Appearance-based Statistical Methods for Face Recognition

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1 47th Internatonal Symposum ELMAR-2005, June 2005, Zadar, Croata Appearance-based Statstcal Methods for Face Recognton Kresmr Delac 1, Mslav Grgc 2, Panos Latss 3 1 Croatan elecom, Savsa 32, Zagreb, CROAIA 2 Unversty of Zagreb, Faculty of EE & Comp, Unsa 3/XII, Zagreb, CROAIA 3 Informaton and Bomedcal Engneerng Centre, Cty Unversty London, UNIED KINGDOM E-mal: delac@eee.org Abstract - Dfferent statstcal methods for face recognton have been proposed n recent years. hey mostly dffer n the type of projecton and dstance measure used. he am of ths paper s to gve an overvew of most popular statstcal subspace methods for face recognton tas. heoretcal aspects of three algorthms wll be consdered and some reported performance evaluatons wll be gven. Keywords - Face Recognton, PCA, ICA, LDA, Subspace Analyss 1. INRODUCION Face recognton has ganed much attenton n recent years and has become one of the most successful applcatons of mage analyss and understandng. Face recognton conferences are emergng and sophstcated commercal systems have been developed that acheve rather hgh recognton rates. A general statement of the problem can be formulated as follows [1]: Gven stll or vdeo mages of a scene, dentfy or verfy one or more persons n the scene usng a stored dataase of faces. hs area of research s mportant not only because of the applcatons n humancomputer nteracton, bometrcs and securty, but also because t s a typcal, pattern recognton problem that, f successfully solved, could help solve other pattern classfcaton problems. he frst approach used for recognzng faces (and the most ntutve one) was correlaton, but all such methods were computatonally expensve so t was only natural to pursue dmensonalty reducton schemes. In ths paper, three appearance-based statstcal methods, namely Prncpal Component Analyss (PCA), Independent Component Analyss (ICA) and Lnear Dscrmnant Analyss (LDA), are descrbed. PCA [2], [3], [4] s a subspace projecton technque wdely used for face recognton. It fnds a set of representatve projecton vectors such that the projected samples retan most nformaton about orgnal samples. he most representatve vectors are the egenvectors correspondng to the largest egenvalues of the covarance matrx. Whle PCA deals wth varance (second-order statstcs), ICA [5] captures both second and hgher-order statstcs and projects the nput data onto the bass vectors that are as statstcally ndependent as possble. We can state that ICA s a generalzaton of PCA. LDA [6], [7], unle PCA or ICA, uses the class nformaton and fnds a set of vectors that maxmzes Fsher Dscrmnant Crteron. It smultaneously maxmzes the between-class scatter whle mnmzng the wthn-class scatter n the projectve feature vector space. Whle PCA and ICA can be called unsupervsed learnng technques, LDA s supervsed learnng technque because t needs class nformaton for each mage n the tranng process. When face recognton was at ts begnnng each research group collected ther own database of mages (e.g. Harvard, USC etc). Later, there emerged a need for a unform benchmar database and thus FERE database was collected at NIS (Natonal Insttute of Standards and echnology) [8] and became the most used face database for testng race recognton algorthms. he mages were collected between 1993 and he proposed gallery set for frontal face recognton conssts of mages of 1,196 ndvduals and probe mages are dvded nto four sets, namely fb, fc, dupi and dupii set (for detals please refer to [8]) However, many authors agree that FERE database favors one sort of algorthms so there are other databases that are comparable to FERE and are often used for testng today (Yale [9], AR [10], XM2VS [11], CMU PIE [12]). hey are collected for specfc purposes and so the AR database contans occlusons due to eye glasses and scarf and the CMU PIE database s collected wth well-constraned pose, llumnaton and expresson. he Yale database contans 160 frontal face mages coverng sxteen ndvduals taen under ten dfferent condtons (dfferent llumnaton and expresson). he XM2VS database s especally desgned for mult-modal bometrcs, ncludng audo and vdeo cues and s not avalable free of charge. 151

