Face Recognition using Wavelet, PCA, and Neural Networks

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1 Proceedng of the Frst Internatonal Conference on Modelng, Smulaton and Appled Optmzaton, Sharjah, U.A.E. February -3, 005 Face Recognton usng, PCA, and Neural Networks Masoud Mazloom Sharf Unversty of Technology Department of Mathematcs P.O.Box 46969, Tehran, IRAN Shohreh Kasae Sharf Unversty of Technology Department of Computer Engneerng P.O.Box , Tehran, IRAN ABSTRACT Ths work presents a method to ncreased the face recognton accuracy usng a combnaton of, PCA, and Neural Networks. Preprocessng, feature extracton and classfcaton rules are three crucal ssues for face recognton. Ths paper presents a hybrd approach to employ these ssues. For preprocessng and feature extracton steps, we apply a combnaton of wavelet transform and PCA. Durng the classfcaton stage, the Neural Network (MLP) s explored to acheve a robust decson n presence of wde facal varatons, also we have used RBF Neural Network but results show that MLP Neural Network outperforms RBF. The computatonal load of the proposed method s greatly reduced as comparng wth the orgnal PCA based method. Moreover, the accuracy of the proposed method s mproved.. INTRODUCTION Over the past few years, the user authentcaton s ncreasngly mportant because the securty control s requred everywhere. Tradtonally, ID cards and passwords are popular for authentcaton although the securty s not so relable and convenent. Recently, bologcal authentcaton technologes across voce, rs, fngerprnt, palm prnt, and face, etc are playng a crucal role and attractng ntensve nterests for many researchers. Among them, face recognton s an amcable alternatve because the authentcaton can be completed n a hands-free way wthout stoppng user actvtes. Also, the face recognton system s economc wth the low-cost of cameras and computers. It s extensvely feasble to dentty authentcaton, access control, and survellance, etc. Over the past 0 years, extensve research works on varous aspects of face recognton by human and machnes [,,, 0,,,3,8] have been conducted by psychophyscsts, neuroscentst and engneerng scentsts. Psychophyscsts and neuroscentsts have studed ssues such as unqueness of faces, how nfants perceve faces and organzaton of memory of faces. Whle engneerng scentst have desgned and developed face recognton algorthms. Ths paper contnues the work done by engneerng scentst n face recognton by machne. Automatc face recognton by computer can be dvded nto two approaches [, ], namely, content-based and face-based. In content-based approach, recognton s based on the relatonshp between human facal features such as eyes, mouth, nose, profle slhouettes and face boundary [3, 4, 5, 6]. The success of ths approach reles hghly on the accurately s dffcult. Every human face has smlar facal features, a small dervaton n the extracton may ntroduce a large classfcaton error. Face-based approach [7, 8, 5, 9] attempts to capture and defne the face as a whole. The face s treated as a two-dmensonal pattern of ntensty varaton. Under ths approach, face s matched through dentfyng ts underlyng statstcal regulartes. Prncpal Component Analyss (PCA) [7, 8, 0, 0, 4] has been proven to be an effectve face-based approach. Srovch and Krby [0] frst proposed usng Karhunen-Loeve (KL) transform to represent human faces. In ther method, faces are represented by a lnear combnaton of weghted egenvector, known as egenfaces. Turk and Pentland [8] developed a face recognton system usng PCA. However common PCA-based methods suffer from two lmtatons, namely, poor dscrmnatory power and large computatonal load. It s well known that PCA gves a very good representaton of the faces. Gven two mages of the same person, the smlarty measured under PCA representaton s very hgh. Yet, gven two mages of dfferent persons, the smlarty measured s stll hgh. That means PCA representaton gets a poor dscrmnatory power. Swets and Weng [] also observed ths drawback of PCA approach and further mprove the dscrmnablty of PCA by addng Lnear Dscrmnant Analyss (LDA). But, to get a precse result, a large number of samples for each class s requred. On the other hand, O'Toole et al. [] proposed dfferent approach for selectng the egenfaces. They ponted out that the egenvectors wth large egenvalues are not the best for dstngushng face mages. They also demonstrated that although the low dmensonal representaton s not optmal for recognzng a human face, gves good results n dentfyng physcal categores of face, such as gender and race. However, O Toole et al. have not addressed much on the selecton crtera of egenvectors for recognton. The second problem n PCA-based method s the hgh computatonal load n fndng the egenvectors. The computatonal complexty of ths s O ( d ) where d s the number of pxels n the tranng mages whch has a typcal value ICMSA0/05-

