Integrated Expression-Invariant Face Recognition with Constrained Optical Flow
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1 Integrated Expresson-Invarant Face Recognton wth Constraned Optcal Flow Chao-Kue Hseh, Shang-Hong La 2, and Yung-Chang Chen Department of Electrcal Engneerng, Natonal Tsng Hua Unversty, Tawan 2 Department of Computer Scence, Natonal Tsng Hua Unversty, Tawan d9395@oz.nthu.edu.tw, la@cs.nthu.edu.tw, ycchen@ee.nthu.edu.tw Abstract. Face recognton s one of the most ntensvely studed topcs n computer vson and pattern recognton. A constraned optcal flow algorthm, whch combnes the advantages of the unambguous correspondence of feature pont labelng and the flexble representaton of optcal flow computaton, has been proposed n our pervous work for face recognton from expressonal face mages. In ths paper, we propose an ntegrated face recognton system that s robust aganst facal expressons by combnng nformaton from the computed ntra-person optcal flow and the syntheszed face mage n a probablstc framework. Our expermental results show that the proposed system mproves the accuracy of face recognton from expressonal face mages. Keywords: Face recognton, expresson recognton, constraned optcal flow, expresson normalzaton. Introducton Face recognton has been studed for the past few decades. Even though the 2D face recognton methods have been actvely studed n the past, there are stll nherent dsadvantages and drawbacks. It was shown that the recognton rate can drop dramatcally when the head pose and llumnaton varatons are too large, or when there s expresson on the face mage. Pose, llumnaton, and expresson varatons are three essental ssues to be dealt wth n the research of face recognton. Some authors have proposed dfferent approaches to deal wth such expresson varatons. One way [] s to compute the optcal flow between the testng and tranng face mage. Another way [2] used a mask or a morphable model for the mage regstraton n a face recognton system. In our prevous work, we combned the advantages of the above two approaches: the unambguous correspondence of feature pont labelng and the flexble representaton of optcal flow computaton. A constraned optcal flow algorthm was proposed, whch can deal wth poston movements and ntensty changes at the same tme when handlng the correspondng feature ponts. We have then appled the algorthm not only to the applcaton of face recognton from expresson normalzaton [3], but also on the nter- and ntra-person T. Wada, F. Huang, and S. Ln (Eds.): PSIVT 29, LNCS 544, pp , 29. Sprnger-Verlag Berln Hedelberg 29
2 Integrated Expresson-Invarant Face Recognton wth Constraned Optcal Flow 73 optcal flow analyss [4], whch can be used for further face and expresson recognton. Both methods can mprove the accuracy of the face recognton from expressonal face mages, even though dfferent nformaton s utlzed n these two algorthms. In ths paper, we propose to explot two dfferent types of nformaton,.e. the computed optcal flow and the syntheszed mage, to mprove the accuracy of face recognton. Expermental valdaton s gven to show the mproved performance of the proposed face recognton system. The remanng of ths paper s organzed as follows. We brefly revew the constraned optcal flow computatonal technque and our prevous works on expresson normalzaton and expresson optcal flow analyss n secton 2 and 3, respectvely. The proposed face recognton system s presented n secton 4. Secton 5 gves some expermental results and secton 6 concludes ths paper. 2 Constraned Optcal Flow Computaton The computatonal algorthms of tradtonal optcal flow cannot guarantee that the computed optcal flow corresponds to the exact pxels n dfferent mages, snce the ntensty varatons due to expresson may mslead the computaton of optcal flow. Teng et al. [5] proposed to mnmze the followng dscrete energy functon to compute the optcal flow, whch used an adaptve smoothness adjustment scheme consdered both flow components (u and v ) and all the brghtness varaton multpler and offset factors (m and c ) Ix, u+ Iy, v+ It, + mi + c f ( u) = w D Ix, Iy, I λ α + α + β + β ( x, ux, y, uy, x, vx, y, vy, ) D ( x, mx, y, my, x, cx, y, cy, ) + μ γ + γ + δ + δ D Furthermore, t can be rewrtten n a matrx-vector form and effcently solved by the ncomplete Cholesky precondtoned conjugate gradent (ICPCG) algorthm [5]. In order to guarantee the computed optcal flow to be consstent to the moton vectors at these correspondng feature ponts, we modfy the unconstraned optmzaton problem n the orgnal formulaton of the optcal flow estmaton to a constraned optmzaton problem [3] gven as follows: T T ( u) = u Ku 2 u b+ c, (, ), (, ), (, ) mnmze f subject to u x y = u and v x y = v x y S where S s the set of feature ponts and (, ) u v s the specfed optcal flow vector at the th feature pont. We appled a modfed ICPCG procedure to solve ths constraned optmzaton problem and the detals are referred to [3]., 2 ()