2 47th Internatonal Symposum ELMAR-2005, June 2005, Zadar, Croata he rest of ths paper s organzed as follows: n Secton II the dea of face space n comparson to mage space s gven, Secton III deals wth lnear subspace analyss descrbng three most popular methods n that area, n Secton IV performance comparson of descrbed methods (as reported by other research groups) s gven. 2. FACE SPACE Generally, a two dmensonal mage (x,y) of sze m-by-n pxels can be vewed as a vector (or a pont) n hgh dmensonal space. he easest way to create a vector from an array s to concatenate ts columns, thus gettng a vector X = [x 1...x N ], where N = mn. Each pxel of the mage then corresponds to a coordnate n N-dmensonal space. We wll refer to ths space as mage space. Such a space has huge dmensonalty ( N ) and recognton there would be computatonally neffcent. However, f an mage of an object s a pont n mage space, a collecton of M mages of the same sort of an object represents a set of ponts n the same subspace of the orgnal mage space. hese ponts may be consdered as samples of probablty dstrbuton. heoretcally, all possble mages of one partcular object defne a lower-dmensonal (possbly dsconnected) manfold, embedded wthn the hgh-dmensonal mage space. For face recognton purposes we refer to ths as face space. Its ntrnsc dmensonalty s determned by the number of degrees of freedom wthn face space. Appearance-based object recognton (.e. subspace analyss) deals wth the followng questons [2]: what s the relatonshp between ponts n mage space that correspond to all mages of a partcular object (face)? Is t possble to effcently characterze ths subset of all possble mages? Can ths subset be learned from a set of tranng mages? What s the "shape" of ths subset? Bascally, the goal of subspace analyss s to determne the ntrnsc dmensonalty and to extract the prncpal modes (bass functons) of the prncpal manfold. By dong ths n a subspace, compresson s acheved (computatonal effcency), data samples are drawn from a normal dstrbuton (meanng that axes of large varance probably correspond to data whle axes of small varance are probably nose) and, because data wll be mean centered, Eucldan dstance n subspace s nversely proportonal to correlaton between source mages. 3. LINEAR (SUBSPACE) ANALYSIS In the followng sectons three classcal lnear appearance-based classfers (PCA, ICA and LDA) wll be descrbed. Each of these has ts own set of bass functons whch are derved based on dfferent statstcal vewponts. After dervng bass vectors, a face mage s projected onto them and the projecton coeffcents are used as the feature representaton of each face mage. he matchng score between the test mage and each tranng mage s calculated between ther coeffcents vectors where the largest value represents the recognzed object. he necessary assumpton for all these classfers s that the prncpal manfold s lnear Prncpal Component Analyss (PCA) Prncpal Component Analyss (PCA) [3], [4] s a method to effcently represent a collecton of sample ponts, reducng the dmensonalty of the descrpton by projectng the ponts onto the prncpal axes, where an orthonormal set of axes ponts n the drecton of maxmum covarance n the data [2]. hese vectors best account for the dstrbuton of face mages wthn the entre mage space. PCA mnmzes the mean squared projecton error for a gven number of dmensons, and provdes a measure of mportance (n terms of total projecton error) for each axs. PCA s closely related to popular sgnal processng technque nown as the Karhunen-Loeve transform (KL). It can n fact be shown that under the assumpton that the data s zero-mean the formulatons of PCA and KL are dentcal [13]. Let us now descrbe the PCA algorthm as proposed n [3]. Frst we wll create the egenspace. hs step s the ntalzaton of the system. Let the tranng set of M face mages be 1, 2,..., M. he average face of the set s defned by: 1 M M n 1 n (1) Each face dffers from the average face by the vector = -, where = 1 to M. We shall rearrange these vectors n a matrx A = [ 1,..., M ] of dmenson NM, whch wll then be subject to PCA. Matrx A has zero-mean (mean value subtracted) vectors of each tranng face mage n ts columns. What we have just done s n fact a translaton of the orgn to the mean face (see Fg. 1. for the llustraton of the mean face). he next goal s to fnd a set of M 1 orthogonal vectors, e, whch best descrbes the dstrbuton of the nput data n a least-squares sense,.e., the Eucldan projecton error s mnmzed. We start by fndng the covaraton matrx: C A A (2) and then we use egenvector decomposton: 152