2 Proceedng of the Frst Internatonal Conference on Modelng, Smulaton and Appled Optmzaton, Sharjah, U.A.E. February -3, 005 of 8x8. The computatonal cost s beyond the power of most exstng computers. Fortunately, from matrx theory, we know that f the number of tranng mages, N, s smaller than the value of d, the computatonal complexty wll be reduced to O ( N ). Yet stll, f N ncreases, the computatonal load wll be ncreased n cubc order. In vew of the lmtatons n exstng PCA-based approach, we proposed a new approach n usng PCA applyng PCA on wavelet subband for feature extracton. In the proposed method, an mage s decomposed nto a number of subbands wth dfferent frequency components usng the wavelet transform. The result n Table show that three level wavelet has a good performance n face recognton. A md-range frequency subband mage wth resoluton 6x6 s selected to compute the representatonal bases. The proposed method works on lower resoluton, 6 x 6, nstead of the orgnal mage resoluton of 8 x 8. Therefore, the proposed method reduces the computatonal complexty sgnfcantly when the number of tranng mage s larger than 6 x 6, whch s expected to be the case for a number of real-world applcatons. Moreover, expermental results demonstrated that applyng PCA on WT sub-mage wth md-range frequency components gves better recognton accuracy and dscrmnatory power than applyng PCA on the whole orgnal mage. Then feature vectors classfy by MLP Neural Network. The results show that, MLP Neural Network better than RBF Neural Network. Ths paper s organzed as follows. Secton 3 revews the background of PCA and egenfaces. MLP Neural Network revews n secton 4.The proposed method s dscussed n secton 5. Expermental results are presented n secton 6 and fnally, secton 7 gves the conclusons. Recognton Rate (%) Tranng Tme (mn) Table. Recognton rates and tranng tmes. Egenface Two Level. Revew of PCA and Egenfaces for Face Recognton Ths secton provdes the background theory of PCA and dscusses the use of egenfaces (egenvectors) for face recognton... Prncpal Component Analyss Three Level Four Level 9. N/A N/A PCA s used to fnd a low dmensonal representaton of data. Some mportant detals of PCA are hghlghted as follows [3]. dxd Let X = { X n, n =,..., N} R be an ensemble of vectors. In magng applcatons, they are formed by row concatenaton of the mage data, wth dxd beng the product of the wdth and the heght of an mage. Let be the average vector n the ensemble. E( X ) = () N N X n n= After subtractng the average from each element of X, we get a modfed ensemble of vectors, X = { X n, n =,..., N} wth X n = X E(X ). () n The auto-covarance matrx M for the ensemble X s defned by M = cov( X ) = E( X X ) (3) Where M s d xd matrx, wth elements M (, j) = X ( ) X ( j),. j d (4) n n N It s well known from matrx theory that the matrx M s postvely defnte (or sem-defnte) and has only real nonnegatve egenvalues [3]. The egenvectors of the matrx M form dxd an orthonormal bass for R. Ths bass s called the K-L bass. Snce the auto-covarance matrx for the K-L egenvectors are dagonal, t follows that the coordnates of the vectors n the sample space X wth respect to the K-L bass are un-correlated random varables. Let { Y n, n =,..., N} denote the egenvectors and let K be the d xd matrx whose columns are the vectorsy,...,y. The adjont matrx of the matrx K, whch maps N the standard coordnates nto K-L coordnates, s called the K-L transform. In many applcatons, the egenvectors n K are sorted accordng to the egenvalues n a descendng order. In determnng the dxd egenvalues from M, we have to solve a d xd matrx. Usually, d=8 and therefore, we have to solve a 6x6 matrx to calculate the egenvalues and egenvectors. The