3 74 C.-K. Hseh, S.-H. La, and Y.-C. Chen 3 Prevous Works In ths secton, we brefly revew expresson normalzaton [3] and nter- and ntraperson optcal flow analyss [4] n our prevous works. 3. Expresson Normalzaton The face recognton problem can be consdered as to determne the class c that mnmzes the dfference between the reference mage R c and the syntheszed neutral mage from the testng facal expresson mage T by usng R c as the reference. After the mage algnment and normalzaton of the nput testng mage T and reference mage R c, where c =,2,,C, and C s the total number of subjects n the face database, we can formulate the face recognton problem as follows: ( ( c) ) arg mn R Syn T; OF T; R c c To further mprove the computatonal effcency, we modfy the face recognton problem as follows: ( Rc ( Rc ) ) ( T ( T ) ) arg mn Syn ; OF ; Syn ; OF ; c where s a unversal neutral face mage. To be more specfc, nstead of transformng the nput mage to the neutral mage for each class, we now transform all mages to a unversal coordnate as. We defne the operaton, Syn( T; OF ( T; R c )), as the OF-Syn operator. The modfed system flow chart s shown n Fg.. Although there are C+ OF-Syn operators n total, the C OF-Syn operatons among them can be performed n advance, thus only one such operaton s needed n the testng or recognton phase. (2) (3) OF-Syn OF-Syn - 2 OF-Syn M OF-Syn Preprocessng Testng after nput - Comparator - Result Fg.. The proposed expresson-nvarant face recognton flow chart accordng to Eq. (3) 3.2 Expresson Optcal Flow Analyss The tradtonal expressve optcal flow s computed from a neutral face mage of person to an expresson mage EX,k wth expresson k of the same subject. However,
4 Integrated Expresson-Invarant Face Recognton wth Constraned Optcal Flow 75 the computed optcal flows are generally not n the same coordnate, snce the geometry of neutral faces s dfferent for dfferent persons. Some research only consdered moton vectors at certan feature ponts to overcome ths problem, but only lmted nformaton about facal movement s used n ths case. EX 2, EX, OF ntra,2_ OF all,2_ OF all,_ OF ntra,_ 2 OF nter, OF nter,2 Fg. 2. Illustraton of decomposng nput optcal flow (OF all ) to nter-person (OF nter ) and ntraperson (OF ntra ) parts We proposed a dfferent soluton for optcal flow normalzaton, as shown n Fg. 3. Instead of computng the ntra-person optcal flow OF ntra,_k drectly from the neutral face to an expressve face mage for each person, we start from a global neutral face to obtan the nter-person optcal flow OF nter, = OF( ; ) and overall optcal OF all,_k = OF( ; EX,k ). The ntra-person optcal flow can then be generated by pxelwse dfferencng as follows: OF ntra,_k = OF all,_k - OF nter,. (4) There are two advantages of dong t ths way: () all expressve face mages of every subject have the same number of moton vectors; (2) all optcal flows are computed on the same geometry of. After obtanng the normalzed optcal flows from dfferent expressons, we consder t as a problem of subspace modelng. In other words, we can extract K optcal flow bases OB ntra,k to descrbe ntra-person optcal flows. Moreover, when there s an nput mage, we can recognze the face by determnng the person, whose nter-person optcal flow OF nter, makes the ntra-person optcal flow be best spanned by the traned optcal flow bases. Ths can be formulated as the followng optmzaton problem: arg mn ( ) nput nter, k ntra, k b, kk, =,..., K k= K OF OF b OB (5) Furthermore, the spannng coeffcents b k of each bass OB ntra,k may be used for expresson recognton. A negatve coeffcent does not make sense n physcal
