio with impulsive ad Gaussia oise ad several geometric modificatios itroduced to the face image such as resizig, rotatio ad shiftig. Fig. 3 Feature vectors extracted from face images of oe perso with differet ages (a) 8 years. (b) 35 years. (c) 40 years. (d) 4 years. (e) 53 years. (f) 57 years. Fig 4 Feature vector extracted from images with differet size of the same perso. 6

8 Issue, Volume 3, 009 The backpropagatio euroal etwork was traied usig feature vectors extracted from 50 differet persos ad tested usig 50 feature vectors amog the face images ot used i the traiig process. I the case of the persoal idetificatio usig face images with differet ages, the eural etworks was traied with 5 feature vectors ad it was evaluated usig 60 feature vectors. To evaluate the verificatio system, the euroal etwork was traied with 50 vector features ad tested with 7 feature vectors that were ot used i the traiig process, while i the case of the persoal verificatio usig face images with differet ages, the eural etworks was traied with 0 feature vectors ad it was evaluated usig 4 feature vectors that were t used i traiig process. The evaluatio results, uder the above metioed coditios are show i Table. This table shows that the proposed system is robust agaist variatio of illumiatio level, facial expressio, ad partial occluded face image with use of accessories such as eyeglasses, muffler, etc. as well as to cotamiatio by differet kid of oise. The proposed system is also eough robust agaist media ad Gaussia filterig as well as to some geometrical trasforms such as resizig ad shiftig. However the proposed system is vulerable to rotatio, because i this situatio the rotated face image caot be idetified. Although i the verificatio task the system shows robustess agaist rotatio operatio of agles util 0º. Fially, the performace of the proposed system whe it is required to verify the idetity of oe perso usig face images registered at differet ages is fairly good, takig i accout that the variatio of face images i differet ages (0 years differeces) is cosiderably large. Figures 5 shows the resultig features vector extracted usig the eigeface method from images face of the same people with differet rotatio, while i Fig. 6 are show the features vectors extracted from 3 differet peoples. Usig the ORL database as metioed before a idetificatio rate of 83% ad a verificatio rate of 99.3% were achieved. Fig. 5 Face images with differet rotatio ad their feature vectors extracted usig the eigefaces method. Table Performace of proposed algorithm uder several face image coditios Image variatio Idetificatio rate Verificatio rate Illumiatio 85.67% 99.33% Facial expressio 83.75% 99.% Accessories 83.50% 99.3% Gaussia filter 84.30% 99.54% Media filter 8.60% 99.9% Gaussia oise 84.7% 99.43% Impulsive oise 84.56% 98.76% Resize 85.40% 99.30% Rotatio % 90.0% Rotatio % 87.0% Shiftig 85.0% 98.6% Age X 83.30% The performace of proposed face recogitio algorithm was compared with the recogitio performace provided by other previously proposed methods such as: The eigefaces method, discrete cosie trasform ad the discrete Walsh trasform based method. To these ed five face images of each oe of the 50 persos, provided by the ORL database, are used for traiig ad the other five for testig. Fig. 6 Face images of several persos together with their feature vectors extracted usig the eigefaces method. A recetly proposed method uses the discrete Walsh trasform (DWT) for face feature vector extractio []. Figure 7 shows the features vectors extract usig the DWT from images of the same people, while i Fig. 8 features vectors extracted from face images of differet peoples are show. Usig the features vector extracted from the DWT the system achieves a recogitio performace of 75.33% ad a verificatio performace of 90.3%. These figures show that 7