computatonal and memory requrement of the computer systems are extremely hgh. From matrx theory that f the number of tranng mages N s much less than the dmenson of M,.e. N < dxd, the computatonal complexty s reduced to O(N). Also, the dmenson of the matrx M n equaton (4) needed to be solved s also reduced to NxN. Detals of the mathematcal dervaton can be found n [7]. Snce then, the mplementaton of PCA for characterzaton of face becomes flexble. In most of the exstng works, the number of tranng mages s small and s about 00. However, computatonal complexty ncreases dramatcally when the number of mages n the database s large, say,000. The PCA of a vector y related to the ensemble X s obtaned by projectng vector y onto the subspaces spanned by d egenvectors correspondng to the top d egenvalues of the autocorrelaton matrx M n descendng order, where d s smaller than d. Ths projecton results n a vector contanng d coeffcents a,..., ad. The vector y s then represented by a lnear combnaton of the egenvectors wth weghts,..., a a d. ICMSA0/05-

3 Proceedng of the Frst Internatonal Conference on Modelng, Smulaton and Appled Optmzaton, Sharjah, U.A.E. February -3, Egenfaces Bascally, egenface s the egenvector obtaned from PCA. In face recognton, each tranng mage s transformed nto a vector by row concatenaton. The covarance matrx s constructed by a set of tranng mages. Ths dea s frst proposed by Srovch and Krby [0]. After that, Turk and Pentland [8] developed a face recognton system usng PCA. The sgnfcant features (egenvectors assocated wth large egenvalues) are called egenfaces. The projecton operaton characterzes a face mage by a weghted sum of egenfaces. Recognton s performed by comparng the weght of each egenface between unknown and reference faces..3. Lmtaton PCA has been wdely adopted n human face recognton and face detecton snce 987. However, n spte of PCA's popularty, t suffers from two major lmtatons: poor dscrmnatory power and large computatonal load. It s well known that PCA gves a very good approxmaton n face mage. However, n egenspace, each class s closely packed. Moghaddam et al. [4] have plotted the largest three egen coeffcents of each class. It s found that they overlap each other. Ths shows that PCA has poor dscrmnatory power. 3. MLP Neural Network Multlayer Perceptron (MLP) Neural Network s a good tool for classfcaton purpose [5, 6]. Neural Network (NN) and multlayer perceptron (MLP), n partcular, are very fast means foe classfcaton of complex objects. It can approxmate almost any regularty between ts nput and output.the NN weghts are adjusted by supervsed tranng procedure called backpropagaton (BP). Back propagaton s a knd of the gradent descent method, whch search an acceptable local mnmum n the NN weght space n order to acheve mnmal error. Error s defned as a root mean square of dfference between real and desred outputs of NN. Durng the tranng procedure, MLP bulds separaton hypersurfaces n the nput space. The MLP can successfully apply acqured sklls to the prevously unseen samples after tranng procedure. It has good extrapolatve and nterpolatve and abltes. Typcal archtecture has a number of layers followng one by one [5, 6]. The MLP wth one layer can buld lnear hypersurfaces, MLP wth two layers can buld convex hypersurfaces, and MLP wth three layers-hypersurfaces of any shape. We wll be consderng the followng chan neurons of MLP n Fgure. Fgure : Scheme of chan of nodes consdered n the back propagaton algorthm. A neuron s the basc element of any artfcal neural network (ANN). It works as: ( ) hj = wjk x (5) k k () Where x k are nput sgnals, w are the weghts of synaptc jk connectons between neurons of and + layers. The output sgnal of the j th neuron s y j = g( h j ), where the actvaton functon g (x) s ether a threshold functon, or a sgmod type functon, lke g( x) =. (6) x + e In the case of a threshold functon and, say two classes, the perceptron attrbutes the vector x to the frst class, f ( ) or to the second class, otherwse. Such a scheme w 0 j j h j admts the followng geometrc nterpretaton.the hyperplane gven by equaton ( ), dvded the space on two wj h j = 0 j halfspace correspondng to classes n queston. If the number of classes s more than two, then several dvdng hyperplanes wll be defned durng the tranng