3 47th Internatonal Symposum ELMAR-2005, June 2005, Zadar, Croata C e e (3) where e and are egenvectors and egenvalues of covaraton matrx C, respectvely. We can do ths because C s real and symmetrc. s a dagonal matrx wth egenvalues on ts man dagonal. All egenvectors wth s greater than a threshold are retaned. A typcal threshold s Some authors also dscard the frst few egenvectors because they seem to capture manly the lghtng varatons (ths can be confrmed by loong at the frst two faces at the top row of Fg. 5.). However, t s rather questonable f ths last step actually mproves recognton rate. Fg. 1. Mean face calculated from 1,196 FERE gallery mages [8]. Once the egenvectors of C are found, they are sorted accordng to ther correspondng egenvalues. Larger egenvalue means that assocated egenvector captures more of the data varance. he effcency of the PCA approach comes from the fact that we can elmnate all but the best egenvectors (wth the hghest egenvalues). Snce PCA assumes the drectons wth the largest varances are the most prncpal (mportant), these egenvectors wll then span the M' dmensonal face space and that s the new feature space for recognton. Elmnatng egenvectors assocated wth small egenvalues actually elmnates the nose from the mage. here are at least three proposed ways to elmnate egenvectors. Frst s the mentoned elmnaton of egenvalues wth smallest egenvalues. hs can be accomplshed by dscardng the last 60% of total number of egenvectors. he second way s to use the mnmum number of egenvectors to guarantee that energy E s greater than a threshold. A typcal threshold s 0.9 (90% of total energy). If we defne E as the energy of the th egenvector, t s the rato of the sum of all egenvalues up to and ncludng over the sum of all the egenvalues: j1 E j1 where s the total number of egenvectors (Fg. 2.). j j (4) he thrd varaton depends upon the stretchng dmenson. he stretch for the th egenvector s the rato of that egenvalue over the largest egenvalue ( 1 ): 1 s (5) Fg. 2. Energy captured by retanng the number of egenvectors wth the largest egenvalues, calculated from 1,196 FERE gallery mages [8]. It s clearly seen that retanng only 200 egenvectors (of total 1,196 vectors) captures more then 90% of the energy. Each egenvector has the same dmensonalty as a face mage and loos as a sort of a "ghost" face (f rearranged and vewed as a pcture), so we call them egenfaces (Fg. 5, top row). ransformng a pont to a new space s a lnear transformaton so egenvectors are merely lnear combnatons of the tranng mages. he last step s to calculate the average face mage for each ndvdual (f there s more than one nstance of that ndvdual) and to project ths mage nto the face space as the ndvdual's class prototype. Ideally, two mages of the same person should project to the same pont n egenspace. Any dfference between the ponts s unwanted varaton. wo mages of dfferent subjects should project to ponts that are as far apart as possble. hs s the man dea behnd the recognton n subspaces. After creatng the egenspace we can proceed to recognton usng egenfaces. Gven a new mage of an ndvdual, the pxels are concatenated the same way as the tranng mages were, the mean mage s subtracted and the result s projected nto the face space: e ( ) (6) for = 1,...,M'. hese calculated values of together form a vector = [ M' ] that descrbes the contrbuton of each egenface n 153

4 47th Internatonal Symposum ELMAR-2005, June 2005, Zadar, Croata representng the nput face mage. In fact, ths s the projecton of an unnown face nto the face space. s then used to establsh whch of the pre-defned face classes best descrbes the new face. he smplest way to determne whch face class provdes the best descrpton of the nput face mage s to fnd the face class that mnmzes the Eucldan dstance: 2 (7) where s a vector descrbng the th face class. A face s classfed as belongng to a certan class when the mnmum (.e. the maxmum matchng score) s below some certan threshold. Besdes Eucldan dstance other smlarty measures or metrcs can be used, such as L1 norm (also called the Cty Bloc Dstance): d( x, y) x y x y, (8) 1 where x and y are any two vectors, or Mahalanobs dstance: 1 d( x, y) x y (9) 1 where s the th egenvalue correspondng to the th egenvector. here s one mportant property of PCA that needs to me mentoned. In order for