On Modeling Variations For Face Authentication

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1 On Modelng Varatons For Face Authentcaton Xaomng Lu Tsuhan Chen B.V.K. Vjaya Kumar Department of Electrcal and Computer Engneerng, Carnege Mellon Unversty Abstract In ths paper, we present a scheme for face authentcaton by usng applyng prncpal component analyss (PCA) to model varatons. To deal wth varatons, such as facal expressons and regstraton errors, wth whch tradtonal appearancebased methods do not perform well, we propose the egenflow approach. In ths approach, the optcal flow and the optcal flow resdue between a test mage and a well-regstered mage n the tranng set are frst computed. The optcal flow s then ftted to a model that s pre-traned by applyng PCA to optcal flows resultng from facal expressons and regstraton errors for the subjects. The egenflow resdue, optmally combned wth the optcal flow resdue usng lnear dscrmnant analyss (LDA), determnes the authentcty of the test mage. Expermental results show that the proposed scheme outperforms the tradtonal methods n the presence of facal varatons. 1. Introducton For decades human face recognton has drawn consderable nterest and attenton from many researchers [1]. A general statement of ths problem can be formulated as follows. Gven stll or vdeo mages of a scene, dentfy one or more persons n the scene usng a stored database of faces [2]. Face authentcaton [3] s a research feld related to face recognton. The dfference between face recognton and face authentcaton s that, n the former, the system has to determne the dentty of the subject, whle n the latter, the system only needs to verfy the clamed dentty of the user. Usually smlar algorthms can be used for both recognton and authentcaton. A comprehensve survey of human and machne recognton technques can be found n [2][5][6]. There are manly two knds of face recognton systems: one s based on feature matchng; the other s based on template matchng. In the latter, applyng PCA n the pxel doman (also known as egenface approach [7]) plays a fundamental role. Several papers propose revsed egenface approaches to dealng wth face mage varablty [8]. Some researchers have noted that applyng PCA to mage pxels drectly s very senstve to shft, rotaton, scale, expresson or lghtng varatons of face [4], whch s because the egenface method s bascally an appearance based approach. In ths paper, we propose a general approach to performng face authentcaton by modelng dfferent knd varatons, such as facal expresson varatons and shft, rotaton, scale type of regstraton errors. Optcal flow s used to capture face appearance moton when there s varaton n facal expresson. For example, the optcal flow between the neutral and happy expresson of one subject tells us how ths subject smles. After we apply PCA to optcal flows, we obtan an egenspace spanned by ts egenvectors, that we call egenflow n ths paper. Ths egenspace models possble expresson varatons. Optcal flow and egenflow can also be used to model other varatons, such as regstraton error, shft, scale, and rotaton. As a general framework, we can also model the llumnant varatons by computng the features for mages under dfferent lghtng condtons, and performng PCA on these features. Optcal flow methods are generally used for moton analyss. Some researchers have used optcal flow n the analyss of human expresson for the purpose of expresson recognton [9][1]. Also Kruznga and Petkov [11] proposed to utlze optcal flow n person dentfcaton. However, they only consdered the optcal flow resdue as the measurement of classfcaton, whle we propose to make use of the egenflow resdue, whch appears to exhbt more classfcaton ablty than the former. Essentally optcal flow can provde us the vsual moton nformaton about face mages. Moghaddam et. al also proposed modelng vsual moton n [12]. They determne pxel dfference between mages, and utlze the Bayesan approach to modelng the pxel dfference for all the subjects. In our case, frst the optcal flow s used to obtan moton feld between mages and then PCA s appled to model facal moton for ndvdual subject. Ths paper s organzed as follows. In Secton 2, we ntroduce the ndvdual egenspace. In Secton 3, we present the ndvdual egenflow based approach n detal. Experments based on dfferent sets are presented n Secton 3. Fnally n Secton 4, we provde the conclusons. 2. The ndvdual egenspace Turk and Pentland [7], ntroduced the egenface approach to performng face recognton. Whle constructng an egenspace, face mages from all tranng subjects are used. We call the resultng egenspace a unversal egenspace. We can see that ths egenspace represents not only the personal dentty, the nter- varaton between dfferent tranng subjects, but also the ntra- varaton of each subject, such as due to expresson changes, llumnaton varablty, age, etc. However, what we need for the authentcaton s robustness to

