www.mer.com Vol.2, Issue.1, pp-060-065 ISS: 2249-6645 An Effcent Illumnaton ormalzaton Meod w Fuzzy LDA Feature Extractor for Face Recognton Behzad Bozorgtabar 1, Hamed Azam 2 (Department of Electrcal Engneerng / Iran Unversty of Scence and echnology, Iran) ABSRAC he most sgnfcant practcal challenge for face recognton s perhaps varablty n lghtng ntensty. In s paper, we developed a face recognton whch s nsenstve to large varaton n llumnaton. ormalzaton ncludng two steps, frst we used Hstogram truncaton as a preprocessng step and en we mplemented Homomorphc flter. he man dea s at, achevng llumnaton nvarance causes to smplfy feature extracton module and ncreases recognton rate. hen we utlzed Fuzzy Lnear Dscrmnant Analyss (FLDA) n feature extracton stage whch showed a good dscrmnatng ablty compared to oer meods whle classfcaton s performed usng ree classfcaton meods : earest eghbour classfer, Support Vector Machnes (SVM) and Feedforward eural etwork(ff).he experments were performed on e ORL (Olvett Research Laboratory) and Yale face mage databases and e results show e present meod w SVM classfer outweghs oer technques appled on e same database and reported n lterature. Keywords - Face Recognton, Homomorphc flter, earest eghbour, Fuzzy LDA, SVM, FF I. IRODUCIO Face recognton has become one of e most actve research areas of pattern recognton snce e early 1990s, and has attracted substantal research efforts from e areas of computer vson, bo-nformatcs and machne learnng. Illumnaton s consdered one of e most dffcult tasks for face recognton. he llumnaton setup n whch recognton s performed s n most cases mpractcal to control, ts physcs dffcult to accurately model and face appearance dfferences due to changng llumnaton are often larger an ose dfferences between ndvduals. Relable technques for recognton under more extreme varatons caused by pose, expresson, occluson or llumnaton s hghly nonlnear, have proven elusve [1]. In s paper, we outlne a hybrd technque for llumnaton normalzaton, after e Hstogram truncaton was appled to nput face mages, e Homomorphc flter was used for normalzaton. he face recognton nvolves two major steps. In e frst step, some features of e mage are extracted. In e second step, on e bass of e extracted features e classfcaton s performed. Fuzzy LDA (Fuzzy Fsherface) recently, was proposed for feature extracton and face recognton [2]. Fuzzy LDA computes fuzzy wn-class scatter matrx and between-class scatter matrx by ncorporatng class membershp of e bnary labeled faces (patterns). Fnally extracted features were consdered as nputs to classfers. In s paper well-known classfers ncludng earest eghbor, SVM and Feedforward eural etworks were employed as classfcaton. hen rest of s paper s as followed. Our proposed meod s ntated n second secton en Fuzzy LDA s ntroduced n rd secton. Classfcaton, expermental results on bo ORL and Yale datasets, and Concluson are depcted n contnue. II. ILLUMIAIO ORMALIZAIO ECHIQUE In s stage, n order to boost e result of normalzaton, we frst truncated a specfed percentage of e lower and upper ends of an mage hstogram. In fact, several studes have shown at hstogram remappng n conjuncton w photometrc normalzaton technques results n better face recognton performance an usng photometrc normalzaton technques on er own. In e next step, Homomorphc flter as a renowned llumnaton reflectance was used. And en fltered face mage s consdered as nput of feature extracton module. A. Homomorphc Flter Homomorphc flterng (HOMO) s a well known normalzaton technque, whch mproves e www.mer.com 60 P a g e