process. For the nput vector of the classfed features X MLP brngs n correspondence an output vectory. The transformaton X Y s completely descrbed by the matrx of synaptc weghts to be found as a soluton of any concrete problem. Let us have some tranng sample as a set of pars of vectors {{ X },{ Z }}. The MLP tranng s accomplshed by mnmzaton of so-called energy functon E = ( Y Z ) mn (7) m () by weghts w as mnmzaton parameters. Such the EBP method jk s usually realzed by the gradent descent method. The number of unts (neuron) n the nput layer s equal to the number of mage pxel. The number of unts n the hdden layer s unknown and t determne wth tral and error algorthm (see table.) and the number of output unts s equal to the number of classes (number of dfferent person n database) 4. Proposed Method A wavelet-based PCA method s developed so as to overcome the lmtaton of the orgnal PCA method; furthermore, we have utlzed a neural network n order to carry out the classfcaton of faces. We adopted a multlayer perceptron archtecture whch s fed by the reduced nput unts, feature vectors generated by combnaton of wavelet and PCA. Utlzed MLP conssts of one hdden layer of 5 unts, and 5 output unts (see Table ). We propose the usage of a partcular frequency band of a face mage for PCA to solve the frst problem of PCA. The second lmtaton can be dealt wth by usng a lower resoluton mage. The combnaton of new wavelet-based PCA and neural network s llustrated n Fgure. ICMSA0/05-3

4 Proceedng of the Frst Internatonal Conference on Modelng, Smulaton and Appled Optmzaton, Sharjah, U.A.E. February -3, 005 Tranng stage Reference mage Recognton stage Unknown Image Transform Transform Submage Submage Prncpal Component Analyss Prncpal Component Analyss Select d Egen vectors wth largest Egen Neural Networks Sub space Projecton Identfed face Neural Networks Fgure. Block dagram of the proposed face recognton system. Our proposed system conssts of two stages, namely tranng step n whch the feature extracton, dmenson reducton and adjustng the weght of neural networks have been performed and the recognton step to dentfy the unknown face mage. The tranng stage ncludes the feature extracton of reference mages and the adjustment of neural network parameters. The extractng feature dentfes the representatonal bass for mages n the doman of nterest. Subsequently, the recognton stage translates the nput unknown mage accordng to the representatonal bass, dentfed n the tranng stage. There are three sgnfcant steps n the tranng stage. In the frst step, wavelet transform (WT) s appled to decompose reference mages; consequently, sub-mages n the form of 6x6 pxels obtaned by three level wavelet decomposton are selected. In the next step, Prncpal Component Analyss (PCA) s performed on the sub-mages to obtan a set of representatonal bass by the selecton of d egenvectors correspondng wth the largest egenvalues and sub-space projecton. Fnally, the feature vectors of reference mages obtaned by prevous steps are used so as to tran neural networks usng back propagaton algorthm. Processng n the recognton stage s smlar to the tranng stage, except that recognton stage also ncorporates steps to match the nput unknown mages wth those reference mages n the database by neural network. When an unknown face-mage s presented to the recognton stage, WT and PCA are appled to transform the unknown face-mage nto the representatonal bass dentfed n the recognton stage, and the classfcaton s acheved by traned neural networks. Table. Percentage of correct classfcaton on test set. Prncpal Net Topology Best Average Component -5 5:5: :30: :30: :5: decomposton of an mage Transform (WT) has been a very popular tool for mage analyss n the past ten years. The mathematcal background and the advantages of WT n sgnal processng have been dscussed n many research artcles. In the proposed system, WT s chosen to be used n mage decomposton because: By decomposng an mage usng WT, the resoluton of the submages are reduced. In turn, the computatonal complexty wll be reduced dramatcally by operatng on a lower a resoluton mage. Harmon [7] demonstrated that mage wth resoluton 6x6 s suffcent for recognzng a human face. Comparng wth the orgnal mage resoluton of 8x8, sze of the sub-mage s reduced by 64 tmes, and