Faces Recognition with Image Feature Weights and Least Mean Square Learning Approach

Transcription

1 Faces Recognton wth Image Feature Weghts an Least Mean Square Learnng Approach We-L Fang, Yng-Kue Yang an Jung-Kue Pan Dept. of Electrcal Engneerng, Natonal Tawan Un. of Sc. & Technology, Tape, Tawan Emal: Abstract - Most of DPCA-enhance approaches mprove face recognton rate whle at the expense of computaton loa. In ths paper, an approach s propose to greatly mprove face recognton rate wth slghtly ncrease computaton loa. In ths approach, the DPCA s apple aganst a face mage to extract mportant mage features for selecton. A weght s then assgne to each of selecte mage features accorng to the feature s mportance to face recognton. The least mean square (LMS) algorthm s further apple to optmze the feature weghts base on the recognton error rate urng learnng process n orer to mprove face recognton performance. The experments have been conucte aganst ORL face mage atabase to make performance comparsons among several better-known approaches, an the expermental results have emonstrate that the propose approach not only has excellent face recognton rate of 99% but also requres only slghtly hgher computaton loa than DPCA, makng the approach more practcal to real face recognton applcatons.. Keywors: face recognton, feature extracton, prncple component analyss, least mean square, weght assgnment, steepest ecent algorthm. 1 Introucton Face recognton n mage processng has been sgnfcantly mportant because t can be apple n human lfe effcacously. Research areas nclue bulng/store access control, suspect entfcaton, securty an survellance [1]- [11]. Seceral algorthms have been propose n face recognton. The best ones shoul be those that try not only to reuce computaton cost but also to ncrease recognton rate [13][14]. Base on ths vewpont, prncpal component analyss (PCA) [15] has become a popular feature extracton algorthm n recent ecaes. After PCA was propose, Yang et al. [13] propose the so-calle two-mensonal prncpal component (DPCA) algorthm amng for better feature extracton of face mages. The DPCA has acheve the goal of ncreasng recognton rate an reucng computaton cost smultaneously [13]. Because DPCA has such goo performance, varous face recognton algorthms base on DPCA ha been propose an enhance. For nstance, the approach of Two-rectonal two-mensonal PCA ((D) PCA) propose by Zhang et al. [17] s to process a face mage from transverse an longtunal axs respectvely an then perform the recognton by analyzng ther shortest menson. Low computaton cost s the avantage of ths approach. Unfortunately, ts mprovement on recognton rate s not ubqutous n relatvely large scale of tranng samples [16]. Sanguansat et al. [18] propose the approach of Twomensonal prncpal component combne two-mensonal Lnear scrmnant analyss (DPCA&DLDA) [18] to face recognton applcatons. Although ths approach solves the small sample sze problem, ts computaton cost s hgh ue to the composton of DPCA an DLDA. Meng et al. [19] propose the combnaton of DPCA wth self-efne volume measure to perform feature extracton by DPCA frst an then conuct classfcaton by computng the stances of matrx volumes. Ths approach s more sutable to process applcatons wth hgh mensonal ata. Wang et al. [0] propose probablstc two-mensonal prncpal component analyss that combnes DPCA wth Gaussan strbuton concept to mtgate the nose nfluence n face mage recognton. Km et al. [1] propose fuson metho base on brectonal DPCA that reuces mensons of both row an column vectors before performng face recognton proceure. It oes ncrease recognton rate, but at the expense of hgh computaton cost []. Aforesa face recognton algorthms all have pros an cons. The algorthm DPCA s especally esgne for face mage ata, so the recognton performance s better than usng tratonal PCA. In ths paper, an approach s propose hopng to acheve the goal of ncreasng the recognton rate whle not at expense of computaton cost n face mage recognton. Ths approach ncorporates weghts n projecte feature vectors of DPCA an uses least mean square (LMS) algorthm to optmze the weghts base on the recognton error rate urng learnng process n orer to acheve better face recognton performance.