www.mer.com Vol.2, Issue.1, pp-060-065 ISS: 2249-6645 pearance of an mage by contrast enhancement and gray-level range compresson. Consder an mage, f(x, y), whch can be stated as e product of e llumnaton (x, y), and e reflectance component r(x, y) as follows [3]: f(x, y) = (x, y). r(x, y) (1) hen nput mage s transformed n to e logarm doman n order to acheve frequency components of e llumnaton and reflectance separately: hen: Or: z(x, y) = ln f(x, y) (2) = ln (x, y) + ln r(x, y) { z(x, y) } = F { ln f(x, y)} = F { ln (x, y)} + F{ ln r(x, y)} Z(u, v) = F (u, v) + F r (u, v) here F (u, v) and F r (u, v), n equaton (2) are e Fourer transforms of e term defned. he Fourer transform of e product of e Z(u, v) and flter functon H(u, v) can be expressed as: S(u, v) = H(u, v). Z(u, v) (3) In e spatal doman: = H(u, v). F (u, v) + H(u, v). F r (u, v) s(x, y) = F -1 { S(u, v)} Fnally by lettng = F -1 {H(u, v). F (u, v) + H(u, v). F r (u, v)} (x, y) = F -1 { H(u, v). F (u, v) } (4) (x, y) = F -1 { H(u, v). F r (u, v) } e equaton becomes: s(x, y) = (x, y) + r(x, y) (5) g(x, y) = e s(x,y) g(x, y) = e (x,y) + e r(x,y) g(x, y) = 0 (x,y) + r 0 (x, y) here 0 and r 0 are e llumnaton and e reflectance components of e output mages. After z(x, y) s transformed nto e frequency doman, e hgh frequency components are emphaszed and e low-frequency components are reduced. As a fnal step e mage s transformed back nto e spatal doman by applyng e nverse Fourer transform and takng e exponental of e result. hs meod s based on a specal case of a class of systems known as Homomorphc system. he flter transform functon H(u, v) s known as e Homomorphc flter[4]. III. FUZZY LDA (FLDA) Fuzzy LDA, whch also was called Fuzzy Fsher Face meod, s consdered to solve bnary classfcaton problems. In conventonal LDA approach, every vector s supposed to have a crsp membershp. But s does not take nto account e resemblance of mages belongng to dfferent classes, whch occurs under varyng condtons. In FLDA, each vector s assgned e membershp grades of every class based upon e class label of ts k nearest neghbours. hs Fuzzy k-nearest neghbour s utlzed to evaluate e membershp grades of all e vectors [5]. he membershp degree to class for obtaned from followng equaton[5]: u n 0.51 0.49 k n 0.49 k In e above expresson e neghbors of e e j pattern s (6) n stands for e number of j data (pattern) at belong to class. As usual, u satsfes two obvous propertes: C u 1 0 j1 1 u, j belong oerwse same class (7) (8) herefore, e fuzzy membershp matrx U can be acheved w result of FK. (9) he results of e FK are used n e computatons of e statstcal propertes of e patterns. to e U [ u ] 1,2,..., c j 1,2,..., www.mer.com 61 P a g e
www.mer.com Vol.2, Issue.1, pp-060-065 ISS: 2249-6645 akng n to account e fuzzy membershp degree, e mean vector of each class s [6]: j1 j1 (10) hen, e membershp degree of each sample (contrbuton to each class) should be consdered and e correspondng fuzzy wn-class scatter matrx and fuzzy between-class scatter matrx can be redefned as follow [7]: FS FS b m c 1 x jw c 1 j1 u u x u ( x m )( x j j j m ) u ( m X )( m X ) (11) (12) here X, s e mean of all samples. So, all scatter matrces w fuzzy set eory are redefned and e contrbuton of each sample s ncorporated. d here n f ( ) ( n) f n f ( j) ( n) 2 (15) () f n s e n element of e feature vector whle e term f n s e standard devaton of e n element over e entre database and s used to normalze e ndvdual feature components. Fnally, a test mage j s assgned to mage n a database w e smallest correspondng dstance d. B. Feedforward eural etworks (FF) FF s sutable structure for nonlnear separable nput data. In FF model e neurons are organzed n e form of layers. he neurons n a layer get nput from e prevous layer and feed er output to e next layer. In s type of networks connectons to e neurons n e same or prevous layers are not permtted. Fg 1 shows e archtecture of e system for face classfcaton [9-10]. Our optmal fuzzy projecton F LDA follows e expresson: F LDA argmax w FSB FS (13) x 1 x 2 o 1 It s dffcult to drectly calculate at because F LDA FS s often sngular [6]. For tackle s problem, PCA s used as a dmenson reducton step and us e fnal transformaton s gven by e followng matrx, FLDA (14) IV. CLASSIFICAIO A. earest eghbour Classfer After evaluatng feature vectors by FLDA, test mages