Histogram-Enhanced Principal Component Analysis for Face Recognition

Transcription

1 Hstogram-Enhanced Prncpal Component Analyss for Face ecognton Ana-ara Sevcenco and Wu-Sheng Lu Dept. of Electrcal and Computer Engneerng Unversty of Vctora Abstract In ths paper we present an enhanced prncpal component analyss (PCA) algorthm for mprovng the rate of face recognton. he proposed method modfes the mage hstogram to provde a Gaussan shaped tonal dstrbuton n the face mages, such that spatally the entre set of face mages presents smlar facal gray-level ntenstes whle the face content n the frequency doman remans mostly unaltered. Computatonally nexpensve, the algorthm proves to yeld superor results when appled as a preprocessng step for face recognton. Expermental results are presented to demonstrate effectveness of the proposed technque.. Introducton Over the last decade, face recognton has been an actve area of research n computer vson and one of the most successful applcatons of mage analyss and understandng. Snce the begnnng of ts expanson n early s [], consderable research endeavors have contnued for enhancng the face recognton process. Startng from basc algorthms such as prncpal component analyss (PCA) [], ndependent component analyss (ICA) [], lnear dscrmnant analyss (LDA) [3], and contnung wth hgher-complexty methods such as Laplacanfaces [4], recent approaches [5]-[9] strve to mprove the recognton process by combnng nown basc technques, ncludng new pre-processng steps and modfyng the exstng steps. he wor of partcular nterest and relevant to the method proposed below s manly found n [] and [5] where PCA-based algorthms are nvolved n face recognton. otvated by the recent results of Lao et al. [5], n whch a flterng preprocessng step s appled to the conventonal statstcs-based methods such as PCA and ICA to mprove the face recognton rate, n ths paper we propose a hstogram-based preprocessng step whch can be utlzed n a smlar framewor, at a very low computatonal cost. Expermental results are presented to demonstrate the effectveness of the proposed technque.. PCA and Whtenng PCA: A evew PCA s among the most popular technques used for mage dmensonalty reducton []. An mpressve number of face recognton algorthms employs ths egendecomposton method. One of them s the whtenedface approach [5] whch combnes a whtenng technque wth PCA/ICA n order to ncrease the rate of face recognton... PCA he PCA [] s an egenface-based approach to face recognton that sees to capture the varaton n a collecton of face mages and uses ths nformaton to encode and compare mages of ndvdual faces. he egenfaces are the egenvectors of the covarance matrx of the set of face mages, where each mage s treated as a pont n a hgh dmensonal space. Egenfaces extract relevant facal nformaton, whch may or may not be drectly related to human ntuton of face features such as eyes, nose, and lps, by capturng statstcal varaton between face mages. herefore, egenfaces may be consdered as a set of features whch characterze the global varaton among face mages. Other advantages of usng egenfaces are an effcent mage representaton usng a small number of parameters and reduced computatonal and dmensonal complexty. Gven a data set Ð, also called tranng set, of face mages of K ndvduals, the egenface-based algorthm proposed n [] starts by transformng each N N mage n Ð nto a vector Γ of dmenson N, by concatenatng the mage rows. he K ndvduals are called members, each one havng L = / K mages n Ð. Next, the average face Ψ s computed as = Ψ= Γ, and subtracted from each vector Γ : Φ = Γ Ψ. he data matrx s then formed as A = [ Φ... Φ ] and the covarance matrx s constructed as /9/$5. 9 IEEE PACI 9