2 expresson and llumnaton varatons wthn a sngle subject, not robust recognton for all the subjects. Ths observaton suggests one potental metrc for face authentcaton. The resdue of a test vector to that vector s ndvdual egenspace, (.e., the squared norm of the dfference between a test vector and ts representaton n the egenspace) s a good measure for authentcaton. Throughout the rest of ths paper, we wll focus for smplcty on one specfed subject. So for a tranng set of K subjects and M mages for each subject, the same approach can be repeated K tmes. In the ndvdual egenspace approach, one egenspace s constructed for each tranng subject. As the followng equaton ndcates, the average face wll be dfferent for each subject. 1 1 M g = j M f (1) j= Now each face dffers from the average by the vector sj = f j g.alsothe A matrx s dfferent for each subject,.e., A = [ s,, s,1,..., s, M 1 ]. Here we denote the egenvector of each space as u, n, and each face s projected to ts own egenspace as follows: T = u, f g f f belongs to Subject (2) wn n ( ) So far we have suggested an ndvdual egenspace for each subject, and each tranng face (wth ts clamed dentty) has correspondng projected egencoeffcents, w n, n ts own egenspace. From these projected vectors, the face mage can be reconstructed by: Q 1 = s ˆ wnu, n (3) n= Where Q s the number of egenvectors n the egenspace. Snce ths egenspace s only an dealzed representaton for one subject, t cannot represent all manfestatons of that subject s face perfectly,.e. there wll be a resdue (.e., dfference or squared error) between the test mage and ts reconstructed verson. The resdue s defned as the squared dstance between the mean-adjusted test nput mage s = f g and reconstructed mage ŝ,.e., 2 e = s ŝ (4) In the next secton, we wll call e the egenflow resdue snce t characterzes how well the egenspace can model the unknown sample. 2. Indvdual Egenflow Based Face Authentcaton The tradtonal egenface approach s not as robust as needed to expresson varatons and to shft, rotaton, and scale changes. Because PCA s an appearance-based approach, ts authentcaton performance wll degrade quckly when the appearance of a subject s face changes sgnfcantly, whch occurs n the presence of expresson changes and regstraton errors. In ths secton, we propose a new method based on optcal flow to deal wth such varatons n face mages. 2.1 Optcal flow for face mages Essentally optcal flow [15] s an approxmaton of the velocty feld. It characterzes approxmately the moton of each pxel between two mages. If two face mages, whch show dfferent expressons of the same subject, are fed nto the optcal flow algorthm, the resultant moton feld wll emphasze the regons of facal features, such as eyes and mouth. Ths s llustrated n Fgure 1. The left half of the fgure shows two face mages from the same subject, but wth dfferent expressons. The resultng optcal flow s shown below these fgures. Also by usng the frst mage and the optcal flow, we can construct a predcted mage that s close to the second mage. The thrd fgure n the top row s the dfference between predcton obtaned va the optcal flow and the second mage. We call t optcal flow resdue mage. For the correct subject, ths resdue mage would have low energy because the moton of most pxels can be modeled well by the optcal flow. The second set shows the same except that the two nput mages are from two dfferent subjects. Obvously, the optcal flow looks more rregular when the two mages are from dfferent subjects. Also the resdue mage of moton predcton has more error. These two clues can help dscrmnatng these two cases, whch s the task of authentcaton. The same dea can be appled to mages wth regstraton errors. Because the tradtonal egenface approach s unacceptably senstve to regstraton errors, even small shfts n nput mages can make the system performance degrade sgnfcantly. However, face mages are usually dffcult to regster precsely, especally n a lve authentcaton system. So here we want to use the optcal flow to buld a system that s tolerance to dfferent knds of regstraton errors. The second mage n the left column of Fgure 2 s an up-shfted verson of the frst mage. The optcal flow shown below captures most of ts moton around facal features, and also the resdue mage has small ntensty. The rght column shows mages of dfferent subjects leadng to an optcal flow that appears to be random, and the resdue mage has larger ntensty. 2.2 The tranng of egenflow Snce the optcal flow provdes a useful pattern for classfyng personal dentty, we propose to use PCA to model ths pattern. Gven two face mages, there are some recommended preprocessng steps pror to the optcal flow determnaton. Snce some regons of face mages wll always contan background, t s better to crop the mage before the optcal flow computaton.

3 Fgure 1 Applcaton of optcal flow to cases of dfferent expressons Fgure 2 Applcaton of optcal flow to two cases of dfferent regstraton. Fgure 3 Fve expresson mages used for tranng egenflow.