PCA to wor one must assume that mean and varance are suffcent statstcs to entrely descrbe the data. he only zero-mean probablty dstrbuton that s fully descrbed by the varance s the Gaussan dstrbuton. In the next secton we shall descrbe an algorthm that wors even f the dstrbuton of data s not Gaussan. In practce though, qute a lot of the real world data are Gaussan dstrbuted (thans to the Central Lmt heorem) and PCA thus represents good means to roughly descrbe the data Independent Component Analyss (ICA) As seen n the prevous secton, PCA maes one mportant assumpton: the probablty dstrbuton of nput data must be Gaussan. When ths assumpton holds, covarance matrx contans all the nformaton of (zero-mean) varables. Bascally, PCA s only concerned wth second-order (varance) statstcs. he mentoned assumpton need not be true. If we presume that face mages have more general dstrbuton of probablty densty functons along each dmenson, the representaton problem has more degrees of freedom. In that case PCA would fal because the largest varances would not correspond to meanngful axes of PCA. Independent Component Analyss (ICA) [5] mnmzes both second-order and hgher-order dependences n the nput. It eeps the assumpton of lnearty but abandons all other that PCA uses. Although the ampltude spectrum s captured by second-order statstcs n PCA, there remans the phase spectrum that les n hgher-order statstcs. It s beleved that ths hgh-order statstcs (.e. the phase spectrum) contans the structural nformaton n mages that drves human percepton [5]. ICA attempts to fnd the bass along whch the data (when projected onto them) are statstcally ndependent. Mathematcally, f (x,y) are two ndependent components (bases), then: P x y Px Py, (10) where P[x] and P[y] are dstrbutons along x and y and P[x,y] s the jont dstrbuton. o put t smply, ICA s a way of fndng a lnear non-orthogonal coordnate system n any multvarate data. he drectons of axes of ths coordnate system are determned by both the second and hgher order statstcs of the orgnal data. he goal s to perform a lnear transform, whch maes the resultng varables as statstcally ndependent from each other as possble. It s a generalzaton of PCA (so PCA can be derved as a specal case of ICA). It s closely related to blnd source separaton (BSS) problem (Fg. 3.), where the goal s to decompose an observed sgnal nto a lnear combnaton of unnown ndependent sgnals [14]. Fg. 3. Blnd source separaton model. Let s be the vector of unnown source sgnals and x be the vector of observed mxtures. If A s the unnown mxng matrx, then the mxng model s wrtten as x = A s, where source sgnals are ndependent of each other and A s nvertble. ICA tres to fnd the mxng matrx A or the separatng matrx W such that U W x W A s (11) s the estmaton of the ndependent source sgnals [13]. here are many algorthms that perform ICA (InfoMax [13], JADE [15], FastICA [16]) but they all seem to converge to the same soluton for any gven data set. her man prncple s to teratvely optmze a smoothng functon whose global optma occurs when the output vectors U are ndependent. 154

5 47th Internatonal Symposum ELMAR-2005, June 2005, Zadar, Croata ICA can be used n face recognton n two dfferent ways [5]. It s standard practce to refer to them as Archtecture I and Archtecture II and ths nomenclature wll be adopted here as well. her basc dfferences can be seen n Fg. 4. Fg. 4. wo archtectures for performng ICA on faces [5]. (a) Performng source separaton on face mages produced ndependent component mages n the rows of U. (b) he gray values at pxel locaton are plotted for each mage. ICA Archtecture I fnds weght vectors n the drectons of statstcal dependences among the pxel locatons. (c) U has factoral code n ts columns. (d) ICA Archtecture II fnds weght vectors n the drectons of statstcal dependences among the face mages. Fg. 5. An llustratve example of dfferences between PCA, ICA Archtecture I, ICA Archtecture II and LDA. op row shows top eght PCA egenfaces. he second row shows localzed feature vectors for ICA Archtecture I. he thrd row shows eght nonlocalzed ICA feature vectors for ICA Archtecture II. Bottom row shows LDA representaton vectors (Fsherfaces). In Archtecture I [5], [14] the nput face mages X are consdered to be a lnear mxture of statstcally ndependent bass mages S combned by an unnown matrx A. Each row vector of X s a dfferent mage. ICA