2 C = Φ Φ = = AA. Instead of drectly computng the egenvectors u and egenvalues λ of matrx C of sze of N by N, whch usually s an ntractable tas for typcal mage szes, [] proposed an ndrect approach by fndng the egenvectors v and egenvalues λ of a reduced-sze matrx L = AA, and expressng the egenvectors of matrx C as.5 u = λ Av for =,..., () he egenvectors u of covarance matrx C, called egenfaces, are used to represent the face mages from Ð, so as to examne a new mage as whether or not t s a face mage and, f t s, whether t s a face of a member or a stranger (non-member). Let U be the matrx composed of p most sgnfcant egenvectors (.e. egenfaces) that are assocated wth p largest egenvalues of C, and let Γ represent a new mage to be examned. Frst, the dstance d between the new mage and the face space s computed as d = Φ Φ () f where Φ=Γ Ψ, Φ = U Ω = UU Φ s the orthogonal f projecton of mage Φ onto face space U and Ω= U Φ s the pattern vector of Φ. Comparng the dstance d wth a chosen threshold δ, the new mage Γ can be classfed as a face or non-face mage. Furthermore, f Γ turns out to be a face mage, t can be classfed as a member or non-member face. And f t s a member then the ndvdual member s dentfed. hese are acheved by evaluatng d = Ω Ω for =,..., K and comparng dmn = mn d (3) wth a prescrbed threshold δ, where the class vector L = ( ) () Ω L s calculated as Ω = Ω, =,..., K, and Ω s the pattern vector of the th mage of the th member... Whtenng PCA (WPCA) As demonstrated by Lao et al. [5], a pre-processng step of whtenng and low-pass flterng, that flattens the power spectrum of face mages and controls the nose at hgh frequences, can mprove recognton rate. he motvaton behnd whtenng technque resdes n spectral behavor of natural scenes and facal mages: ther power spectra roughly fall wth the ncreasng spatal frequency accordng to a power law / f α. hs unbalanced power spectra may result n potental problems when used n searchng for structural nformaton n the mage space, as the nformaton at low frequences may swamp the equally useful nformaton at hgh frequences [5]. he soluton n [5] employs a whtenng flter to attenuate the low frequences and boost the hgh frequences so as to yeld a roughly flat power spectrum across all spatal frequences, and a low-pass flter to control the nose at the hgh frequences. hs flterng component s ntegrated as a preprocessng step nto the conventonal PCA/ICA algorthms, and the entre method s called whtenedfaces recognton. In [5], a low-pass flter wth frequency response n L = exp( ( f / f c ) ) (4) s appled n order to avod ncreasng the nose ampltude n mage, where f =.6 f, n = 5 and c max f = u + v s the absolute spatal frequency. Subsequently, the whtenng flter s appled for balancng the power spectrum. Its frequency response has the expresson α / ω W( f) = f (5) where the optmal value of whtenng parameter α ω s found to be.5. From (4) and (5), the whtenng preprocessng s acheved by applyng the combned flter as W ( f) = W( f) L( f). (6) L 3. Hstogram-enhanced PCA (HPCA) otvated by the wor n [5], we propose a smple, yet effectve preprocessng algorthm. Instead of adjustng the frequency content of the face mage, here the enhancement taes place n the spatal doman by modfyng the mage hstogram. Specfcally, our objectve s to obtan a more homogeneous tonal dstrbuton for all the face mages n Ð, by equalzng the lghtng condtons and ntenstes across the entre mage set. As a result, the data set becomes more unform n terms of facal gray level and lght ntensty level. he hstogram of a dgtal mage wth gray levels n range [,55] s a dscrete functon hr ( ) = n, where r s the th gray level and n s the number of pxels n the mage havng gray level r. For dscrete values, the probablty of occurrence of gray level r n an mage s approxmated by pr( r) = n / n wth =,...,55 and n denotng the total number of pxels n the mage. Hstograms are the bass for numerous spatal doman processng technques, beng straghtforward to calculate 76

3 Fgure. Gaussan shape of the mposed hstogram. Fgure 3. op row from left to rght: the orgnal face mage, ts whtened verson and ts hstogram-enhanced verson. Bottom row: ther correspondng power spectra. Fgure. he effect of hstogram-enhancng: orgnal mages (top row) and ther processed counterparts (bottom row). and havng effcent hardware mplementatons for realtme mage processng. Hstogram-based technques have been encountered n mage processng applcatons such as mage compresson and segmentaton. For face recognton purposes, a helpful utlty s the hstogram cumulatve dstrbuton functon (CDF) [] whch s defned by n j s = ( r) = pr( rj) =, =,...,55. (7) j= j= n Hstogram matchng [] s the method used to generate a processed mage that has a specfed hstogram. For a gven mage I wth hstogram h I, and a reference hstogram h, the hstogram matchng can be acheved by () computng the CDFs of h I and h, denoted by s I and s, respectvely; () fndng the correspondent gray levels r from the reference hstogram for whch s I = s ; and () assgnng the values r to r I n the orgnal mage hstogram. In ths way, the CDF of the orgnal mage, s I, s matched to the reference CDF, s. For mproved face recognton, we propose to apply hstogram matchng for the tonal dstrbuton n a face mage to match a desred hstogram h. For a natural and homogeneous appearance across the face mages n data set Ð, the Gaussan functon Fgure 4. Hstogram of orgnal mage (left) and ts enhanced verson (rght). ( x b) c f( x) = ae (8) s chosen to be the desred reference hstogram, where parameter b s the poston of the center of the pea, c controls the wdth of the bell shape, and a s the heght of the curve s pea wth a = /( c π ). For example, a smooth tonal dstrbuton of gray levels llustrated n Fgure can be obtaned by choosng the center of the pea n the mddle of the gray level scale to offer a balanced gray level dstrbuton,.e. b = 7, wdth c = 8 as t provdes a wde range of mddle gray level tones for a natural appearance of faces, and computng the correspondng heght a. Applyng the above hstogram dstrbuton to three dfferent mages n the frst row of Fgure results n the second row n Fgure. For comparson purpose, the effect n spatal and frequency domans of the whtenng flter from (6) and the hstogrambased processng usng (8) s llustrated n Fgure 3 usng one of the test mages. Usng the same test mage, Fgure 4 shows how the dstrbuton of the orgnal dar mage s changed approxmatng (but not perfectly matchng) the shape of the mposed hstogram as seen n Fgure. 4. A Case Study 77