4 Fgure 4 The frst three egenflows traned from expresson mages of one subject. Some promnent movement of facal features, such as mouth corner, eyebrow, scale, nasolabal furrow, can be seen from them. Followng the tradtonal PCA approach, optcal flow vectors are regarded as sample vectors for tranng. Suppose that n the tranng dataset, there are a few mages wth dfferent expressons for each subject, such as fve mages shown n Fgure 3. Usng these mages, twenty optcal flow mages (correspondng to twenty pars) can be obtaned. The three prncpal egenflow mages of twenty optcal flow mages are shown n Fgure 4. Obvously large moton can be observed n the regon of facal features, such as mouth corner, eyebrow, nasolabal furrow. So all the expresson varatons occurrng n a sngle subject can be represented by a space spanned by these egenflows. In contrast, the optcal flow between ths subject and other subjects cannot be represented well by ths space. Smlarly egenflows can be used to model the optcal flow caused by mage regstraton errors. In the lve applcaton of face authentcaton, face regon needs to be regstered from a whole frame. Usually t s done va a crop operaton based on the locaton of two eyes. In our approach, we synthesze mages wth regstraton errors from one well-regstered mage. Agan the egenflows can ndcate the actual moton pattern appearng n the tranng set. In the testng stage, both the optcal flow resdue and the egenflow resdue wll be used for authentcaton, where the optcal flow resdue s computed n determnng optcal flow between the testng mage and tranng mages, and the egenflow resdue s obtaned n projectng the optcal flow nto the egenflow space. Eventually lnear dscrmnant analyss [13] wll combne these two resdues and obtan the fnal measurement for authentcaton. 3. Experment Results Experments and evaluatons are mportant parts of any face authentcaton system. In order to solate the effects of facal expresson varatons and regstraton errors, we assume that all the tranng and test mages are captured under the same lghtng condton. Before dscussng the results, we wll present some detals about our algorthm. Gven any two tranng mages, we generate the optcal flow usng four steps. Frst the background regons below the cheek n the face mage are removed because the background seems to affect the optcal flow calculaton, and thus nterferes wth the authentcaton. Zero s flled nto the two trangle regons n the lower part of the face square. Next, we determne the optcal flow usng Lucas- Kanade algorthm[2]. Thrd the optcal flow s down sampled to be half ts orgnal sze n order to speed up the PCA tranng and to clean up the nosy moton vectors. Fnally wthn ths smaller-sze optcal flow, the background and four sde boundares are removed because usually the boundary does not result n accurate moton estmaton n the optcal flow algorthm. Now the down-sampled optcal flow mage can be scanned nto a vector, whose dmenson s much lower than the unsampled one. The frst data set has only expresson varatons. 13 subjects are ncluded n ths set. Each has 5 mages for tranng, and 7 mages for testng. The reason we use more test mages than tranng mages s that we want to get a smother ROC curve. Also, only a few mages may be avalable for tranng n a practcal setup. Each of the fve tranng mages represents dfferent expressons, such as neutral, happy, angry, sad, and surprse. All of these mages are well regstered by the locaton of the eyes. Here we mplement three algorthms: the ndvdual PCA approach on mage doman, the unversal PCA approach, and the ndvdual egenflow approach. From the result, we can see that for most part of the curve, our approach yelds better performance. Also the mprovement s sgnfcant compared to the unversal PCA approach.

5 Recever Operatng Characterstc: Expresson dataset Recever Operatng Characterstc: Regstraton error dataset Indvdual Egenflow Approach Indvdual PCA Approach Unversal PCA Approach Indvdual Egenflow Approach Indvdual PCA Approach Unversal PCA Approach FRR(%) FRR(%) FAR(%) FAR(%) Fgure 5 The experment results on the expresson dataset. Fgure 6 Experment results on the data set wth regstraton errors. The second data set has the regstraton varaton for each subject. Gven one well-regstered face mage, we synthesze 625 mages by croppng face regon based on 25 ponts around the eye locatons. These mages are used for tranng one subject. The same method s used to generate the 625 test mages except there s larger offset whle selectng the eye neghbors, whch means test mages have larger regstraton errors than tranng one. So all these syntheszed tranng mages can represent dfferent knds of regstraton errors. Based on ths set, the egenflow-based approach has shown much better performance than the PCA approach. The thrd data set has both expresson varatons and regstraton errors. Frst, for each one of the 13 subjects, 5 expresson mages are obtaned to be the reference mages. Then, for each reference mage, 624 mages can be syntheszed to nclude all knds of regstraton errors. Thus, 3125 mages are collected for each subject. We also generate 312 test mages for each subject usng the same approach, but there are two dfferences. One s that all the test mages have dfferent expressons compared to the reference mages. The other s that the testng mages have larger regstraton errors than the tranng one. Snce n ths experment, we have many more test mages than n the prevous two experments, the denomnator n 5. Conclusons computng FAR and FRR wll be much larger. That s why a much smoother ROC curve can be observed from Fgure 7. FRR(%) Recever Operatng Characterstc: Expresson varaton and regstraton error dataset Indvdual Egenflow Approach Indvdual PCA Approach Unversal PCA Approach FAR(%) Fgure 7 Experment results on the data set contanng both expresson varatons and regstraton errors. In ths paper, we present a scheme for face authentcaton by modelng varatons va applyng prncpal component analyss (PCA). To deal wth varatons, such as facal expressons and