learns the weghts matrx W (Fg. 4. (a), (b)) such that the rows of U = W X are as statstcally ndependent as possble. In ths archtecture, the face mages are varables and pxel values are observatons. he source separaton s performed n face space and the source mages estmated by the rows of U are then used as bass mages to represent faces. he compressed representaton of a face mage s a vector of coeffcents used for lnearly combnng the ndependent bass mages to generate the mage (much le the PCA). Eght sample bass mages (rows of U, each one rearranged to orgnal mage format) derved ths way can be seen n the second row of Fg. 5. Notce the spatal localzaton, unle the PCA (top row) or Archtecture II (bottom row). he followng concluson can be drawn from ths example: each row of the mxng matrx W found by ICA represents a cluster of pxels that have smlar behavor across mages. We say that Archtecture I produces statstcally ndependent bass mages. Although the bass mages obtaned n Archtecture I are approxmately ndependent, the coeffcents that code each face are not necessarly ndependent. In Archtecture II [5], [14], the goal s to fnd statstcally ndependent coeffcents for nput data. he rows of data matrx X are now dfferent pxels and the columns are dfferent mages. he pxels are now varables and the mages are observatons (Fg. 4. (c), (d)). he source separaton s performed on pxels and each row of the learned weght matrx W s an mage. A (nverse matrx of W) contans the bass mages n ts columns. he statstcally ndependent source coeffcents n S that comprse the nput mages are recovered n the columns of U. Eght sample bass mages derved ths way can be seen n the thrd row of Fg. 5. In ths approach, each column of the mxng matrx W -1 found by ICA attempts to "get close to a cluster of mages that loo smlar across pxels". hs way, Archtecture II tends to generate bass mages that are even more face-le than the one derved by PCA. In fact, the bass found by ICA wll average only mages that loo ale. We say that Archtecture II produces statstcally ndependent coeffcents (t s sometmes called factoral code method as well). If tranng data for face recognton system would have 500 mages, ICA algorthm would try to separate 500 ndependent components, whch has hgh computatonal complexty, f not mpossble. hat s why t s common practce to perform ICA on the PCA coeffcents (rather then drectly on the nput mages) to reduce the dmensonalty [5]. Face recognton usng ICA can be summarzed by the followng: compare the test mage ndependent components wth the ndependent 155

6 47th Internatonal Symposum ELMAR-2005, June 2005, Zadar, Croata components of each tranng mage by usng a smlarty measure. he result (the recognzed face) s the tranng mage, whch s the closest to the test mage. Smlarty measure used n [5] was the nearest neghbor algorthm wth cosne smlarty. Let b denote the coeffcent vector. Coeffcent vectors n each test set were assgned the class label of the coeffcent vector n the tranng set that was most smlar as evaluated by the cosne of the angle between them: btest btran c (12) btest btran Comparson of reported performance wll be gven n Secton IV Lnear Dscrmnant Analyss (LDA) Both PCA and ICA do not use face class (category) nformaton. he tranng data s taen as a whole. Lnear Dscrmnant Analyss (LDA) fnds an effcent way to represent the face vector space by explotng the class nformaton [6], [7]. It dfferentates ndvdual faces but recognzes faces of the same ndvdual. LDA s often referred to as a Fsher's Lnear Dscrmnant (FLD). he mages n the tranng set are dvded nto the correspondng classes. LDA then fnds a set of vectors W LDA such that Fsher Dscrmnant Crteron s maxmzed: W SB W WLDA arg max (13) W W SW W where S B s the between-class scatter matrx and S W s the wthn-class scatter matrx, defned by: S S W B c 1 c N ( x ) ( x ) (14) 1 x X ( x ) ( x ) (15) where N s the number of tranng samples n class, c s the number of dstnct classes, s the mean vector of samples belongng to class and X represents the set of samples belongng to class. S W represents the scatter of features around the mean of each face class and S B represents the scatter of features around the overall mean for all face classes. hese vectors, the same as the PCA vectors, f rearranged are very face-le, so they are often called Fsherfaces (Fg. 5, bottom row). It s not dffcult to demonstrate that the