9 Issue, Volume 3, 009 the eigefaces method provides a good itra-perso cosistecy ad a eough large iter-perso variability allowig a reasoable good recogitio performace. (a) Fig. 7 Face images with differet rotatio ad their feature vectors extracted usig the discrete Walsh trasform. (b) (c) Fig. 9 Face images with differet expressios ad their feature vectors extracted usig the discrete cosie trasform. (a) (b) Fig. 0 Face images of two persos together with their feature vectors extracted usig the discrete cosie trasform. Fig. 8 Face images of several persos together with their feature vectors extracted usig the discrete Walsh trasform. Other method used for feature extractio is the discrete cosie trasform (DCT) [9]. Figure 9 shows the features vectors extract usig the DCT from images of the same people, while i Fig. 0 features vectors extracted from face images of differet peoples are show. Usig the features vector extracted from the DCT the system achieves a recogitio performace of 78.33% ad a verificatio performace of 95.%. Fially, the performace of proposed system ca be improved combiig the features vectors extracted usig the discrete Gabor trasform, together the eigefaces method. I such case the classificatio performace becomes 9% while the verificatio performace becomes 99.85%. Table 3 provides a summary of the classificatio ad verificatio performace of a face recogitio systems usig the four features vector extractio metioed above together with the performace of the face recogitio system usig a feature vector extracted usig a combiatio of the Gabor trasform ad the eigefaces methods. Evaluatio results show that proposed face recogitio Gabor-Eigefaces algorithm provides better performace tha other previously proposed methods such as the Eigefaces, Gabor, discrete Cosie trasform ad the discrete Walsh trasform based methods. Figure shows the way i which the features vectors were uited for the combiatio. Oe ca see that the iput vector for the euroal etwork has a greater legth, i.e. 58 coefficiets. Figure shows the propoed system i this paper. 8

10 Issue, Volume 3, 009 ad geometrical trasformatio (rotatig, shiftig, resizig). Computer simulatio shows that the proposed system performs better tha some previously proposed algorithms usig such as the eigefaces method, the Discrete Cosie Trasform ad the Discrete Walsh Trasform. The combiatio of methods to obtai the feature vector, such as Gabor ad Eigefaces, deliver a higher percetage of recogitio. Therefore, the system proposed i this paper is a combied system. Fially, we ca emphasize four advatages of the proposed system: Compact extractio of the face iformatio, easy implemetatio, robustess agaist several coditio chages ad commo image processig. Fig.. Combiatio of Eigefaces ad Gabor i a euroal etwork. ACKOWLEDGMETS We thaks to the atioal Sciece ad Techology Coucil of Mexico (COACyT) ad the IP for fiacial support provided us for the realizatio of this research. Fig.. Proposed System. Table 3 Recogitio performace of proposed algorithms ad other previously reported face recogitio algorithms Algorithm Idetificatio Verificatio Eigefaces (EF) 83.00% 99.67% Discrete Walsh Trasform 75.33% 90.33% Discrete Gabor Trasform 85.67% 99.33% Discrete Cosie Trasform % 95. % Discrete Gabor Trasform together with eigefaces 9.0% 99.85% IV. COCLUSIOS I this paper we proposed a automatic face recogitio system i which the face image is divided i 08 receptive fields. ext the cross-correlatio of each receptive field with 54 Gabor fuctios with 9 differet agles ad 6 frequecies are estimated, which are the averaged to obtai the feature vectors of each oe of the 08 receptive fields. The feature vector is the fed ito a multilayer eural etwork to recogize the face image. The evaluatio results by computer simulatio show that the performace of proposed face idetificatio system is quite robust agaist chages i illumiatio, wardrobe, facial