Face Recognition Methods Based on Feedforward Neural Networks, Principal Component Analysis and Self-Organizing Map

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1 RADIOENGINEERING, VOL. 16, NO. 1, APRIL Face Recognton Methods Based on Feedforward Neural Networks, Prncpal Component Analyss and Self-Organzng Map Mloš ORAVEC, Jarmla PAVLOVIČOVÁ Dept. of elecommuncatons, Faculty of Electrcal Engneerng and Informaton echnology, Slovak Unversty of echnology, Ilkovčova 3, Bratslava, Slovak Republc Abstract. In ths contrbuton, human face as bometrc [1] s consdered. Orgnal method of feature extracton from mage data s ntroduced usng (multlayer perceptron) and PCA (prncpal component analyss). hs method s used n human face recognton system and results are compared to face recognton system usng PCA drectly, to a system wth drect classfcaton of nput mages by and RBF (radal bass functon) networks, and to a system usng as a feature extractor and and RBF networks n the role of classfer. Also a twostage method for face recognton s presented, n whch Kohonen self-organzng map s used as a feature extractor. and RBF network are used as classfers. In order to obtan deeper nsght nto presented methods, also vsualzatons of nternal representaton of nput data obtaned by neural networks are presented. Keywords Bometrcs, face recognton, neural networks, PCA, multlayer perceptron, radal-bass functon network, self-organzng map, vsualzaton, LDA, kernels. 1. Introducton 1.1 Multlayer Perceptron Basc multlayer perceptron () buldng unt s a model of artfcal neuron. hs unt computes the weghted sum of the nputs plus the threshold weght and passes ths sum through the actvaton functon (usually sgmod) [2]: v y p = 1 p = θ + w x = w x (1) ( v ) = 0 = ϕ (2) where v s lnear combnaton of nputs, x 2,, of the neuron, w 0 =θ s the threshold weght connected to the specal nput x 0 =-1, y s the output of the neuron and φ ( ) s ts actvaton functon. Heren we use the well-known logstc functon, whch s the specal form of sgmodal (non-constant, bounded, and monotone-ncreasng) actvaton functon y 1 = 1+ exp ( v ). (3) In a multlayer perceptron, the outputs of the unts n one layer form the nputs to the next layer. he weghts of the network are usually computed by tranng the network usng the backpropagaton (BP) algorthm. A multlayer perceptron represents nested sgmodal scheme [2], ts form for sngle output neuron s ( ) F x, w = ϕ w oϕ w kϕ Kϕ wl x K (4) k where φ( ) s a sgmodal actvaton functon, w o s the synaptc weght from the neuron n the last hdden layer to the sngle output neuron o, and so on for the other synaptc weghts, x s the -th element of the nput vector x. he weght vector w denotes the entre set of synaptc weghts ordered by layer, then neurons n a layer, and then number n a neuron. 1.2 Radal Bass Functon Network Radal bass functon (RBF) network [3], [4], [2] s based on a multvarable nterpolaton: Gven a set of N dstnct vectors {x 0 R p = 1,, N} and N real numbers {d 0 R = 1,, N}, the am s to fnd a functon f: R p R satsfyng the condton f(x )=d, =1,, N. RBF approach works wth N radal bass functons (RBF) Φ, where Φ : R p R, =1,,N and Φ = (2x-c 2), where Φ: R + R, x 0 R p, 2 2 s a norm on R p, c 0 R p are centers of RBFs. Centers are set to c = x 0 R p, =1,,N. A very often used form of RBF s the Gaussan functon Φ(x)=exp(-x 2 /2σ 2 ), where σ s a wdth (parameter). Functons Φ, =1,,N form the bass of a lnear space and the nterpolaton functon f s ther lnear combnaton