5 76 C.-K. Hseh, S.-H. La, and Y.-C. Chen expresson moton, thus we proposed a modfed egenvector algorthm to enforce non-negatve projecton coeffcents. 4 Proposed Face Recognton System There are two types of nformaton generated by the constraned optcal flow algorthm: the optcal flow and the syntheszed neural face mage by mage warpng wth the computed optcal flow. As dscussed n the prevous secton, the two face recognton methods based on the expresson normalzed mages and the computed optcal flow are descrbed n secton 3. and 3.2, respectvely. In the frst method, the optcal flows for the nput expresson-varant mages are dfferent from dfferent subjects n terms of geometry and dmensonalty, thus the optcal flow nformaton was not used for comparson n the frst method. On the other hand, n the second method, we compute the optcal flow n the opposte drecton,.e. from the global neutral face to an nput expresson varant face, to preserve the same geometry for the computed optcal flow, but t cannot be used drectly to synthesze the correspondng neutral mage for comparson. Only partal nformaton was exploted n each of these two methods. In ths paper, we ntend to ntegrate these two methods nto the proposed expresson-nvarant face recognton system to fully explot the nformaton of the optcal flow and the syntheszed neutral mage for face recognton. To do ths, we formulate the problem as follows: N, E ( N I ) max P, E, =,2,..., N where I s the nput mage, N s a neutral face mage n tranng data set, and E denotes the expresson optcal flow vector between I and N. Based on the posteror probablty, equaton (6) can be rewrtten as N, E ( ) ( ) ( ) max P N P E P I N, E. Furthermore, the occurrence probablty of each canddate s assumed equally probable,.e. P(N ) s a constant for all. The formulaton can be smplfed as N, E ( ) ( E) max P E P I N,. There are two parts n equaton (8),.e. the probablty of the expresson movement P(E), and the probablty of the nput mage under the condton of the subject N wth the expresson E. As dscussed before, a sngle type of optcal flow cannot keep the unformty of dmensonalty and geometry n both crcumstances. Thus. we defne P(E) and P(I N, E) separately. To further defne P(E) wth preservaton of dentcal geometry and dmensonalty for each N, we use the same strategy n method 2,.e. the ntra-person optcal flow. Wth equaton (4), the moton nformaton E n P(E) s defned as ( xy, ) = ( xy, ) ( @ u v w, (9) (6) (7) (8)
6 Integrated Expresson-Invarant Face Recognton wth Constraned Optcal Flow 77 where v(x, y) s the overall optcal flow from global neutral face to nput mage I, w(x, y) s the nter-person optcal flow from to the guessed neutral face N, and u(x, y) s the ntra-person optcal flow from N to I. Moreover, and the denotes the optcal flow represented wth the geometry of, even though the ntra-person optcal flow s defned as the pxel-wsed movement from N to I. The probablty of P(I N, E) s then defned as the smlarty between nput mage I and the syntheszed mage from neutral face N and the computed optcal flow movement,.e. P I Syn N, exp ( I N E) ( ; u ) N. 2 σ Snce the optcal flow used for syntheszng neutral face N to a certan expresson must be represented wth the same geometry of N, the ntra-person optcal flow u ( xy, ) n equaton (9) s not approprate n ths crcumstance. An ntra-person optcal flow under the geometry of N s needed n equaton (). The MAP optmzaton problem s now rewrtten as ( ; u@ N ) 2 I Syn N max P( E) P( I N, E) = max P( ) exp, 2,, E E σ N N Thus two components are needed to compute n the above formulaton: one s the ntra-person optcal flow at the geometry of (Intra@ ), and the other s the ntra-person optcal flow at the geometry of (Intra@N ). We can frst compute the optcal flow Intra@ drectly and warp t to obtan Intra@ (Fg., defned as procedure ), or oppostely, we can compute Intra@ frst and then warp to Intra@ (Fg., defned as procedure 2). In the frst flow, we compute Intra@ as the dagram shown n Fg. 3,.e. (2) = OF ; Input OF ;. ( ) ( ) The optcal flow Intra@ can be smply obtaned by computng OF( ; Input). After collectng one type of ntra-person optcal flow, we can further obtan the other one by nonlnear warpng wth the nter-person optcal flow as shown n Fg. 4. Take Intra@ to Intra@ for example. The movement of each pxel has been obtaned n Intra@ calculaton. The correspondng poston n of each pxel n can be determned easly through nter-person optcal flow Inter@. In most cases, the correspondng poston s not on nteger grd. We can estmate the moton of each non-nteger pxel by blnear nterpolaton. The overall system flowcharts of procedure and 2 are depcted n Fg. 5 and Fg. 6, respectvely. In procedure, snce the OF block of OF( ; ) can be pre-computed n the tranng process, only one optcal flow calculaton, the Input@ s needed n the testng process. However, the optcal flow used for synthess, whch requres more precson, s obtaned through a long computatonal procedure. Ths may damage the () ()
