Real Time Face Recognition Using Polynomial Regression and Sub-region Color Component Distribution

Transcription

1 Real Tme Face Recognton Usng Polynomal Regesson and Sub-egon Colo Component Dstbuton Manshanka Mondal, Md. Almas Hossan, Md. Matu Rahman, Kamul Hasan Talukde* Compute Scence and Engneeng Dscplne Khulna Unvesty, Khulna-98, Bangladesh * Gaduate School of Engneeng, Hoshma Unvesty Hoshma, Japan. {manshankamondal, almas_ku}@yahoo.com, matu_ku@hotmal.com, khtalukde@hoshma-u.ac.jp Abstact An effcent achtectue fo eal tme face ecognton s pesented hee usng Polynomal Regesson fo featue edge detecton and by detemnng colo-component dstbuton fo featue-egons. Hee we detemne second ode polynomal equaton by polynomal egesson fo the edges of eyeld and chn. Chn does not change n dffeent expessons, the change of eyeld s also ae and these show clea edges n the pctue. Fo detemnng polynomal equatons the coodnate system s vey mpotant hee. The same cuve may have dffeent equatons dependng on the poston of the cuve on the gaph. We have elmnated ths poblem. As we deve second-ode polynomal equatons we have thee constants fo each cuve whch we can call A, B and C. We also detemne ed, geen and blue colo-dstbuton values fo thee egons - eye-egon, lpegon and nose-egon. Fo the tanng values elated to the same peson these values ae aveaged. Fnally the ecognton s pefomed based on the weghted sum of eos obtaned fom A, B, C values of the edges and colo dstbuton values of the egons. Ths method s too much faste and ts ecognton effcency s hgh Keywods: Polynomal Regesson, Face Recognton, Laplacan Opeato, Pncpal Component Analyss (PCA), Independent Component Analyss (ICA), Lnea Dscmnant Analyss (LDA) etc. I. INTRODUCTION Face ecognton s coveng a vast aea n the ealm of eseach. A lot of eseaches ae pefomed and papes ae submtted elatng to the detecton and ecognton of faces. Many pactcal mplementatons ae pesent egadng face ecognton. Face ecognton s of two knds statc face ecognton and dynamc face ecognton o vdeo based face ecognton. The fst one s concened wth face ecognton n one sngle face of a peson only but the late mples face ecognton technques of a peson whle he o she s movng n vdeo sequences. Many poweful technques have been developed fo ecognzng statc faces. But vdeo based face ecognton technques have some lackng as compaed to the statc face ecognton technques. Ou pape dscusses an effcent way of vdeo based face ecognton. Dffeent papes focus on dffeent technques fo face ecognton. PCA s basc method fequently not only used n the ealy age of statc face ecognton but also n ths age of dynamc face ecognton ths s also used as the coe technque. Some papes also focus on ICA whch has opened anothe eseach aea n face ecognton. Buce A. Dape et al. [] n the pape descbed PCA and ICA and the capablty of face ecognton n dffeent contexts. PCA deco-elates the nput data usng second-ode statstcs and theeby geneates compessed data wth mnmum mean-squaed epojecton eo whee ICA mnmzes both second-ode and hghe-ode dependences n the nput. They have poved that ICA s the genealzaton of PCA. Thee ae two achtectues of ICA. To descbe the compason of these thee methods they sad that dffeent methods ae best fo dffeent tasks such as facal dentty detecton, face ecognton etc. Fo facal dentty detecton ICA achtectue- pefoms the best. Yongbn Zhang et al. [7] n the pape used sub-space pojecton method fo ecognzng faces. The concept was such that a test face may have some expessons whch ae not pesent n the tanng mages of the same face. In ths case they sepaated dffeent potons o sub-spaces fom a face-mage and then weghted these spaces such that the sub-spaces that show lttle change n dffeent expessons wll get geate weghts than those whch show huge changes. They used PCA, ICA and LDA fo pojectng sub-spaces and poved that LDA s the most pomsng method. Ram Qahwaj and Roge Geen n the pape developed the ecognton of face by a eal tme pepocessng. The pepocesso steps wll emove the backgound and ambguous potons of the mage. The pepocessng acton wll be done fom wth the face database. A. Pavan Kuma et al. [1] n the pape ntoduced Weghted Modula PCA. Hee they do not take the whole face as the only egon to be consdeed fo face ecognton. They dvde a face nto dffeent subegons consstng of foehead, eyes, nose and chn. Fo each sub-egon they apply PCA and detemne the egen vectos. Most sgnfcant S egen vectos ae consdeed. Then they expess each sub-egon as a lnea * Also afflated wth CSE Dscplne, Khulna Unvesty, Bangladesh A-1