2 52 M.ORAVEC, J. PAVLOVIČOVÁ, FACE RECOGNIION MEHODS BASED ON f N ( ) = w ( x c ) x φ (5) = 1 Interpolaton problem s smple to solve, n contrast to approxmaton problem (there s N gven ponts and n 0 functons Φ, where n 0 < N.), whch s more complcated. hen t s a problem to set centers c, =1,,n 0, also the parameter σ of each RBF can be not the same for all RBFs. One possble soluton f approxmaton problem s a neural network soluton. RBF network s a feedforward network consstng of nput, one hdden, and output layer. he nput layer dstrbutes nput vectors nto the network, the hdden layer represents RBFs Φ. Lnear output neurons compute lnear combnatons of ther nputs. RBF network learnng conssts of more dfferent steps (a descrpton of RBF network learnng can be found n [3], [4]). 1.3 Self-Organzng Map Self-organzng map [5] s a neural network, whch we use here for the desgn of a codebook for vector quantzaton [6]. It usually conssts of two-dmensonal lattce of neurons wth weght vectors w. We denote nput vectors as x. he updatng process (n dscrete-tme notaton) s: w h c ( n ) = w ( n) + h ( n) [ x( n) w ( n) ] +1 (6) 2 2 ( n) h0 ( n) exp( - r rc / β ) c = (7) where the neurons coordnates c and are denoted by the vectors r c and r, h 0 = h 0 (n) and β = β(n) are sutable decreasng functons of tme. More detals about self-organzng map tranng can be found n [5]. and synthess (nverse transform) s represented by p 1 = x = Ua a u. (10) = 0 Fg. 1. Subects n the face database. 1.4 Prncpal Component Analyss Prncpal component analyss PCA [2] s a standard statstcal method used for feature extracton. It transforms the nput data represented by a random vector x=[x 0,,x 2,,-1 ], E[x]=0 wth a correlaton matrx R x =E[xx ]=R x to a set of coeffcents (prncpal components) a = u x = x u, = 0,1, K, p 1 (8) represented by the vector a=[a 0,a 1,a 2, a p-1 ]. Unt vectors u =[u 0,u 1,u 2, u p-1 ], (2u2= u u = 1) form the matrx U=[u 0,u 1,u 2,,u p-1 ] and they are egenvectors of the correlaton matrx R x assocated wth the egenvalues λ 0,λ 1,,λ p-1, where λ 0 >λ 1 > >λ p-1 and λ 0 =λ MAX. he most mportant egenvectors are those correspondng to the largest egenvalues of R x. he representaton of nput data (analyss, forward transform) s defned by a = x U = U x (9) Fg. 2. Examples of one subect. It s possble to represent the nput data by a reduced number of prncpal components (dmensonalty reducton). he transform uses the egenvectors correspondng to the largest egenvalues of R x, and those correspondng to small egenvalues are dscarded m 1 = x a u. m < p (11) = 0 hen the vector x s an approxmaton of x, whle λ 0 >λ 1 > λ m-1 >λ m > >λ p-1.

3 RADIOENGINEERING, VOL. 16, NO. 1, APRIL Face Database We use the face database from MI (Massachusetts Insttute of echnology) [7]. MI face database, frst tme used n [8] belongs to the well known publc doman face databases [9], such as Yale [10] and ORL databases [11]. It s mentoned and used n up-to-date works relatng to facal bometrc, e.g. [9], [12], [13], [14]. MI database conssts of face mages of 16 people (shown n Fg. 1), 27 of each person under varous condtons of llumnaton, scale, and head orentaton. It means, the total number of face mages s 432. Each mage s 64 (wdth) by 60 (heght) pxels, eght-bt grayscale. An example of dfferent face mages (patterns) belongng to the same class s shown n Fg Face Recognton Methods We use several dfferent methods here; they are shown n Fg. 3, wth the summary of results shown n Fg. 12. At frst, we are concerned wth one-stage recognton systems wthout feature extracton stage: a. he drect classfcaton of nput face mages by multlayer perceptron () and radal-bass functon network (RBF) s shown n Fg. 3a). he confguraton of was 64x60-16 (.e nput neurons and 16 output neurons). he nput layer of ths confguraton agrees wth number of pxels n an nput mage (64x60=3840). was traned on the tranng face set contanng 48 faces (those 16 shown n Fg. 1 plus other 32 mages - two dfferent scales of Fg. 1). correctly classfed % of test faces, (300 successfully recognzed faces from the total 384 test faces). Receptve felds of output neurons of such classfer are vsualzed n Fg. 4. We traned also s contanng one hdden layer wth a dfferent number of neurons (16, 32, 48, 96, 144, and 192). Recognton results were from 66.2 % to 78.24%. he confguraton of RBF network was 64x (48 tranng faces f network classfer, whch gves the best results