7 78 C.-K. Hseh, S.-H. La, and Y.-C. Chen ( ; Input ) OF ( ; ) OF Inter Intr a@ N Fg. 3. Intra-person optcal flow, Intra@ calculaton n procedure ( ; ) OF Input Intra@ ( ) OF ; Fg. 4. Dagram of ntra-person optcal flow mappng from one person to another qualty of the syntheszed result f any non-neglgble naccuracy s nvolved durng the flow. In procedure 2, on the other hand, even though the operaton OF( ; ) can be pre-computed n the tranng process as well, the OF block OF( ; Input) s requred to compute for each guess. There are totally C tmes of OF computatons n the testng procedure, whch are drectly followed by mage synthess block. The objectve functon can be computed after the two types of ntra-person optcal flow are calculated. We consdered the probablty of ntra-person optcal flow as a mxture of Gaussan probablty dstrbuton wth centers correspondng to the samples n the tranng optcal flow dataset, that s, P u f y y y y y = = 2 T T T ) = ( ) exp ( ) ( ) Σ, (3) where y s the ntra-person optcal flow n the tranng data, s the ndex and T s the number of tranng sample, and y denotes u. As for the smlarty between nput mage and the syntheszed mages, we drectly calculate the recprocal of the
8 Integrated Expresson-Invarant Face Recognton wth Constraned Optcal Flow 79 of_ntra@ C Fg. 5. System flowchart of procedure C C Fg. 6. System flowchart of procedure 2 of_ntra@ C of_ntra@ C Fg. 7. Modfed system flowchart of procedure 2 average of pxel-wse dfference between them. Accordng to the orgnal defnton, snce the two values are under dfferent scales, one wll domnate the result of fnal probablty. Instead of comparng the fnal result after combnng the two values as
9 7 C.-K. Hseh, S.-H. La, and Y.-C. Chen shown n Fg. 6, we modfy the flow to Fg. 7. We compare and score the two values separately frst, and then combne the scores for fnal decson as S Fnal = r S P(E) + S P(I N, E), (4) where r s a weght determned emprcally. S P(E) and S P(I N, E) stand for the score of P(E) and P(I N, E) respectvely. 5 Expermental Results Our experments were performed on the Bnghamton Unversty 3D Face Expresson (BU-3DFE) Database [6]. The BU-3DFE database contans the face mages and 3D face models of subjects (56 females and 44 males) each wth a neutral face and 6 dfferent expressons (angry, dsgust, fear, happy, sad, and surprsed) at dfferent levels (from level (weakest) to 4 (strongest)). Note that only the 2D face mages were used n our experments. Among them, 34 subjects are randomly selected for ntra-person optcal flow tranng, and the others are used as the testng set. 5. Pre-processng We manually labeled 2 feature ponts, ncludng 3 ponts for each eyebrow and 4 ponts for each eye, one at the nose tp and the other 6 around the mouth regon. Wth the labeled ponts, the dstance between the outer corners of both eyes s used as the reference to normalze face mages. 5.2 Face Recognton wth Proposed System As descrbed n the prevous secton, we follow the modfed flowchart shown n Fg. 8. We apply a mask (Fg. 8(b)) defned from the global neutral face (Fg. 8(a)) to extract the regon of nterest. Moreover, the regon nsde the mouth s dscarded, as llustrated n Fg. 8(e). Both the optcal flow and the grayscales of the syntheszed mage wthn the mask wll be used n face recognton process. Some expermental mages are shown n Fg. 8. For an nput mage (Fg. 8(d)), we frst poston the correspondng mask (Fg. 8(e)) to obtan the masked mage (Fg. 8(f)). After that, for each canddate n the database (Fg. 8(g) and 8(j)), the ntra-person optcal flow,.e. ntra@, s computed and used for vrtual mage synthess (Fg. 8(h) and Fg. 8(k)). The masked mages (Fg. 8() and 8(l)) can fnally be appled for smlarty comparson. Expresson-nvarant face recognton results are lsted n Table -3. Accordng to the results, the average face recognton rates based on the syntheszed mage or the ntra-person optcal flow ndvdually are 85.86% and 82.39%, respectvely. In addton to usng the syntheszed mage and optcal flow nformaton separately, we also carry out the face recognton experment by usng the proposed ntegrated soluton,.e. based on Equ. (4). In ths experment, to ponts are gven to the top ten canddates n each comparson, and we equally weght the nformaton of syntheszed mage and ntra-person optcal flow,.e. r =. The recognton rate s mproved to 9.28% as shown n Table 3.