4 In the case study descrbed below, the method proposed n Secton 3 wll be referred to as the hstogram-based preprocessng PCA (HPCA). Our study ams to evaluate and compare the performance of HPCA wth the exstng WPCA and PCA algorthms under varous condtons. For all the tests carred out, we chose to use the Yale face database [] as t ncludes more mages per class (subject) than other test data sets, such as FEE database. It contans a set of 65 grayscale mages n GIF format of 5 subjects (Fgure 5), wth poses per subject (Fgure 6), namely center-lght, wth glasses, happy, left-lght, wthout glasses, normal, rght-lght, sad, sleepy, surprsed, and wn, denoted as pose a, b,, and, respectvely. All the mages have been cropped to a 8 8 pxel sze, wth the mage center approxmately placed between the nostrls of subject s nose, as s llustrated n Fgures 5 and 6. he challenges arse not only n terms of varable lghtng condtons and sn level ntenstes, whch are addressed by utlzng the hstogram-based preprocessng, but also n terms of dfferent facal expressons, as can be observed n Fgure 6. Heren we carred out an examnaton more thorough than n [5] by nvestgatng both face dentfcaton and face dscrmnaton ssues on several dstnct tranng and testng sets, employng p egenvectors whch usually were chosen as less than half or a quarter of the avalable egenvectors. Implementaton was done n ALAB, employng the functon hsteq for the hstogram enhancng step, wth the settngs used to generate Fgure. Fgure 5. he 5 ndvdual members from the data set pose a pose b pose c pose d pose e pose f pose g pose h pose pose j pose Fgure 6. he poses of one member from the data set able. Numercal results for face/non-face and member/non-member dscrmnaton Image PCA WPCA HPCA d d mn d d mn d d mn mg nonmembers mg mg non-face arplane max ( d ) / max ( d mn ) gap (%) able. Nne cases consdered for face dentfcaton ranng Set: All 5 members wth pose(s) estng Set: All 5 members wth one pose Case a, c, d, e, g, h, f normal pose 78

5 Case a, d, e, g f normal pose Case 3 a, e f normal pose Case 4 a f normal pose Case 5 a, d, e, g c happy pose Case 6 a, d, e, g h sad pose Case 7 a, d, e, g sleepy pose Case 8 a, d, e, g j surprsed pose Case 9 a, d, e, g wn pose 85 8 Case Case Case Case Case 5 Case 6 Case Case 8 Case 9 Fgure 7. Comparson results for PCA (dashed lne wth plus), WPCA (sold lne wth square) and HPCA (sold lne wth cross) for all nne cases 4.. Face/non-face and member/non-member dscrmnaton he tranng set Ð used n ths case had a total of = 48 mages wth K = members out of the 5 subjects, each one wth L = 4 poses: a, d, e and g. As a result, there were avalable = 48 egenfaces from whch a subset of p = was chosen to represent the face mages. A set of mages, called testng set, was used to evaluate the dscrmnaton performance of PCA, WPCA and HPCA. he test set conssted of pose f of all 5 ndvduals n the database, plus one non-face mage called arplane. Among the 5 face mages, there were 3 non-members, namely mg8, mg and mg5. o evaluate the dscrmnaton performance of the three methods, we ntroduce a measure called gap, whch quantfes the dstance between the class of non-face mages C and the class of face mages C nto the face space U. hs measure s defned by mn( d ) max( d ) gap(%) = (9) mn( d ) 79