wth 48 RBF neurons n the hdden layer). Receptve felds of hdden neurons of RBF classfer are shown n Fg. 5. RBF network behavor was comparable to the network correctly classfed % of test faces. hese results are shown as methods No. 6 and 7 n Fg.12. We traned also RBF networks wth a dfferent number of hdden neurons (16, 32, 96, 144, and 192). Recognton results were from % to %. x 2 classfer x2 PCA a) b) Eucldan dstance x2 block HLO mage compresson & formaton x2 ML P block compresson x 2 X 1 X 2 X p & Non-block compresson VQ by SOM c) HLO mage formaton d) e) Index mage PCA classfer Classfer classfer Eucldan dstance f) Fg. 3. Face recognton methods used n ths paper. he methods followng from ths pont, n contrary to the method a) are based on two-stage systems, contanng both feature extracton stage and classfcaton stage: b. wo-stage system, where PCA s appled drectly to face mages wth Eucldan dstance as a classfcaton measure s shown n Fg. 3b). he correlaton matrx was computed from 48 tranng faces (the same as method a)) and for classfcaton frst 48 egenvectors of the correlaton matrx are used (Fg. 6 shows the frst 48 egenfaces of the correlaton matrx) % of test faces was recognzed successfully (313 from the total 384). hs result corresponds to the method No. 3 n Fg. 12. c. Our proposed method s shown n Fg. 3c). As the frst stage, block compresson s used. 64x60 nput face mages are dvded to 16x15 blocks. confguraton s 16x x15 (.e. 240 nput and output neurons and 15 hdden neurons). Each face mage s then represented by 240 hdden layer outputs. he compresson perceptron was traned on the frst twelve faces from Fg. 1, remanng four face mages were used for testng purposes. Compresson capablty of s llustrated n Fg. 7, where a low qualty of reconstructons can be seen. After tranng, all nput faces were represented by hdden layer outputs (HLO), whch were used for HLO mage formaton, 240 HLO for each nput mage were used for formaton of the 60x4 HLO mage. 16 HLO mages correspondng to faces n Fg. 1 are shown n Fg. 8. hen, PCA was appled on ths representaton of nput data - correlaton matrx 240x240 was computed from 48 HLO mages correspondng to 48 tranng mages (used also n the two prevous methods). hese 48 egenvectors (or, better sayng, 48 prncpal components obtaned by proecton of nput data onto these egenvectors) are used for classfcaton, where classfcaton crteron s Eucldan dstance. hs proposed system recognzes % of the test faces successfully (319 of the total 384). See method No. 1 n Fg. 12.

4 54 M.ORAVEC, J. PAVLOVIČOVÁ, FACE RECOGNIION MEHODS BASED ON d. For comparson purposes, we present the method based on c), where classfer s replaced by network (see Fg. 3d). It means 240 hdden layer outputs (60x4 HLO mage) of compresson are now nput to classfcaton wth 240 nput and 16 output neurons. hs system recognzes 73.7 % test faces successfully (283 of the total 384). hs result s shown as the method No. 9 n Fg. 12. We tred also s wth one hdden layer con tanng 16, 32, 48, 96, and 144 neurons and also two hdden layers contanng 96 and 48 neurons. he results vared from 61.2 % to %. In the case of RBF network classfer of confguraton gves recognton success % (316 of 384 test faces). hs result s shown as the method No. 2 n Fg. 12. Other RBF confguratons wth 16, 32, 96, and 144 hdden neurons gave results from % to %. Fg. 4. Receptve felds of output neurons of classfer 64x Fg. 5. Receptve felds of 48 hdden neurons of RBF classfer 64x e. In order to compare results of recognton usng compresson networks for feature extracton, we present also non-block compresson workng n autoassocatve mode [15], [16] followed by network classfer (Fg. 3e). he tranng set for compresson agan conssted of 48 faces (dentcal wth the tranng set n method a). he confguraton of compresson was 64x x60 (s wth 16 and 96 hdden neurons were also examned, but reconstructon results were of lower qualty). Fg. 9 shows reconstructons of a