2 combnaton of these S egen vectos. When a face s ecognzed the egen vectos fo all the sub-egons of the tanng face ae compaed wth the coespondng. We have not used the blnd PCA method fo face ecognton. We detect the face by ts actual shape and colo combnaton by detemnng ts chn-edge and eyeldedge and edge-lne equatons and aveage colo contbuton of thee colo-components fo thee dstngushed featues-eyes, lps and nose. Fo detemnng the edge-lne equaton we have used the second ode polynomal egesson. We detemne the edge of the chn and eyeld of a face, then detemne the edge-lne equaton of chn-lne and eye-lne and stoe the coeffcents fo these lnes. We also detemne the contbutons of thee colo components of the thee egons stated above and stoe the component values. The est of the pape s oganzed as follows: Secton: descbes Polynomal Regesson, Secton: 3 descbes edge detecton wth matx convoluton, Secton: 4 descbes achtectue of face ecognton, Secton 5: descbes ecognton mechansm and Secton: 6 descbes Pefomance consdeatons. Secton: 7 s concluson. II. POLYNOMIAL REGRESSION The least squae pocedue can be used to ft the data to a hghe ode polynomal. Fo example, suppose that we ft a second ode polynomal o quadatc: y = a + a1x + a x + e (1) Hee e expesses the eo. Fo ths case the sum of the squae f the esduals s S = n = 1 ( y a a1x a x ) () Followng the pocedue of the pevous secton, we take the devaton of the above equaton wth espect to each of the unknown coeffcent of the polynomal, as n S a S a1 S a = ( y a = x ( y a = x ( y a x 1 a a1 x a x 1 a x ) a x ) a x ) (3) (4) (5) These equatons can be set equal to zeo and eaanged to develop the followngs: n ) a + ( x ) a + ( x ) a = 1 ( ) a + ( ) a + ( 3 ) a = ( y (6) x x 1 x x y (7) ( ) a + ( 3 ) a + ( 4 ) a = x x 1 x x y (8) whee all the summatons ae fom = 1 though n. The above thee lnea equatons and have thee unknowns: a, a1, and a. The coeffcents of the unknowns can be calculated dectly fom the obseved data. Fo ths case, we see that the poblem of detemnng a least-squaes second-ode polynomal s equvalent to solvng a system of thee smultaneous lnea equatons. We have used hee Gauss Jodan method fo detemnng the coeffcents. The two-dmensonal case can be easly extended to an m-th -ode polynomal as y = a + a1x + a x am x + e (9) The foegong analyss can be easly extended to ths moe geneal case. Thus, we can ecognze that to detemne the coeffcents of an m th-ode polynomal m +1 smultaneous lnea equatons must be solved and hee we use by Gauss-Jodan method fo solvng. III. EDGE DETECTION WITH MATRIX CONVOLUTION Hee we have used a vey popula second-ode Laplacan opeato to detect edge. The Laplacan of a func- x, y, s defned by: ton f(x,y), denoted by ( ) ( ) ( ) x, y ( x, y) x, y = + (1) x y Once moe we can use dscete dffeence appoxmatons to estmate the devatves and epesent the Laplacan opeato as the followng 3 x 3 convoluton mask : Fg. 1 Convoluton Mask Howeve thee ae dsadvantages to the use of second ode devatves. (We should note that fst devatve opeatos exaggeate the effects of nose.) Second devatves wll exaggeate nose twce as much. No dectonal nfomaton about the edge s gven. Laplacan convoluton matx woks as follows: Suppose some whee we ae at a pont x n the mage. We have thee basc colos fo ths pont. Now suppose ths pont coespond to the mddle element -4 of the above convoluton matx. We consde 9 pxel elements of the mage the cuent pxel x beng the mddle of the 3x3 matx. Then we add ed colos of these 9 pxels wth the coespondng coeffcents multpled wth the ed colos. Ths esultant colo dvded by 9 wll be the colo of the mddle pont that s the pxel x. Thus we detemne the geen and blue colo of x. Now ths RGB m A-