10 Integrated Expresson-Invarant Face Recognton wth Constraned Optcal Flow 7 (a) (b) (c) (d) (e) (f) (g) (h) () (j) (k) (l) Fg. 8. Illustraton of expermental mages: (a) global neutral face, (b) mask mage, (c) masked mage of (a), (d) nput mage, (e) warped mask mage, (f) masked nput mage, (g) guessed subject, (h) syntheszed face from (g) to (d), () masked syntheszed mage (g) usng mask mage (e), (j) guessed subject 2, (k) syntheszed face from (g) to (d), and (l) masked syntheszed mage (k) usng mask mage (e) Table. Recognton result usng the syntheszed face mages only Expresson Level (%) Level 2(%) Level 3(%) Level 4(%) Average AN DI FE HA SA SU % The mpact of dfferent weghtng s also dscussed n our experment. We try dfferent weghtngs rangng from.5 to 2 and the face recognton accuraces are depcted n Fg. 9. We can see that the proposed system can acheve the best accuracy at 93% when r =.7, whch means the syntheszed mage s of hgher sgnfcance.
11 72 C.-K. Hseh, S.-H. La, and Y.-C. Chen Table 2. Recognton result usng ntra-person optcal flow only Expresson Level (%) Level 2(%) Level 3(%) Level 4(%) Average AN DI FE HA SA SU % Table 3. Recognton result usng the ntegrated nformaton, ncludng the syntheszed mages and ntra-person optcal flow Expresson Level (%) Level 2(%) Level 3(%) Level 4(%) Average AN DI FE HA SA SU % 94% 92% 9% 88% 86% Fg. 9. Recognton result on the test data wth dfferent weghtng parameters n eq.(4) 6 Concluson In ths paper, we proposed an ntegrated expresson-nvarant face recognton system based on the constraned optcal flow. In the prevous works on optcal flow based face recognton, ether the syntheszed face mage or the ntra-person flow s used ndvdually for face and expresson recognton. In ths work, we proposed to ntegrate the nformaton of syntheszed mages and the ntra-person optcal flow dstrbuton probablty to mprove the face recognton accuracy. As the expermental results shows, the proposed system mproves the accuracy of face and expresson recognton on expressonal face mages. However, the proposed ntegrated system s more computatonally costly compared to the prevous works, snce the optcal flow computaton, ntra-person optcal flow mappng and mage synthess are needed for all canddates n the database. Ths s the man research topc n our future study.
12 Integrated Expresson-Invarant Face Recognton wth Constraned Optcal Flow 73 References. L, X., Mor, G., Zhang, H.: Expresson-nvarant face recognton wth expresson classfcaton. In: Proc. 3rd Canadan Conf. on Computer and Robot Vson (June 26) 2. Martnez, A.M.: Recognzng expresson varant faces from a sngle sample mage per class. In: Proc. IEEE Conf. Computer Vson Pattern Recognton (June 23) 3. Hseh, C.-K., La, S.-H., Chen, Y.-C.: Expresson-nvarant face recognton wth accurate optcal flow. In: Ip, H.H.-S., Au, O.C., Leung, H., Sun, M.-T., Ma, W.-Y., Hu, S.-M. (eds.) PCM 27. LNCS, vol. 48, pp Sprnger, Hedelberg (27) 4. Hseh, C.-K., La, S.-H., Chen, Y.-C.: Expressonal face mage analyss wth constraned optcal flow. In: Proc. of ICME, Hannover, Germany, June (28) 5. Teng, C.-H., La, S.-H., Chen, Y.-S., Hsu, W.-H.: Accurate optcal flow computaton under non-unform brghtness varatons. In: Computer Vson and Image Understandng, vol. 97, pp (25) 6. Yn, L., We, X., Sun, Y., Wang, J., Rosato, M.J.: A 3D facal expresson database for facal behavor research. In: Proc. Intern. Conf. on Automatc Face and Gesture Recognton, pp (Aprl 26)
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