expressios ad additive oise, blurred images (filters), resizig, shiftig ad eve with some age chages. The proposed idetity verificatio system ca verify correctly the iput face images with differet illumiatio level, differet facial expressio, with some accessories, as well as whe the face images pass through some commo image processig such as filterig, cotamiatio by oise REFERECES [] P. Reid, Biometrics for etworks Security, Pretice Hall, ew Jersey 004. [] S. Weicheg, M. Surette, R. Khaa, Evaluatio of automated biometrics-based idetificatio ad verificatio systems, Proceedigs of the IEEE, vol. 85, o.9, pp [3] R. J. Baro. Mechaisms of huma facial recogitio. Iteratioal Joural of Ma-Machie Studies, pp: 37-78, 98. [4] R. Chellappa, C. Wilso, ad S. Sirohey, Huma ad Machie Recogitio of Faces: A Survey, Proc. IEEE, vol. 83, o. 5, pp , 995. [5] L. Sirovich ad M. Kirby, Low-dimesioal procedure for the characterizatio of huma faces, J. Opt. Soc. Am. A., Vol. 4, o. 3 March 987, [6] Bruelli R., Poggio T., Face recogitio: Features vs. Templates, IEEE Trasactios o Patter Aalysis ad Machie Itelligece, Vol. 5, o. 0, 993. [7] M. Turk ad A. Petlad, Eigefaces for Recogitio, J. Cogitive eurosciece, vol. 3, o., 99. [8] M. Turk ad A. Petlad, Face Recogitio usig Eigefaces, Proc. IEEE Cof. o Computer Visio ad Patter Recogitio, pp , 99. [9] Moghaddam B., Wahid W. & Petlad A., Beyod eigefaces: Probabilistic matchig for face recogitio, Proceedigs of the Secod Iteratioal Coferece o Automatic Face ad Gesture Recogitio, ara, 998, pp [0] I. Smith, A tutorial o Pricipal Compoets Aalysis, February 6, 00. [] Taaka H.T., Ikeda M & Chiaki H., Curvature-based face surface recogitio usig spherical correlatio Pricipal directios for curved object recogitio, Proceedigs of the Secod Iteratioal Coferece o Automatic Face ad Gesture Recogitio, ara, 998, pp [] M. Yoshida, T. Kamio ad H. Asai, Face Image Recogitio by - Dimesioal Discrete Walsh Trasform ad Multi-Layer eural etwork, IEICE Tras. Fudametals, Vol. E86-A, o.0, pp , Oct [3] Shaks, J. L., Computatio of the Fast Walsh-Fourier Trasform, IEEE Tras. Comput., Vol. 8, o. 5, pp , 969. [4] Laitis A., Taylor C.J. & Cootes T.F., A uified approach to codig ad iterpretig face images, Proceedigs of the Iteratioal Coferece o Computer Visio ICCV 95, Cambridge, 995. [5] Kirby M. & Sirovich L., Applicatio of the Karhue-Loeve procedure for the characterizatio of huma faces, IEEE Trasactios o Patter Aalysis ad Machie Itelligece, Vol., o., 990. [6] P. Hallia, G. Gordo, A. Yullie, P. Gabli ad D. Mumford, Two ad Three Dimesioal Patters of Face, K. Peters Ltd, atick, Ma, USA,

11 Issue, Volume 3, 009 [7] I. Hog, Y. Wa ad A. Jai, Figerprit image ehacemet algorithm ad performace evaluatio, IEEE Tras. o Patter Aalysis ad Machie Itelligece, vol. 0, o.8, pp , August 998. [8] C. Cruz, R. Reyes, M. akao-miyatake ad H. Perez-Meaa, Verificacio de firmas usado la trasformada de Gabor, Revista Iteracioal Iformacio Tecologica, Vol. 5, o. 3, pp , Jue 004. [9] J. G. Daugma, Complete discrete D Gabor trasform by eural etworks for image aalysis ad compressio, IEEE Tras. o Acoustic Speech ad Sigal Proc., vol. 36, o. 7, pp , July 988. [0] Du, D., Higgis, W. E., Optimal Gabor Filters for Texture Segmetatio, IEEE Tras. Image Proc., Vol. 4, o. 7, Jul [] H. Feichtiger, T. Strohmer, Gabor Aalysis Algorithms, ed. Birkhauser, Bosto, Ma. USA, 998. [] T. Kamio, H. iomiya, ad H. Asai, A eural et approach to discrete Walsh trasform, IEICE Tras. Fudametals, vol.e77-a, o.. pp , ov [3] H.T.L. Mar ad C.L. Sheg, Fast Hadamard trasform usig the H diagram, IEEE Tras. Comput., vol.c-, o.0, pp , 973. [4] Scott E., Computer Visio ad Image Processig,Pretice Hall PTR, Pretice Hall,Ic,Upper Saddle River,J 07458,ISB : ,USA,999 [5] Corad S., Kuldip K., Fast Features for Face Autheticatio Uder Illumiatio Directio Chages, Patter Recogitio Letters, , 003. [6] Eicheler, S., Muller, S. ad Rigoll, G., Recogitio o JPEG Compressed Face Images Based o Statistical Methods, Image Visio Compute. 