3 colo got fom the calculaton s assgned to the pxel x. Ths opeato does not gve the edge lnes but gves gay coloed edge on a black back gound. A man face, ts detected face by matx convoluton method and the detected chn-lne ae gven hee: Face aea s detected by matx convoluton method stated above. When an mage of a peson ncludng hs face s gven as nput, ou pocess detemnes the headtop and the neck of the peson fom the mage and keeps the poton between these two boundaes dscadng all othe potons of the peson s body. One of ou pogam geneated examples s gven below n Fg. 4: Fg. Man Face, Detected Face, Chn Lne espectvely. In the second pctue of ths fgue the blue lne detemnes the bounday of the face and n the thd pctue the blue lne detemnes the detected chn-lne. IV. ARCHITECTURE OF FACE RECOGNITION The pocess how we wll stoe the values fo the tanng faces s gven as a dagam. It conssts of detectng face aea, detemnng thee man egons that ae eyeegon, lp egon and nose egon, detemnng the colo dstbuton of each egon, chn-lne and eyeld detecton, detemnng co-odnates fo chn-lne and eyeld of the face, then cuve fttng of each face s pefomed by second ode polynomal egesson. At last we detemne the aveages of dffeent values detemned fo some faces of the same peson and these aveages ae stoed n the data base. Input Image Detect Face Aea Regon Detecton Eye Detecton Nose Detecton Edge Detecton Chn Lne Detecton Eye-Ld Detecton Cuve Fttng Lp Detecton Coeffcent detemnaton Colo Component Stong Detemnaton Fg. 3 Achtectue of Face Recognton A. Face Aea Detecton Fg. 4 Face Detecton and Extacton B. Regon Detecton and colo component detemnaton The face s detected by flteng pocess. Once the face s detected the hghest and lowest Y-axs co-odnates ae detemned. Fom ths the pependcula length of the face s detemned. Fom a geat many faces we have detemned the featues that the eyes, nose and lps ae placed at defnte dstance atos fom the top of the head. We have detemned that f we multply the total pependcula length of the face by.49 we get the dstance of eyes fom the top of the head. If we multply the total pependcula length of the face by.77 we can go to the lps fom the top of the head. Fo gettng the egon of eyes we detemne two hozontal lnes one at the dstance of (total pependcula length *.41) fom the top pont and the othe at the dstance of (total pependcula length *.53) fom the head top. Fo a lot of faces we have seen that these two lnes exactly cove the eye-egon. Fo lp detecton we also detemne two lnes, one of whch s placed at the dstance of (total pependcula length *.71) fom the top poston and the othe emans at the dstance of (total pependcula length *.85) fom the head top. Of the two lnes enclosng the nose-egon the fst one emans at the dstance of (total pependcula length *.54) fom the top of the head and the second one s placed at the dstance of (total pependcula length *.71) fom the top. Fo each egon we detemne thee aveage values of ed, geen and blue colos by the followng equaton. total _ pxels ed( ) = egon _ ed _ aveage = (11) total _ pxels Hee egon_ed_aveage s the value of aveage ed component of a egon, total_pxels gves the value of the total numbe of pxels of the egon and ed() means the ed colo component of -th pxel of the egon. The aveage values ae stoed n the database. Fo the above face the values that ou pogam detemnes ae gven hee: A-3

4 Table 1 Stoed values fo thee egons Red Geen Blue Eye Lp Nose A = B = C=.1195 C. Chn-lne detemnaton We detemne two edges fo chn. Fst one begns fom just below the ea up to the end pont of the face whch ncludes a lttle pat of the neck and t s shown. The othe s of the bottom pat of the chn. We detemne the co-odnates fom the chn lnes and fom the second ode polynomal egesson detemne the chn-lne equaton and the thee coeffcents. The flow gaph of detemnng the bottom pat of the chn fo the man face n fgue-1 s gven hee. Fg. 5 Chn-lne Detemnaton Steps The blue lne detemnes the detected chn-lne. Fo the detected chn-lne the thee coeffcents afte applyng the second ode polynomal egesson ae shown hee: Table Values fo A, B and C A B C D. Eyeld detemnaton Detemnaton of eyeld-lne s a vey dffcult pocess. Fom the appoxmaton of the eye-egon gven above the eye-egon s cut. Dffeent steps that ou pogam pefoms n eyeld detemnaton ae shown gaphcally. The edge of one eye s consdeed and the othe s gnoed. Fg. 6 Eyeld Detemnaton Steps Hee the blue lne at the end detemnes the eyeld-lne. Its coodnates ae detemned and applyng polynomal egesson ts equaton and thee coeffcents ae detemned. The coeffcents that ou pogam detemnes ae shown hee: Table 3 Values fo A, B and C A B C E. Cuve Fttng and Co-effcent Detemnaton Fo detemnaton of the tanng