the mples a 64 tmes reducton n recognton computatonal load. Under WT, mages are decomposed nto subbands, correspondng to dfferent frequency ranges. These subbands meet readly wth the nput requrement for the next major step, and thus mnmze the computatonal overhead n the proposed system. decomposton provdes the local nformaton n both space doman and frequency doman, whle the Fourer decomposton only supports global nformaton n frequency doman. Through out ths paper (see table 3), the well known Daubeches wavelet D4 [8, 9] s adopted and ts four coeffcent arc: h = h = h = h = An mage s decomposed nto four subbands as shown n Fgure 3. The band LL s a coarser approxmaton to the orgnal mage. The bands LH and HL record respectvely the changes of the ICMSA0/05-4

5 Proceedng of the Frst Internatonal Conference on Modelng, Smulaton and Appled Optmzaton, Sharjah, U.A.E. February -3, 005 mage along horzontal and vertcal drectons whle the HH band shows the hgher frequency component of the mage. Ths s the frst level decomposton. The decomposton can be further carred out for the LL subband. After applyng a three-level transform, an mage s decomposed nto subbands of dfferent frequency as shown n Fgure 4.f the resoluton of an mage s 8x8 the subbands,,3,4 are of sze 6x6, the sub bands 5,6,7 are of sze 3x3 and the subbands 8,9,0 are of sze 64x64. Table 3. Recognton rate by applyng dfferent wavelets on Yale face database Daubeches wavelet Daub() Daubeches wavelet Daub(4) Daubeches wavelet Daub(6) Daubeches wavelet Daub(8) Bortoghonal wavelet Wsplne(4,4) Battle-Lemare wavelet Lemare(4) Tranng Tmes(s) Testng Tmes(s) Recognton Rate (%) Sze of Image for subband x x x x x x6 Brefly the followng steps are used for recognton usng dmensonalty reducton: Step. The combnaton of wavelet and PCA s used to reduce the nput space Step. The mage vectors are normalzed. Step 3. The tranng set used contans 8 samples per subject. Step 4. The testng set used contans 3 samples per subjects, wth 3 samples not ntroduced n the tranng phase. Step 5. The MLP Neural Network structure wth the reduced nput unts s used (5), one hdden layer of 5 unts, and 5 output unts. Fgure 4. Face mages wth one-level, two-level, and three-level wavelet decomposton. 5. Expermental Result To evaluate the performance of the proposed method, we used the face-mages database of Yale Unversty [9]. Ths database conssts of a total of 65 mages (5 persons (males and females), wth mages for each person). These mages are of varous llumnaton and facal expresson, as well as of wearng glasses. All of these mages have a resoluton of 60x. But the dmenson of these mages s not the power of, so that the wavelet transform can not be appled effectvely. For solvng ths problem, we crop these mages to 9x9 and, then resze them nto 8x8. And we the Leavng-one-out strategy [30] for our algorthm. Ths strategy uses 64 mages for tranng and the rest one mages for recognton. We appled ths strategy 50 tmes for tranng and recognton of all mages. In ths work, the resoluton of mages s changed n from of 8x8 to 6x6 usng the thrd level of wavelet decomposton. The result (lsted Table 4) shows that combnaton of wavelet and PCA outperforms: PCA, DWT, and DCT. It also determned that usng of the MLP outperforms RBF Neural Networks [7], NN [5] and NFL [6]. Table 4. Performance comparson of recognton rate. Classfer Type Coeffcents Type Recognton Rate (%) MLP/BP NN WT+PCA (proposed method) MLP/BP NN WT MLP/BP NN LDA 89.4 MLP/BP NN PCA 8.7 Nearest Feature Lne(NFL) WT Nearest Feature Space(NFS) WT 90.0 Fgure 3. decomposton. ICMSA0/05-5

6 Proceedng of the Frst Internatonal Conference on Modelng, Smulaton and Appled Optmzaton, Sharjah, U.A.E. February -3, Conclusons Ths paper presents a hybrd approach for face recognton by handlng three ssues put together. For preprocessng and feature extracton stages, we apply a combnaton of wavelet transform and PCA. Durng the classfcaton phase, the Neural Network (MLP) s explored for robust decson n the presence of wde facal varatons. The experments that we have conducted on the Yale database vndcated that the combnaton of, PCA and MLP exhbts the most favorable performance, on account of the fact that t has the lowest overall tranng tme, the lowest redundant data, and the hghest recognton rates when compared to smlar so-far-ntroduced methods. Our proposed method n comparson wth the present hybrd methods enjoys from a low computaton load n both tranng and recognzng stages. As another llustraton of the prvleges of our ntroduced method, we can menton ts great precson. 