are projected on feature space and e dstances to e tranng mages are computed usng nearest neghbour algorm for e purpose of classfcaton as follows [8]: () ( j) For two mages and j, let f and f representng e correspondng feature vectors, e dstance d between e two patterns n e feature space s defned as: PCA x n Fg.1. Archtecture of FK for classfcaton In s experment e number of nodes n hdden layer s set to 15. A large neural network for all people n e database was mplemented. After calculatng e features, e feature projecton vectors are calculated for e faces n e database. hese feature projecton vectors are used as nputs to tran e neural network. Fg 2 llustrates e schematc dagram for e tranng phase. C. Support Vector Machne (SVM) SVM s a bnary classfcaton meod at ntends to fnd e optmal lnear/nonlnear decson surface based on e concept of structural rsk mnmzaton. he decson surface s a weghted representaton of e elements of tranng set. he elements on e o 2 o n www.mer.com 62 P a g e
www.mer.com Vol.2, Issue.1, pp-060-065 ISS: 2249-6645 decson surface are defned by a set of support vectors whch characterzes e boundary between two (or more) classes [11]. he problem of mult-class s solved by combnng multple two class SVMs. e select e one-versus-e-rest approach at constructs SVMs whch e tran k model chooses e k class as e postve examples and e remanng k 1 classes as e negatve examples. Comparson w one-versus-one, t sgnfcantly needs less tranng tme. At last, ndexed SVM classfer s learned rough quadratc programmng n order to fnd e class s boundares w maxmum margns. hs technque helps to fnd e accurate relatons between nearest smlarty faces. V. SIMULAIO AD RESULS A. ORL Face Database he ORL database conssts of 40 groups, each contanng ten 112 92 gray scale mages of a sngle subject [12]. Each subject s mages dffer n lghtng, facal expresson, detals (.e. glasses/no glasses) and even sldng. Some of e database s mages are llustrated n Fg 3. 1 mages k mages M mages he ORL database conssts of 40 groups, each contanng ten 112 92 gray scale mages of a sngle subject. Each subject s mages dffer n lghtng, facal expresson, detals (.e. glasses/no glasses) and even sldng. Some of e database s mages are llustrated n Fg 3. Fg 4 shows an orgnal mage from ORL database and ts hstogram respectvely. hs mage s chosen specfcally because t had led to msclassfcaton n many feature extracton meods. Beng taken under ambent lghtng n a neutral facal expresson and e wore glasses, e mages of s class lead to ncrease n error rate. In e next step,e Homomorphc flter was appled to e selected mage for normalzaton. he fltered mage and ts hstogram are dsplayed by Fg5. Intally we mplemented e Hstogram truncaton, n s step e lower and upper ends of an mage hstogram at must be truncated, were set to 20 percent and 60 percent respectvely. hen Homomorphc flter was used, e performance of s flter rely on ts parameters. e set e cut-off frequency of e flter to 0.5 and second order of e modfed Butterwor style flter s used. In e next step, we shortened half of upper ends of fnal hstogram. After preprocessng step, FLDA was appled n order to extract features. hen descrbed classfers are mplemented. Feature Extracton eural etwork 0 0 1 0 k Fg.2. ranng stage for eural etwork Fg.3. Samples of ORL face database www.mer.com 63 P a g e
www.mer.com Vol.2, Issue.1, pp-060-065 ISS: 2249-6645 able2 llustrates recognton rates of depcted meods w nearest neghbour classfer for two sets. able2. Comparson of recognton rates of dfferent meods for two sets Fveto-Fve Leave one -out PCA 88% 89.% LDA 90% 91% FLDA 94% 95% 2DPCA 93% 94.