soluton of the maxmzaton problem of (13) s the soluton of generalzed egensystem: S V S V (16) B W where V s the egenvector (fsherfaces) matrx and are the correspondng egenvalues of the wthnclass and between-class scatter matrces. hs system s easly solved f wrtten le ths: S 1 S V V (17) W B hs approach can produce some problems. Let us state some of them: 1) ths egensystem does not have orthogonal egenvectors because S 1 S s, n W B general, not symmetrc, 2) matrces S B S W are usually too bg, 3) S W could be sngular and then nonnvertble. All these problems can be bypassed by usng the PCA decomposton prevous to LDA [6]. However, the system n (13) wll then gve reduced egenvectors v, that need to be transformed nto true egenvectors V usng V FF =vv EF, where V EF and V FF are the PCA and fsher projecton matrces, respectvely [17]. After the egenvectors have been found (and only the ones correspondng to largest egenvalues have been ept), the orgnal mages are projected onto them by calculatng the dot product of the mage wth each of the egenvectors. Recognton s agan done by calculatng the dstance of the projected nput mage to all the tranng mages projectons, and the nearest neghbor s the match. 4. PERFORMANCE COMPARISON Let us now mae a comparson between these methods. In all three algorthms, classfcaton s performed by frst projectng the nput mages nto a subspace va a projecton (bass) matrx and then comparng the projecton coeffcent vector of the nput to all the pre-stored projecton vectors or labeled classes to determne the nput class label. Varous groups have reported varous performance results for these three algorthms over the years and no straghtforward concluson can be easly drawn. Zhao et al [18] report mproved performance for combned PCA and LDA approach over the pure LDA. In [6] four methods were compared (correlaton, a varant of lnear subspace method, PCA and PCA+LDA). he results showed that PCA+LDA performed sgnfcantly better than the other three methods. In [17] authors state that LDA wth cosne dstance measure outperformed all other tested systems, clamng that LDA dmensonalty reducton wors better than other projecton methods. However, Beverdge et al [19] state that on ther tests usng dfferent dstance measures the LDA algorthm performed unformly worse than PCA, but they do not gve any explanaton as to why t s so. Martnez et al [7] argued that for a small tranng set (two mages per class) PCA can outperform LDA, but ths s not the case for a larger tranng set. 156

7 47th Internatonal Symposum ELMAR-2005, June 2005, Zadar, Croata able 1. Results reported by dfferent research groups testng three descrbed algorthms Research group Database Algorthms tested Best result Zhao [18] FERE & USC LDA, PCA+LDA PCA+LDA Belhemur [6] Harvard & Yale Correlaton, Lnear Subspace, PCA, LDA LDA Navarrete [17] FERE & Yale PCA, LDA, EP LDA Beverdge [19] FERE PCA, PCA+LDA PCA Bartlett [5] FERE PCA, ICA ICA Bae [20] FERE PCA, ICA PCA Lu [21] FERE PCA, LDA, ICA ICA Comparng PCA and ICA, Bartlett et al [5] report that both ICA representatons (Archtecture I and II) outperformed the pure PCA, for recognzng mages of faces sampled on a dfferent day from the tranng mages. A classfer that combned two representatons outperformed PCA on all test sets. However, the wor done n [20] clearly contradcts the one n [5]. Lu et al [21] suggest that for enhanced performance ICA should be carred out n a compressed and whtened space where most of the representatve nformaton of the orgnal data s preserved and the small egenvalues dscarded. he dmensonalty of the compressed subspace s decded based on the egenvalue spectrum from the tranng data. he dscrmnant analyss shows that the ICA crteron, when carred out n the properly compressed and whtened space, performs better than the egenfaces and Fsherfaces methods, but ts performance deterorates sgnfcantly when augmented by an addtonal dscrmnant crtera such as the FLD. Many other authors clam that PCA (or some of ts modfcatons) by far outperforms both ICA and LDA. 5. CONCLUSION As seen n the prevous secton, no straghtforward concluson can be drawn on overall performance results of three descrbed algorthms. At best, we can state that each of these algorthms performs best for a specfc tas. However, we beleve that there are not enough ndependently conducted comparsons of these three algorthms, performed under the