value we take N dffeent faces of the same peson. Fom each face we cut the chn-lnes and eyeld lne. Fo these lnes polynomal egesson s appled fo obtanng second ode polynomal equatons. Suppose n co-odnates fo an edge ae as follows: (x1,y1) (x,y) (x3,y3) (xn,yn). Then the equaton s geneated fo each of the lnes whch take the fom Y = A + Bx + Cx Fom ths equaton the coeffcents A, B and C ae stoed. Fo N faces elated to the same peson we have detemned the edge equatons and fo each of the edges we have N values elatng to the coeffcent A, N values elatng to the coeffcent B and also fo C. We detemne the aveages fo each of the coeffcents that ae stoed n the database. F. Co-odnate Equalzaton System The same cuve placed at two dffeent places n a gaph wll have two dffeent equatons. But these two can gve the same equatons. If we select a decton fo the cuves to stat fom and go though then by subtactng the x and y coodnate values of the fst pont fom all the x and y coodnate values fo all the ponts we can make the two cuves such that they both ae geneated fom the (,) pont of the coodnate system. Thus the same cuves that wee gvng two dffeent equatons wll now gve dentcal equatons. Fo edge detecton n ou appoach ths thought s used. So the two edges fo the same peson that mght gve two dffeent equatons fo two dffeent templates wll gve the almost same equatons. Fg. 7 Co-odnate system equalzaton The two cuves n the two gaphs denoted by P11-P1 and P1-P wll show dffeent equatons but by the above coodnate-system these two wll gve the same equatons. A-4

5 G. Rotaton of lnes Thee s anothe facto that s the otaton of lnes. The same lne depcted on the gaph two tmes wth elatve angle between them wll not have the same equatons. But ths eo s mnmzed because we take many tanng values of the same face and the esultant coeffcents ae aveaged. V. RECOGNITION Fo ecognton pupose we use weghtng mechansm. Fo a face we detemne eghteen values that ae thee colo values fo each of the thee egons eye-egon, lp-egon and nose-egon, the thee coeffcents got fom each of the two chn-lnes and thee coeffcents got fom eyeld. Fo each of the stoed faces we detemne the absolute dffeences fo the coespondng values of the face to be ecognzed. These dffeences ae multpled wth pedefned weght values and then ae summed togethe. Fo eye-egon and nose-egon ths value s 1 and fo the lp-egon t s.5. The lpegon gets the lowe weght because ths may be changed to dffeent shapes n dffeent expessons. We detemne the exact absolute dffeences fo the chnlne and eyeld-lne coeffcents and these dffeences ae added to the weghted-eo. The face wth the lowest total weghted eo s taken as the matched face. VI. PERFORMANCE CONSIDERATIONS PCA based methods ae blnd methods n the sense that the actual shape of a peson s not detemned, on the othe hand the summaton, multplcaton, tanspose etc of the face mage matx s pefomed and some egen vectos ae detemned that helps ecognzng the face. But n ou method we have detemned the actual shape of the chn of a face and detemne the equaton of the chn lne. We also consde the contbuton of thee colo components fo thee mpotant featues of a face whch wll be dffeent fo dffeent pesons. A. Tme Complexty Ths pocess of ecognzng faces s too much faste than exstng PCA elated methods. PCA based methods contan huge multplcatons of matces whch s vey much tme consumng. In ou pocess the matx elated calculatons ae pefomed by the phase of applyng Gauss Jodan ule. Fo ths eason ths pocess s too much faste than any PCA based method. B. Stoage Complexty All PCA based methods need to stoe a huge quantty of data at the un tme. But n ou pocess we need a lttle un tme tempoay stoage. C. Detecton Effcency Ous s a eal tme pocess whee the vdeo camea wll at fst take the pctue of a peson fom head top to any poton of hs body ncludng the face and then fom ths pctue ou pogam wll detect the face. An example s gven hee: Fg. 8 Dffeent potons of body ncludng face Thee ae fou faces of a peson wth dffeent potons of body and these mages ae also of dffeent szes. Ou method detects only the face potons fom these mages and uses them fo ecognton. D. Recognton Rate We have used the pctues of 4 pesons and each of the pesons had moe than 5 samples. We have used thee samples pe peson fo mplementaton of PCA and WMPCA. D.1. Vaable