% Proposed 95% 96% Fg.4.Orgnal mage and e correspondng hstogram Fg.5.Fltered mage and e correspondng hstogram wo set of mages were created from e ORL face database; For e Fve-to-Fve dataset, fve random mages of each group were selected for tranng whle e oers were used for testng. For e Leave-One- Out set, 9 mages were used for tranng and e remanng mage was kept for valdaton. able 1 shows comparson among dfferent meods n Fve-to Fve set at smulaton results show SVM classfer w proposed meod has a better performance compared to oer classfers. able 1. Comparson of recognton rates of dfferent classfers based on varous feature extractors for ORL face database earst SVM FF eghbour PCA 88% 90% 89% LDA 90% 92% 91% FLDA 94% 95% 92% 2D-PCA 93% 94.5% 93% Proposed 95% 96.5% 94.5% B. Yale Face Database he Yale face database contans 165 mages of 15 ndvduals (each provdng 11 dfferent mages) under varous facal expressons and lghtng condtons [13]. Fg 6 shows sample mages of one. Smlar procedure was done for Yale face database. In s set 6 mages were used for tranng from each class and remanng mages were employed for test module. As far as recognton rate s concerned proposed meod outranks oers w 96.5 and 95.5 percent for SVM and two oer classfers respectvely. In addton e outcomes of Feedforward eural etworks and earest eghbour are close to each oer. he results were shown n able 3. Fg.6. Samples of Yale face database able3. Comparson of recognton rates of dfferent classfers based on varous feature extractors for Yale face database earest SVM FF eghbour PCA 89% 90% 90% LDA 91% 93% 92% FLDA 93.5% 94% 91% 2D-PCA 94% 95% 93.5% Proposed 95.5% 96% 95.5% www.mer.com 64 P a g e
www.mer.com Vol.2, Issue.1, pp-060-065 ISS: 2249-6645 VI. COCLUSIO In s paper, e Face Recognton problem was addressed by mproved meod based on modfed Homomorphc flter, whch s nsenstve to large varaton n llumnaton. Homomorphc flter s a celebrated normalzaton technque whch was gnored n face recognton. In contnue Fuzzy LDA (FLDA) was used at compared to oer feature extractors, t had a good ablty n dscrmnatng of classes. Fnally proposed meod n collaboraton w approprate classfers was used whch e result showed proposed meod w SVM classfer had a best performance. REFERECES [1] Y A. Georghades, P. Belhumeur, and D. Kregman,, From few to many: Illumnaton cone models for Face Recognton under varable lghtng and pose, IEEE ransactons on Pattern Analyss and Machne Intellgence, 23(6), 2001, 643-660. [2] Kw K C, Pedry, Face recognton usng a fuzzy fsher classfer, Pattern Recognton, 38(10), 2005, 1717-1732. [3] hammzharas,a.m.e, Performance Analyss Of Face Recognton By Combnng Multscale echnques And Homomorphc flter usng Fuzzy k-nearest neghbour classfer, Proc. IEEE Conf. on Communcaton Control and Computng echnologes (ICCCCI 10), 2010, 643-650. [4]. Ahmed Surobh, Md. Ruhul Amn, Employment of Modfed Homomorphc flters n Medcal Imagng, Internatonal Unversty Journal of scence and echnology n Daffodl, 1(1), 2006. [5] M.Keller, M.R.Gray, J.A.Gvern, A Fuzzy K earest eghbor Classfer Algorm, IEEE ransactons on Systems, Man and Cybernetcs, 15(4), 1985,580-585. [6]. Yang, Hu Yan, J. ang, J. Yang, Face Recognton usng Complete Fuzzy LDA, Proc. 19 Internatonal Conf. on Pattern Recognton, ICPR,2008, 1-4. [7] X Song,Y Zheng, A complete Fuzzy Dscrmnant Analyss Approach for Face Recognton, Appled Soft Computng, 2010,208-214. [8] Peter. Belhumeur, Joao P. Hespanha, Davd J. Kregman, Egenfaces vs. Fsherfaces: Recognton Usng Class Specfc Lnear Projecton, IEEE ransactons on Pattern Analyss and Machne Intellgence, 19(7), 1997. [9] A. Eleyan, H. Demrel, Face recognton system Based on PCA and Feedforward eural etworks, Proc. Computatonal Intellgence and Bonspred Systems, Barcelona, Span, 2005, 935-942. [10] Lawrence, S., Gles, C. L., so, A. C., Back, A. D., Face Recognton: A Convolutonal eural- etwork Approach, IEEE ransactons on eural etworks, 8(1), 1997. [11] J. Huang, V. Blanz and B. Hesele, Face recognton usng component-based SVM. Classfcaton and morphable models, Lecture otes n Computer Scence, 23(88), 2002, 334-341. [12]ORL, he Database of Faces, 2011. http://www.cl.cam.ac.uk/research/dtg/attarchve/f acedatase.html. [13]Yale, he Database of Faces, 2011. cvc.yale.edu/projects/yalefaces/yalefaces.html www.mer.com 65 P a g e