7. References []. R. Chellappa, C. L. Wlson and S. Srohey, "Human and machne recognton of faces: a survey," Proceedngs of the IEEE, Vol. 83, No. 5, , May 995. []. G. Chow and X. L, "Towards a system for automatc facal feature detecton," Pattern Recognton, Vol. 6, No., , 993. [3]. F. Goudal, E. Lange, T. Iwamoto, K. Kyuma and N. Otsu, "Face recognton system usng local autocorrelatons and multscale ntegraton," IEEE Trans. PAMI, Vol. 8, No. 0, 04-08, 996. [4]. K. M. Lam and H. Yan, "Locatng and extractng the eye n human face mages", Pattern Recognton, Vol. 9, No , 996. [5]. D. Valentn, H. Abd, A. J. O'Toole and G. W. Cottrell, "Connectonst models of face processng: A Survey," Pattern Recognton, Vol. 7, 09-30, 994. [6]. A. L. Yulle, P. W. Hallnan and D. S. Cohen," Feature extracton from faces usng deformable templates," Int. J. of Computer Vson, Vol. 8, No., 99-, 99. [7]. M. Krby and L. Srovch," Applcaton of the Karhunen- Loeve procedure for the characterzaton of human faces, "IEEE Trans. PAMI., Vol., 03-08, 990. [8]. M. Turk and A. Pentland," Egenfaces for recognton, "J. Cogntve Neuroscence, Vol. 3, 7-86., 99. [9]. M. V. Wckerhauser, Large-rank "approxmate component analyss wth wavelets for sgnal feature dscrmnaton and the nverson of complcated maps, "J. Chemcal Informaton and Computer Scences, Vol. 34, No. 5, , 994. [0]. L.Srovch and M. Krby, "Low-dmensonal procedure for the characterzaton of human faces," J. Opt. Soc. Am. A, Vol. 4, No. 3, 59-54, 987. []. D. L. Swets and J. J. Weng, "Usng dscrmnant egenfeatures for mage retreval," IEEE Trans. PAMI., Vol. 8, No. 8, , 996. []. A. J. O'Toole, H. Abd, K. A. Deffenbacher and D. Valentn, "A low-dmensonal representaton of faces n the hgher dmensons of the space, "J. Opt. Soc. Am., A, Vol. 0, 405-4, 993. [3]. A. K. Jan," Fundamentals of dgtal mage processng," pp.63-75, Prentce Hall, 989. [4]. B Moghaddam, W Wahd and A pentland, "Beyond egenfaces: Probablstc matchng for face recognton," Proceedng of face and gesture recognton, pp , 998. [5]. A.I. Wasserman."Neural Computng: Theory and Practce " New York: Van Nostrand Renhold, 989. [6]. Golovko V., Gladyschuk V." Recrculaton Neural Network Tranng for Image Processng,". Advanced Computer Systems P [7]. L. Harmon, "The recognton of faces," Scentfc Amercan, Vol. 9, 7-8, 973. [8]. I. Daubeches, "Ten Lectures on s, CBMS-NSF seres n Appled Mathematcs," Vol. 6, SIAM Press, Phladelpha, 99. [9]. I. Daubeches, "The wavelet transform, tme-frequency localzaton and sgnal analyss," IEEE Trans. Informaton Theory, Vol. 36, No. 5, , 990. [0]. A. Pentland, B. Moghaddam and T. Starner," Vew-based and modular egenspaces for face recognton," Proc. IEEE Conf. Computer vson and Pattern Recognton, Seattle, June, 84-9, 994. []. H. A. Rowley, S. Baluja and T. Kanade, "Neural networkbased face detecton," IEEE Transacton on PAMI, Vol. 0, No.,3-38, 998. []. E.M.-Tzanakou, E. Uyeda, R. Ray, A Sharma, R. Ramanujan and J. Dong, "Comparson of neural network algorthm for face recognton," Smulaton, 64,, 5-7, 995. [3]. D. Valentn, H. Abd and A. J. O'Toole, "Prncpal component and neural network analyses of face mages: Exploratons nto the nature of nformaton avalable for classfyng faces by sex," In C. Dowlng, F. S. Roberts, P. Theuns, Progress n mathematcal psychology, Hllsdale: Erlbaum, (n press, 996) [4]. K.Fukunaga, "ntroducton to Statstcal Pattern Recognton,", Academc press. [5]. T.M.Cover and P.E. Hart, "Nearest Neghbor Pattern Classfcaton,"IEEE Trans. Informaton theory, vol. 3, pp.- 7, Jan [6]. S.Z. L and J. Lu, "Face Recognton Usng the Nearest Feature Lne Method, "IEEE Trans. Neural Networks, vol. 0, no.,pp , mar [7]. A.Jonathan Howell and H.Buxton, "face Recognton Usng Radal Bass Functon Neural Networks", Proceedngs of Brtsh Machne Vson Conference, pages , Ednburgh, 996. BMVA Press, March 999. [8]. Y. Meyer, "s: Algorthms and Applcatons," SIAM Press, Phladelpha, 993. [9].Yale face database: [30]R. Duda, P. Hart, Pattern Classfcaton and Scene Analyss, Wley, New York, 973. ICMSA0/05-6