2 The least mean square-two mensonal prncpal component analyss.1 Two-mensonal prncpal component analyss (DPCA) The DPCA approach by Yang et al. [13] n 004 s propose partcularly for two mensonal mage ata. Suppose there s an mage ata set Z={A 1, A,, A N } wth N mages, an the menson of every mage s n n. The covarance matrx of the mage ata set s compute by Eq. (1) an the average value of the ata set s compute by Eq. (). N 1 T R = ( A A )( A A ) (1) N = 1 A N 1 N = 1 = where A s an mage n the ata set, R s covarance matrx, an A s ata average. After egen-ecomposton s performe for covarance matrx, k egenvectors corresponng to the k bggest egenvalues are selecte. These egenvectors are the projecton vectors of the orgnal mage ata set an the features of the mage can therefore be extracte from those projecton vectors as shown n Eq. (3). Y = A X =1,,,k (3) where Y are projecte feature vectors, X means egenvectors. Suppose there are k bggest egenvalues beng selecte, then a feature vector set B=[Y 1,Y,,Y k ] n escenng orer of egenvalues can be obtane an these projecte feature vectors are the resultant prncpal components of an orgnal mage ata A by DPCA. Because DPCA processes a -mensonal face mage rectly, t can get better result of feature extracton. On the contrary, the conventonal PCA nees to transform an mage nto one-mensonal ata an therefore loses some feature nformaton. Consequently, the recognton rate by DPCA s better than conventonal PCA for -mensonal face mages.. Least mean square algorthm (LMS) Least mean square (LMS) s an aaptve flter algorthm n sgnal process [3], an t s apple n many engneerng fels. Its nput sgnals u(n) are compute by transversal aaptve flter to result n the output y(n). The esre sgnal s (n) an e(n) s the fference between actual output y(n) an esre output (n). After tranng by teraton process, e(n) becomes smaller an smaller meanng the aaptve flter s closer to the eal state. The man essence of LMS s to make the error rate e(n) as smaller value as possble. Hence, the cost functon s efne as the expecte value of squarng error rate, as shown n Eq. (4). Jn ( ) = Ee [ ( n)] (4) A () In Eq. (4), the square operaton s neee to avo the problem cause by fferent sgn characterstcs because the error rate coul be a ether postve or negatve value. The steepest ecent algorthm[3] s then performe aganst the cost functon to make the resultant error rate as small as possble. Ths operaton process s shown as Eq. (5). wˆ( n+ 1) = wˆ( n) +μu ( n) e( n) (5) Eq. (5) represents the process of ajustng weghts by teraton operaton. The symbol μ s step sze. The learnng process s repeate untl the error rate has reache a pre-set satsfactory value..3 The ntegraton of least mean square wth two-mensonal prncpal component analyss The feature extracton algorthm DPCA has goo performance n face recognton. Important features that are represente by projecte feature vectors are selecte urng the process of egen-ecomposton. One projecte feature vector represents one extracte feature. The projecte feature vector that correspons to the bggest egenvalue represents the most mportant feature; the one that correspons to secon bggest egenvalue represents the secon mportant feature; an so on. After egen-ecomposton, the projecte feature vectors are arrange n a row n the escenng orer of feature mportance. For DPCA an most of ts extensons, every projecte feature vector has equal weght. Ths s not a goo ea n terms of mprovng recognton performance snce the mportance of each projecte feature vector, meanng each feature, s fferent. Rather, the weght assgne to a projecte feature vector shoul be relate to the mportance of the feature to that a projecte feature vector correspons. That s, the projecte feature vector corresponng to the bggest egenvalue shoul have hghest weght urng the process of face recognton. Although methos have been propose to assgn fferent weghts to projecte feature vectors, most of them ece these weghts base on tral-an-error process whch s not only tme-consumng but neffcent. In ths paper, an approach s propose by ntegratng least mean square wth