subset of tranng and test sets by such compresson. Its receptve and proectve felds are shown n Fg. 10. Hdden layer outputs serve as nput to classfcaton networks. he best classfcaton results were obtaned by (74.74 %,.e. 287 of 384 faces were recognzed successfully) and RBF network (72.40 %,.e. 278 of 384). hese results correspond to the methods No. 8 and 10 n Fg. 12. Other and RBF network confguratons gave the results from % to %. f. Our last method s based on self-organzng systems wth compettve learnng. hs method uses feature extracton method from mage data, whch s based on vector quantzaton (VQ) of mages usng Kohonen selforganzng map for codebook desgn. he ndexes used for mage transmsson are used to recognze faces. hs method s descrbed n detal n [17]. We perform vector quantzaton on 64x60 face mages dvdng orgnal mages to 4x4 blocks. For mage vector quantzaton, we used the confguraton of the self-organzng map of 16x16 neurons wth 16-dmensonal weght vectors, what corresponds to bt rate 0.5 bt/pxel compared to 8 bt/pxel orgnal mages. For tranng ths map, frst twelve 64x60 mages from Fg. 1 dvded to 4x4 blocks were used. Remanng four mages from Fg. 1 were used for testng. Each face mage s after vector quantzaton represented by 240 eght-bt ndexes, we form them to 16x15 eght bt/pxel mage (examples of such ndex mages correspondng to orgnal faces from Fg. 1 are shown n Fg. 11) whch then serves as the nput to network classfer. hs s shown n Fg. 3f). Both networks had 240 (16x15) nputs. he confguraton of was and confguraton of RBF network was hs system usng RBF network recognzes % test faces successfully (310 of 384 test faces). In the case of classfer of confguraton gves recognton success % (307 of total 384 test faces). hese results are shown as the methods No. 4 and 5 n Fg. 12. Other confguratons of and RBF networks reached from 61.2 % to %. Fg. 6. Frst 48 egenvectors of correlaton matrx of nput data (egenfaces).

5 RADIOENGINEERING, VOL. 16, NO. 1, APRIL Fg. 7. Orgnals and reconstructons of face mages from Fg. 1 by (left-to-rght 12 tranng faces and 4 test faces). Fg. 8. Images of hdden layer outputs (HLO mages) of for 16 faces from Fg. 1 (dmensons are 60x4 pxels). Fg. 9. Reconstructon of subset of tranng set (top) and subset of test set (bottom) by compresson 64x x60. Fg. 10. Receptve and proectve felds of compresson 64x x60 (holons). Fg.11. Index mages (each of 16 mages s 16x15 pxels) correspondng to Fg. 1, zoomed.

6 56 M.ORAVEC, J. PAVLOVIČOVÁ, FACE RECOGNIION MEHODS BASED ON Methods ordered by recognton success 1) PCA-hlo{} 2) block-rbf 3) PCA 4) blocksom-rbf 5) blocksom- 83,07 82,29 81,51 80,73 79,95 6) RBF 7) 78,12 78,12 8) - 9) block- 10) -RBF 72,4 73,7 74, Fg. 12. Comparson of presented methods for 384 test faces (% of successfully recognzed faces). 4. Conclusons We presented the orgnal method for nternal representaton of nput data by. It uses multlayer perceptron for block compresson of mage data and t s based on formaton of outputs of hdden layer to an mage (so called HLO mage-hdden layer outputs mage), whch s then further processed by PCA. hs method s heren successfully appled n human face recognton system. Although one can note relatvely poor results for reconstructed mages n the compresson stage (Fg. 7), the proposed face recognton system gves the best results, what can be seen whle comparng ths method to all other presented methods. hese methods cover one- and twostage recognton systems and they nclude feedforward neural networks both n the role of feature extractor and classfer. Also self-organzed map s used n the role of feature extractor. Snce nternal representaton of nput data created by neural networks (Fg. 4, 5, 8, 10, 11) and reconstructon of nput data s shown (Fg. 7, 9), we hope ths paper gves deeper nsght nto face recognton systems usng PCA, feedforward neural networks and self-organzng systems. In ths paper, we have not consdered mage preprocessng. he