8(4), 79-87,000. [7] Willie L. Scott, II, Block-Level Discrete Cosie Trasform Coefficiets for Autoomic Face Recogitio, Ph.D Thesis Submitted to Graduate Faculty of Louisiaa State U. ad Agricultural ad Mechaical Collage, USA, May 003. [8] Almas M., Youus M. ad Basit A., Aew Approach to Face Recogitio Usig Dual Dimesio Reductio, Iteratioal Joural of Sigal Processig Volume umber,isb , 005. [9] Hazem K.,Raier S., Local Appearace Based Face Recogitio Usig Discrete Cosie Trasform, 3th Europea Sigal Processig Coferece (EUSIPCO), Atalia, 005. [30] B. Widrow ad A. Lehr, 30 years of adaptive eural etworks: Perceptro, madalie ad backpropagatio, Proc. of The IEEE, vol. 78, o. 9, pp , Sept Prof. akao is a member of the IEEE, RISP ad the atioal Researchers System of Mexico. Her research iterests are sigal ad image processig, patter recogitio watermarkig, stegaography ad related field. Hector Perez-Meaa received the BS Degree i Electroics Egieers from the Uiversidad Autooma Metropolitaa (UAM) Mexico City i 98, the M.S. degree from the Uiversity of Electro-Commuicatios, Tokyo Japa i March 986, ad a Ph. D. degree i Electrical Egieerig from Tokyo Istitute of Techology, Tokyo, Japa, i 989. I 98 he joied the Electrical Egieerig Departmet of the Metropolita Uiversity where he was a Professor. From March 989 to September 99, he was a visitig researcher at Fujitsu Laboratories Ltd, Kawasaki, Japa. I February 997, he joied the Graduate Departmet of The Mechaical ad Electrical Egieerig School o the atioal Polytechic Istitute of Mexico, where he is ow a Professor. I 99 Prof. Perez-Meaa received the IEICE excellet Paper Award, ad i 999 ad 000 the IP Research Award. I 998 Prof.Perez-Meaa was Co-Chair of the ISITA 98. His pricipal research iterests are sigal ad image processig, patter recogitio, watermarkig, stegaography ad related fields. Dr. Perez-Meaa is a seior member of the IEEE, a member of the IEICE, the IET, the atioal Researchers System of Mexico ad the Mexica Academy of Sciece. Gualberto Aguilar-Torres received the BS degree o Electroic ad Commuicatios Egieer; ad The MS degree o Microelectroic Egieerig, i 003 ad 005, respectively, from the atioal Polytechic Istitute of, Mexico, Mexico. Actually he is a PhD degree studet at the Mechaical ad Electrical Egieerig School of the atioal Polytechic Istitute of Mexico. I 005 he received the Best Thesis award from the atioal Polytechic Istitute of Mexico for his Master research work. Gabriel Sachez-Perez received the BS degree o Electroic ad Commuicatios Egieer; ad The MS degree o Microelectroic Egieerig, i 999 ad 005, respectively, from the atioal Polytechic Istitute of, Mexico. From Jauary 00 to October 006 he joied the Computer Egieerig Departmet Electrical ad Mechaical Egieerig School of the atioal Polytechic Istitute of Mexico as a Assistat Professor. I October 006 he joits the Graduate ad Departmet of the Mechaical Egieerig School of the atioal Polytechic Istitute of Mexico where he is ow a Professor. Prof. Sachez-Perez is a member of the IEEE ad a member of the atioal Researchers System of Mexico. Mariko akao-miyatake received the M.E. degree i Electrical Egieerig from the Uiversity of Electro-Commuicatios, Tokyo Japa i 985, ad her Ph. D i Electrical Egieerig from The Uiversidad Autooma Metropolitaa (UAM), Mexico City, i 998. From March 985 to December 986 she was with Toshiba Corp. Kawasaki Japa, from Jauary 987 to March 99 she worked at Kokusai Data Systems Ic. Tokyo, Japa. From July 99 to February 997 she joied the Departmet of Electrical Egieerig of the UAM Mexico as a Professor. I February 997, she joied the Graduate Departmet of The Mechaical ad Electrical Egieerig School of The atioal Polytechic Istitute of Mexico, where she is ow a Professor. 30