6 where mn( d ) s the smallest d defned by () for C n Ð, and max( d ) denotes the largest d for C n Ð. he above measure also apples for quantfyng the dstance between the class of non-member mages C and the class of member mages C nto the face space U, where the measure gap s defned n a smlar way as mn( dmn ) max( dmn ) gap(%) = () mn( dmn ) where mn( d mn ) s the smallest d mn defned by (3) for C n Ð, and max( d mn ) denotes the largest d mn for C n Ð. Obvously, a bgger postve gap ndcates easer dscrmnaton between C and C, respectvely C and C, whle a negatve value of ths measure ndcates that no dscrmnaton can be done, as there s no gap but an overlappng. he evaluaton results are summarzed n able from whch one can see that PCA offered the hghest gap for face/non-face dscrmnaton, but faled for members/non-members dscrmnaton, WPCA provded only a small gap for face/non-face dscrmnaton, whle HPCA offered a reasonable gap for member/non-member dscrmnaton and a substantal gap for face/non-face dscrmnaton. 4.. Face dentfcaton For face dentfcaton, we nvestgated nne cases n whch dfferent poses of members were consdered n formng the tranng and testng sets (able ). Fgure 7 llustrates the comparson results of the three methods n terms of recognton rate versus number of egenfaces employed (p), for the above nne cases. he plots n Fgure 7 show how the recognton rate was mproved by utlzng the HPCA algorthm when more than 3 egenvectors were employed for mage representaton. We also note that the performance of HPCA algorthm was qute robust versus the number of mages used n the tranng set. Indeed, even for a reduced tranng set, such as n Cases 3 and 4, the HPCA method outperformed the WPCA and PCA algorthms. A major mprovement was acheved by HPCA when more dffcult mages were to be recognzed, such as n Cases 5-9, whle the WPCA algorthm yelded more false detectons than the orgnal PCA method. In terms of computatonal complexty, on an average bass, the hstogram-based mage preprocessng was.3 tmes faster than the whtenng mage preprocessng, as t requres only a pxel ntensty dstrbuton as opposed to the two stages of flterng descrbed n Secton., equatons (4), (5) and (6). 5. Concluson he hstogram-enhancng method proposed n ths paper can be used n combnaton wth statstc-based methods and s shown to be a useful preprocessng tool for mprovng the face recognton rate, as demonstrated by the expermental results. As future wor we plan to develop a strategy of tunng the parameters of the desred Gaussan hstogram for optmal face recognton performance. Acnowledgements he authors are grateful to NSEC for supportng ths wor and to r. Sergu Sevcenco for hs techncal support. eferences [].A. ur, and A.P. Pentland, Face recognton usng egenfaces, n Proc. IEEE Computer Socety Conf. on Computer Vson and Pattern ecognton, 99, pp [].S. Bartlett, J.. ovellan, an.j. Sejnows, Face recognton by ndependent component analyss, IEEE rans. on Neural Networs,, vol. 3, pp [3] K. Etemad, and. Chellappa, Face recognton usng dscrmnant egenvectors, n Proc. IEEE ICASSP, 996, vol. 4, pp [4] X. He, S. Yan, Y. Hu, P. Nyog, and H.-J. Zhang, Face recognton usng Laplacanfaces, IEEE rans. on Pattern Analyss and achne Intellgence, 5, pp [5] L.-Z. Lao, S.-W. Luo, and. an, Whtenedfaces recognton wth PCA and ICA, IEEE Sgnal Processng Letters, 7, vol. 4, pp. 8. [6] F. Chchzola, L. De Gust, A. De Gust, and. Naouf, Face recognton: reduced mage egenfaces method, ELA 47th Internatonal Symposum, 5, pp [7] K.J. Karande, and S.N. albar, Smplfed and modfed approach for face recognton usng PCA, Internatonal Conference on ICES, 7, pp [8] K.-C. Kwa, and W. Pedrycz, Face ecognton Usng an Enhanced Independent Component Analyss Approach, IEEE rans. on Neural Networs, 7, vol. 8, pp [9] X. Qng, and X. Wang, Face ecognton usng Laplacan+OPA-faces, 6th World Congress on Intellgent Control and Automaton, 6, vol., pp []. C. Gonzalez, and. E. Woods, Dgtal Image Processng, Second Edton, Prentce-Hall, New Jersey,. [] Yale Face Database, Yale Unversty, C, USA. 8