two-mensonal prncpal component analyss n orer to effcently obtan proper weght for each of selecte features hopng to mprove face recognton performance. The propose approach uses LMS to ynamcally ajust the weghts of projecte feature vectors assocate wth mage features. Weghts are ajuste base on the feeback of error rate calculate by each teraton. Fg. 1 shows the propose system structure base on the concept of an aaptve flter. In Fg. 1, u(n) s the projecte feature vectors generate by DPCA, an s multple by weght matrx to get the output y(n) through the transversal aaptve flter. The error rate e(n) s then calculate by nearest neghbor rule (NNR) an then further use by LMS nse the weght-control mechansm to ynamcally ajust the weghts of projecte feature vectors. The weght matrx s ntally set

3 as w ˆ ( n ) N m that has menson N m an value 1 n all matrx elements, where n means n-th teraton startng from ntal value 1. The N means ata amount an m s the menson of every ata. 10 fferent mages makng totally 400 face mages n the atabase. The mages were taken wth a tolerance of some tltng an rotaton of the face for up to 0 egrees [13][4]. In ORL atabase, all mages are grayscale wth menson of The pxel value range s 0~55. Among the 10 fferent mages of each nvual face, 5 face mages are selecte as tranng ata an the rest of 5 face mages are use as testng ata, makng totally 00 mages for tranng ata an 00 mages for testng ata. Fg shows the error rate values urng the frst 300 LMS teratons respectvely n the conucte experment. In Fg., the lowest error rate takes place at aroun 5 th LMS teraton. It can also be observe n Fg that the error rate s stablze at certan value after aroun 135 th LMS teraton, whch means the feature weghts have been learne to be the most approprate values. Fg 1: The system structure To smplfy the computaton, the error rate of face recognton system s calculate by the nearest neghbor rule that s base on Euclean stance shown n Eq. (6). = V P (6) The symbols V an P are vectors, an s Euclean stance. The operaton of Eq. (6) computes the norm of V-P. Suppose V=(v 1, v, v 3 ) an P=(p 1, p, p 3 ), the norm of the two vectors s obtane as Eq. (7). V P = ( v (7) 1 p1) + ( v p) + ( v3 p3) After calculatng the error rate by NNR, t s use by LMS teraton to ajust the feature weghts as shown n Eq. (5). A threshol value s set for the error rate to avo nfnte teraton. The face recognton rate s calculate as below. Suppose there are N face mages, represente as B 1, B,, B N, an each mage s represente by a projecte feature vector, such as [Y 1 1, Y 1,, Y 1 ] for B 1 wth m menson. The classes of these N mages are alreay known. Suppose a classunknown mage T k =[T 1, T,, T ] s to be recognze aganst these N face mages. The computaton process s shown n Eq. (7). ( BT, ) = B T (8) k = 1 where s the calculate stance by NNR between the two mages. The class of T k s classfe as the class of B k f these two have mnmum stance n Eq. (8). The face recognton rate can therefore be obtane after classfyng all N face mages. 3 Experments an analyss The ORL atabase [4] s a well-known face mage atabase an s use n ths paper for experments. There are 40 nvual faces n ORL atabase. Each nvual face has k k Fg. : Error rate urng LMS teratons (300 tmes) To see the mprovement on face recognton urng the LMS learnng proceure, the face recognton rate s performe after each LMS teraton. The expermental result s shown n Fg. 3. The face recognton rate reaches the best value of 99% startng from aroun 5 th LMS teraton n Fg. 3, whch conces wth Fg. that shows the lowest error rate takes places at 5 th LMS teraton. Snce then, the face recognton rate mantans at value 99% as the feature weghts have been ajuste to approprate values by the LMS learnng proceure at ths moment. Fg. 3: Face recognton rate urng LMS teratons