6 regstraton errors, wth whch tradtonal appearance-based methods do not perform well, we propose the egenflow approach. In ths approach, the optcal flow and the optcal flow resdue between a test mage and a well-regstered mage n the tranng set are frst computed. The optcal flow s then ftted to a model that s pre-traned by applyng PCA to optcal flows resultng from facal expressons and regstraton errors for the subjects. The egenflow resdue, optmally combned wth the optcal flow resdue usng lnear dscrmnant analyss (LDA), determnes the authentcty of the test mage. Expermental results show that the proposed scheme outperforms the tradtonal methods n the presence of facal varatons. The advantage of ths proposed approach s ts tolerance to dfferent knds of varatons, such as expresson varatons and regstraton errors, because all these varatons have been modeled by PCA. As a general framework, our method can also been extended to model other varatons that appear n faces, such as llumnants, poses. References [1]. T. Kanade. Pcture processng system by computer complex and recognton of human faces. Department of Informaton Scence. Kyoto Unversty. [2]. R. Chellappa, C.L. Wlson, S. Srohey, Human and machne recognton of faces: a survey. Proceedngs of the IEEE, 83 (5) (1995) [3]. C.L. Kotropoulos, A. Tefas, I. Ptas, Frontal Face Authentcaton Usng Dscrmnatng Grds wth Morphologcal Feature Vectors. IEEE Transactons on Multmeda. 2 (1) (2) [4]. P.N. Belhumeur, J.P. Hespanha, D.J. Kregman, Eegnfaces vs. Fsherfaces: Recognton Usng Class Specfc Lnear Projecton. IEEE Transacton on Pattern Analyss and Machne Intellgence. 19 (7) (1997) [5]. R. Brunell, T. Poggo, Face Recognton: Features versus Templates. IEEE Transacton on Pattern Analyss and Machne Intellgence. 15 (1) (1993) [6]. T. Fromherz, P. Stuck, M. Bchsel, A Survey of Face Recognton, MML Techncal Report, No 97.1, Dept. of Computer Scence, Unversty of Zurch, Zurch, [7]. M. Turk, A. Pentland, Egenfaces for Recognton. Journal of Cogntve Neuroscence. 3 (1) (1991) [8]. A. Pentland, B. Moghaddam, T. Starner, Vew-Based and Modular Egenspaces for Face Recognton. Techncal report 245, MIT Meda Lab Vsmod, [9]. J.J. Len, A. Zlochower, J.F. Cohn, T. Kanade, Automated Facal Expresson Recognton. Proceedngs of the Thrd IEEE Internatonal Conference on Automatc Face and Gesture Recognton. Nara, Japan. Aprl, [1].Y. Yacoob, L.S. Davs, Recognzng Human Facal Expressons From Long Image Sequences Usng Optcal Flow. IEEE Transactons on Pattern Analyss and Machne Intellgence. 18 (6) (1996) [11].P. Kruznga, N. Petkov, Optcal flow appled to person dentfcaton. Proceedng of the 1994 EUROSIM Conference on Massvely Parallel Processng Applcatons and Development, Delft, The Netherlands, June 1994, Elsever, Amsterdam, [12].B. Moghaddam, T. Jebara, A. Pentland. Bayesan face Recognton. Pattern Recognton. 33 (2) [13].R.O. Duda, P.E. Hart, D.G. Stork, Pattern classfcaton, Second edton. John Wley & Sons. Inc., New York, 21. [14].H. Murase, B.V.K.V. Kumar, Effcent calculaton of prmary mages from a set of mages. IEEE Transacton on Pattern Analyss and Machne Intellgence. 4 (5) (1982) [15].C.L. Fennema, W.B. Thompson, Velocty determnaton n scenes contanng several movng objects. Computer Graphcs and Image Processng, 9 (1979) [16].K. Fukunaga, Statstcal Pattern Rcognton. Academc Press, New York, [17].W. Zhao, R. Chellappa, P.J. Phllps, Subspace Lnear Dscrmnant Analyss for Face Recognton. Technque Report. CS-TR-49. Unversty of Maryland at College Park. Aprl [18].A. Ortego, K. Ramchandran, Rate-dstorton methods for mage and vdeo compresson. IEEE Sgnal Processng Magazne. 15 (6) (1998) [19].K. Fukunaga, D. Kessell, Estmaton of Classfcaton Error. IEEE Transactons on Computers C-2. (1971) [2].B.D. Lucas, T. Kanade, An teratve mage regstraton technque wth an applcaton to stereo vson. Proc. DARPA IU Workshop, [21].P.J. Phllps, M. Hyeonjoon, S.A. Rzv, P.J. Rauss, The FERET evaluaton methodology for face-recognton algorthms. IEEE Transactons on Pattern Analyss and Machne Intellgence, 22 (1) (2)

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