Szed Images If the mages ae of dffeent szes the PCA and WMPCA methods do not wok because the fst and foemost condton of PCA-based methods s that the mages wll be of same sze that s the wdths as well as heghts wll be same. The followng gaph shows the ecognton ate whle faces ae of same szes but mages ae of dffeent szes. Recognton Rate Numbe of Pesons Ou- Method Fg. 9 Recognton Rate of Vaable Szed Images D.. Dffeent szes of faces of the same peson Ou method ecognzes faces to a geat extent when the faces ncluded n the mages ae of dffeent szes whee the mages may be of the same szes o dffeent szes. Fg. 1 Dffeent szes of face of the same peson In the above fgue thee ae thee mages each contanng dffeent szes of faces of the same peson. Fo these thee nputs ou pogam wll ecognze them as the same peson. A-5

6 Compasons fo the same szes of mages wth dffeent szes of faces ae shown hee: Recognton Rate Numbe of Pesons Ou- Method WMPCA PCA Fg. 11 Recognton Rate of faces fo dffeent zoomng. D.3. Why Ou Method Pefoms Best 1. The PCA based methods pefom a pxelwse coespondence among moe than one sample faces. It s not possble to detemne egen vectos fom only one sample.. If the faces between two o thee mages ae dsplaced n mage template PCA, WMPCA etc gves vey low pefomance. 3. If the faces ae of dffeent szes n the mage fame t s tuly mpossble fo PCA based methods to ecognze them. Ou method ovecomes the above thee man poblems. VII. CONCLUSION The poposed pocess of face ecognton has a fne ecognton ate and ts man faclty s that t mnmzes tme complexty and un tme stoage complexty. Moeove, as ou pocess ntegates shape detemnaton technque wth the knowledge of colo component dstbuton of sub-egons ths suvves n many ctcal stuatons whee the PCA based methods fal. Futue mplementaton can be on the cuve fttng mechansm. Fo mpoved and moe accuate ecognton ate thd, fouth o even any hghe ode polynomal egesson can be used. In ths pocess we have used second ode edge detecton opeato that s Laplacan opeato. We have also ted wth gadent based method whch some tmes poduces too much complexty. Consequently ous s an mpovement ove the tadtonal technques. Refeences [1] A. Pavan Kuma V. Kamakot Sukhendu Das. An Achtectue Fo Real Tme Face Recognton Usng WMPCA. Depatment of Compute Scence & Engneeng Indan Insttute of Technology Madas, Chenna 636 [] Wendy S. Yambo Buce A. Dape J. Ross Bevedge. Analyzng PCA-based Face Recognton Algothms: Egenvecto Selecton and Dstance Measues. Compute Scence Depatment Coloado State Unvesty Fot Collns, CO, U.S.A 853, July 1,. [3] Teóflo Emído de Campos Rogéo Schmdt Fes Robeto Macondes Cesa Juno. A Famewok fo Face Recognton fom Vdeo Sequences Usng GWN and Egenfeatue Selecton. Depatamento de Cênca da Computação Insttuto de Matemátca e Estatístca Rua do Matão. [4] Anulf B. A. Gaf and Felx A. Wchmann. Gende Classfcaton of Human Faces. Max Planck Insttute fo Bologcal Cybenetcs pemannstasse 38, 776 T ubngen, Gemany [5] Yongmn L, Shaogang Gong and Heathe Lddell. Vdeo-Based Onlne Face Recognton Usng Identty Sufaces. Depatment of Compute Scence, Queen May, Unvesty of London, ondon E1 4NS, UK [6] Thomas Heseltne, Nck Peas, Jm Austn. THREE-DIMENSIONAL FACE RECOGNITION: AN EIGENSURFACE APPROACH. Advanced Compute Achtectue Goup, Depatment of Compute Scence, The Unvesty of Yok [7] Yongbn Zhang and Alex M. Mat ýnez. Recognton of Expesson Vaant Faces Usng Weghted Subspaces Depatment of Electcal and Compute Engneeng. The Oho State Unvesty [8] Deepak S. Tuaga and Tsuhan Chen. FACE RECOGNITION USING MIXTURES OF PRINCIPAL COMPONENTS. Vdeo and Dsplay Pocessng Electcal and Compute Engneeng. Phlps Reseach USA Canege Mellon Unvesty Baclff Mano, NY 151 Pttsbugh, PA 1513 deepak.tuaga@phlps.com [9] L. Toes L. Loente Josep Vla. AUTOMATIC FACE RECOGNITION OF VIDEO SEQUENCES USING SELF-EIGENFACES. Depatment of Sgnal Theoy and Communcatons Polytechnc Unvesty of Catalona Bacelona, Span. [1] Cut Heshe Anuj Svastava Godon Elebache. Automated Face Tackng and Recognton. [11] Rajkan G. and Vjayan K. An mpoved face ecognton. technque based on modula PCA appoach. Patten Recog-nton. Lettes, 5, No. 4:49 436, 4. [1] Ram Qahwaj and Roge Geen. Impovng the Recognton Pefomance fo PCA. School of Infomatcs, Unvesty of Badfod, BD7 1DP. School of Engneeng, Unvesty of Wawck, CV4 7A. A-6