4 In Table 1, the expermental result of the propose LMS-DPCA n ths paper s compare aganst some other methos whch are enhancements from DPCA. The experments are conucte aganst ORL atabase for all the methos ncate n Table 1. The table shows that the propose approach has the best face recognton rate of 99% whle the computaton loa s only normal. Although metho 1 [17] has slghtly lower computaton loa than the propose approach, ts face recognton rate s much lower. The goo recognton performance of the propose approach comes from the goo ajustment to the mage feature weghts by LMS learnng proceure. The normal computaton loa s contrbute by the LMS smple algorthm, makng the whole computaton cost s only slghtly more than pure DPCA Table 1: Performance comparson between the propose approach an other methos Metho number Metho Recognto n rate Computaton cost 1 (D) PCA [17] 90.5% normal DPCA+Fuson metho base on brectonal [1] 9.5% normal 3 DPCA+DLDA 93.5% normal [18] 4 DPCA+Kernel 94.58% hgh [5] 5 OP-SRC[6] 95.00% hgh 6 RCDPCA[7] 96.65% Very hgh 7 DPCA+Feature fuson approach [8] 98.1% very hgh 8 MMDA[9] 98.31% Very hgh 9 Propose 99% normal approach 4 Conclusons The DPCA s a goo approach for -mensonal face mage recognton. Although enhance approaches base on DPCA have been propose, most are ether too tmeconsumng or no much mprovement to face recognton. The DPCA treats all selecte mage features same weght n terms of recognton. However, the mportance or nfluence to face recognton from each mage feature s fferent from one another, meanng each mage feature shoul be assgne an approprate weght accorng to ts nfluence to face recognton. Therefore, ths paper proposes an approach that ntegrates DPCA wth LMS learnng proceure. The DPCA s apple aganst a face mage to extract mportant mage features for selecton. Then the LMS learnng proceure s apple to the tranng samples to assgn the most approprate weght to each of selecte mage features hopng to ncrease the face recognton rate. Because the goal s to make the face recognton error rate as small as possble, the mage feature weghts are ajuste base on the feeback of face recognton error amount by LMS teratons. Due to the smple algorthm, the atonal computaton cost requre to run LMS learnng proceure s only to a small extent of slghtly more than pure DPCA. The experments conucte n ths paper has shown that the propose approach not only has excellent face recognton rate of 99% but also requres only slghtly hgher computaton loa than DPCA, makng the approach more practcal to real face recognton applcatons. 5 References [1] Q. Lu, X. Tang, H. Lu an S. Ma, Face recognton usng kernel scatter-fference-base scrmnant analyss, IEEE Trans. Neural Netw., vol. 17, no. 4, pp , Jul [] W. Zheng, X. Zhou, C. Zou an L. Zhao, Facal expresson recognton usng kernel canoncal correlaton analyss (KCCA), IEEE Trans. Neural Netw., vol. 17, no. 1, pp , Jan [3] X. Tan, S. Chen, Z. H. Zhou an F. Zhang, Recognzng partally occlue, expresson varant faces from sngle tranng mage per person wth SOM an soft k-nn ensemble, IEEE Trans. Neural Netw., vol. 16, no. 4, pp , Jul [4] P. Meln, O. Menoza an O. Castllo, Face recognton wth an mprove nterval type- fuzzy logc Sugeno ntegral an moular neural networks, IEEE Trans. Syst., Man, Cybern. A, Syst., Humans, vol. 41, no. 5, pp , Sep [5] N. Suha, A. R. Mohan an P. K. Meher, A selfconfgurable systolc archtecture for face recognton system base on prncpal component neural network, IEEE Trans. Crcuts Syst. Veo Technol., vol. 1, no. 8, pp , Aug [6] W. W. W. Zou an P. C. Yuen, Very low resoluton face recognton problem, IEEE Trans. Image Process., vol. 1, no. 1, pp , Jan. 01. [7] N. S. Vu an A. Capler, Enhance patterns of orente ege magntues for face recognton an mage matchng, IEEE Trans. Image Process., vol. 1, no. 3, pp , Mar. 01. [8] J. Y. Cho, Y. M. Ro an K. N. Platanots, Color local texture features for color face recognton, IEEE Trans. Image Process., vol. 1, no. 3, pp , Mar. 01. [9] H. Chen, Y. Y. Tang, B. Fang an J. Wen, Illumnaton nvarant face recognton usng FABEMD ecomposton wth etal measure weght, IJPRAI, vol. 5, pp , 011. [10] H. Yu, J. J. Zhang an X. Yang, Tensor-base feature representaton wth applcaton to multmoal face recognton, IJPRAI, vol. 5, pp , 011. [11] G. Chacha, A. N. Marana, T. Ruf an A. C. Ernst,

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