preprocessng could mprove recognton results, ts mplementaton s llustrated e.g. n [18], [19]. Generally, mage preprocessng deals wth dgtal mage processng procedures such as mage resamplng, hstogram equalzaton, color balance, etc. Other mportant procedures nclude face detecton [12],.e. localzaton of a face n an mage wth determnng face sze (dstance from camera), rotaton wth followng normalzaton of face to scale, llumnaton, rotaton, etc. We accent that all used methods cover the broad spectrum of tools used for face recognton purposes: two types of feedforward neural networks ( and RBF network), standard statstcal tool PCA, and Kohonen self organzng map. It s nterestng, that all these tools appeared even n 4 best methods (ordered by recognton success) n Fg. 12. Of course, other algorthms or combnaton of presented methods wth other methods s possble for face recognton. For example, t s possble to combne PCA wth some other standard technque. In [20] a fuson of PCA wth lnear dscrmnant analyss LDA s presented. LDA was found to have useful propertes t s nsenstve to large varaton n lghtng drecton and facal expresson. It s generally beleved, that algorthms based on LDA are superor to those based on PCA. In [21], however, authors show that when the tranng data set s small, PCA can outperform LDA, and also that PCA s less senstve to dfferent tranng data sets. Such result s ustfed also n [22], where agan combnaton of PCA and LDA n the form of boosted hybrd dscrmnant analyss s presented. Nonlnear boostng process was used for effcent parameter searchng and to combne classfers adaptvely. At present, the range of these tools becomes even broader. Kernel methods are utlzed also for recognton purposes [23-27]. Kernel-based prncpal component analyss KPCA, kernel-based lnear dscrmnant analyss KLDA, kernel radal bass functon networks KRBF and support vector machnes SVM are examples of kernel methods. hey can be used for feature extracton, as well as classfcaton. Several papers dealng wth kernel methods for face recognton have appeared, e.g. [24-27]. he kernel algorthms are computatonally very complex, but they seem to be promsng alternatve to conventonal lnear methods. Due to computatonal complexty, KPCA and KLDA are often used for nput mages of dmensons

7 RADIOENGINEERING, VOL. 16, NO. 1, APRIL x23 pxels [24], [25] or 80x80 pxels [27]. It can be seen, that all these tools play an mportant role n up-to-date face recognton systems. Face recognton s consdered to be a part of a bometrc system. Its ncludng nto multmodal bometrc systems [1] can ensure hgher level of securty n an open socety. Acknowledgements he research descrbed n the paper was fnancally supported by the Slovak Grant Agency VEGA under grant No. 1/3117/06. References [1] JAIN, A. K., ROSS, A., PRABHAKAR, S. An ntroducton to bometrc recognton. IEEE rans. Crcuts and Systems for Vdeo echnology, 2004, vol. 14, no. 1, p [2] HAYKIN, S. Neural Networks - A Comprehensve Foundaton. New York: Macmllan College Publshng Company, [3] HLAVÁČKOVÁ, K., NERUDA, R., Radal bass functon networks. Neural Network World, 1993, no. 1, p [4] POGGIO,., GIROSI, F. Networks for approxmaton and learnng. Proc. of the IEEE, 1990, vol. 78, no. 9, p [5] KOHONEN,. he self-organzng map. 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Prof. degrees n telecommuncaton engneerng from the Faculty of Electrcal Engneerng and Informaton echnology, Slovak Unversty of echnology (FEI SU) n Bratslava n 1990, 1996 and 2002, respectvely. He s wth the Dept. of elecommuncatons, FEI SU. He s a member of the IE. Hs research nterests nclude mage processng, neural networks and communcaton networks. Jarmla PAVLOVIČOVÁ receved the MSc., PhD. and Assoc. Prof. degrees n telecommuncaton engneerng from the FEI SU n Bratslava n 1986, 2002 and 2006 respectvely. She s wth the Dept. of elecommuncatons, FEI SU Bratslava. Her research nterests nclude mage processng, especally mage segmentaton.