same ntal condtons (.e. the same preprocessng mage rotaton, croppng, enhancement). Furthermore, never are all possble mplementatons consdered (varous projecton methods combned wth varous dstance measures). Our further wor wll consst of mplementng the descrbed algorthms n Matlab and testng them usng as many as possble dfferent smlarty measures, to try to produce the best combnaton for a specfc tas. We expect to face some dffcultes n drectly comparng LDA to other two algorthms because of ts need for more than one mage of an ndvdual, so we wll have to thn of the methodology to overcome that ssue (followng the lead of [19] and [20] perhaps). Also, a far comparson technque should be desgned regardng the dmensonalty of recognton and ntermedate subspaces and algorthm performance. Perhaps the best way s to test couple of possble dmensonaltes and to report and compare only the best results for a specfc algorthm gven the same tas. ACKNOWLEDGMEN Portons of the research n ths paper use the Color FERE database of facal mages collected under the FERE program. REFERENCES [1] W. Zhao, R. Chellappa, J. Phllps, A. Rosenfeld, "Face Recognton n Stll and Vdeo Images: A Lterature Surrey", ACM Computng Surveys, Vol. 35, Dec. 2003, pp [2] M. ur, "A Random Wal through Egenspace", IEICE rans. Inf. & Syst., Vol. E84-D, No. 12, December 2001, pp [3] M. ur, A. Pentland, "Egenfaces for Recognton", Journal of Cogntve Neuroscence, Vol. 3, No. 1, 1991, pp [4] M. ur, A. Pentland, "Face Recognton usng Egenfaces", Proc. of the IEEE Conf. on Computer Vson and Pattern Recognton, June 1991, pp

8 47th Internatonal Symposum ELMAR-2005, June 2005, Zadar, Croata [5] M.S. Bartlett, J.R. Movellan,.J. Sejnows, "Face Recognton by Independent Component Analyss", IEEE rans. on Neural Networs, Vol. 13, No. 6, November 2002, pp [6] P. Belhumeur, J. Hespanha, D. Kregman, "Egenfaces vs. Fsherfaces: Recognton Usng Class Specfc Lnear Projecton", Proc. of the Fourth European Conference on Computer Vson, Vol. 1, Aprl 1996, Cambrdge, UK, pp [7] A. Martnez, A. Ka, "PCA versus LDA", IEEE rans. on Pattern Analyss and Machne Intellgence, Vol. 23, No. 2, February 2001, pp [8] P.J. Phllps, H. Moon, S.A. Rzv, P.J. Rauss, "he FERE Evaluaton Methodology for Face Recognton Algorthms", IEEE rans. on Pattern Analyss and Machne Intellgence, Vol. 22, No. 10, October 2000, pp [9] Yale Unversty Face Image Database, [10] AR Face Database, [11] XM2VS Face Database, [12] CMU PIE Face Database, [13] J.F. Cardoso, "Infomax and Maxmum Lelhood for Source Separaton", IEEE Letters on Sgnal Processng, Vol. 4, No. 4, Aprl 1997, pp [14] B. Draper, K. Bae, M.S. Bartlett, J.R. Beverdge, "Recognzng Faces wth PCA and ICA", Computer Vson and Image Understandng (Specal Issue on Face Recognton), Vol. 91, Issues 1-2, July-August 2003, pp [15] M. Zbulevsy and B. A. Pearlmutter, "Blnd Separaton of Sources wth Sparse Representatons n a Gven Sgnal Dctonary", Internatonal Worshop on Independent Component Analyss and Blnd Sgnal Separaton, June 2000, Helsn, Fnland [16] A. Hyvarnen, "he Fxed-pont Algorthm and Maxmum Lelhood Estmaton for Independent Component Analyss", Neural Processng Letters, Vol. 10, Issue 1, August 1999, pp. 1-5 [17] P. Navarrete, J. Ruz-del-Solar, "Analyss and Comparson of Egenspace-Based Face Recognton Approaches", Internatonal Journal of Pattern Recognton and Artfcal Intellgence, Vol. 16, No. 7, November 2002, pp [18] W. Zhao, R. Chellappa, A. Krshnaswamy, "Dscrmnant Analyss of Prncpal Components for Face Recognton", Proc. of the 3rd IEEE Internatonal Conference on Automatc Face and Gesture Recognton, Aprl 1998, Nara, Japan, pp [19] J.R. Beverdge, K. She, B. Draper, G.H. Gvens, "A Nonparametrc Statstcal Comparson of Prncpal Component and Lnear Dscrmnant Subspaces for Face Recognton", Proc. of the IEEE Conference on Computer Vson and Pattern Recognton, December 2001, Kau, HI, USA, pp [20] K. Bae, B. Draper, J.R. Beverdge, K. She, "PCA vs. ICA: A Comparson on the FERE Data Set", Proc. of the Fourth Internatonal Conference on Computer Vson, Pattern Recognton and Image Processng, Durham, NC, USA, 8-14 March 2002, pp [21] C. Lu, H. Wechsler, "Comparatve Assessment of Independent Component Analyss (ICA) for Face Recognton", Second Internatonal Conference on Audo- and Vdeobased Bometrc Person Authentcaton, Washngton D.C., USA, March

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