Combination of Local Multiple Patterns and Exponential Discriminant Analysis for Facial Recognition

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1 Sensors & ransducers 203 by IFSA Combnaton of Local Multple Patterns and Exponental Dscrmnant Analyss for Facal Recognton, 2 Lfang Zhou, 2 Bn Fang, 3 Wesheng L, 3 Ldou Wang College of Computer Scence, Chongqng Unversty, Chongqng, , Chna 2 College of softare, Chongqng Unversty of Posts and elecommuncatons Chongqng, , Chna 3 Insttute of Computer Scence and echnology, Chongqng Unversty of Posts and elecommuncatons, Chongqng , Chna el.: , fax: E-mal: zhoulf@cqupt.edu.cn Receved: 26 Aprl 203 /Accepted: 4 June 203 /Publshed: 25 June 203 Abstract: Global features-based methods and local features based methods have been very successful n face recognton system, yet they can be combned together and jontly optmzed so as to mnmze the error of a nearest-neghbor classfer. We consder both descrptor for face mages th Local Multple Pattern, and dscrmnant learnng technques th Exponental Dscrmnant Analyss. A combnaton frameork based on Local Multple Pattern and Exponental Dscrmnant Analyss has been proposed n ths paper. Frstly, our approach encodes the mult-scale face feature by Local Multple Pattern, and then they have been extended to strengthen the dscrmnatve ablty by Exponental Dscrmnant Analyss; Secondly, e suggest to use the above feature on dfferent layers ndependently so that a multple classfer system can be attaned. Usng these technques, e obtan the state-of-the-art performance on to publc avalable databases. Copyrght 203 IFSA. Keyords: Face recognton, Local multple pattern, Exponental dscrmnant analyss, Combnaton frameork, Multple classfer.. Introducton Face recognton has been a hot research topc n recent years due to the ncreasng demands of realorld applcatons [, 2]. Snce face recognton ncludes to major components: face representaton and face matchng, to jobs should be taken nto account. Frstly, the extracted descrptor s requred to be not only dscrmnatve but also nvarant to apparent changes and nose. Moreover, the matchng should be robust to varatons from pose, expresson, and llumnaton. Among the most dely used methods for face recognton based on feature extracton can be dvded nto to classes: global features approaches, such as Prncpal Component Analyss (PCA), Lnear Dscrmnant Analyss (LDA) [3] and 2D PCA have taken nto account the hole mage; local features approaches, such as Local Features Analyss (LFA), Gabor avelet-based features and Local Bnary Pattern (LBP) [4] consder only the local regon thn the mage, so the dstrbutons of faces are less affected by varous changes. Recently, local bnary pattern (LBP) s ganng more attenton. 92 Artcle number P_224

2 Ahonen et al. proposed to use the hstogram of Local Bnary Pattern (LBP) to descrbe the mcrostructures of the face because t s nvarant to monotonc photometrc change and can be effcently extracted. Hoever, the method stll suffers to drabacks. On one hand, LBP may not dscrmnate multple patterns due to ts bnary patterns only comprsng of 0s and s. In addton, another lmtaton of LBP s ts senstvty to random and quantzaton nose n unform and near-unform mage regons such as the forehead and cheeks. he dsadvantage of LBP method results from the threshold at exactly the value of the central pxel. Hence, many methods have been proposed to tackle the above problem that exsts n LBP. Lastly, Local multple patterns (LMP) [5], a generalzaton of LBP, Local ernary Patterns (LP) [6] and Local Multple Layer Contrast Pattern (LMLCP) [7] has been proposed. he LMP extends bnary patterns to multple patterns, hch can preserve more structural nformaton, and be more robust to apparent changes and nose. Hoever, the LMP method suffers to drabacks. Frstly, the exstng encodng method of LMP ll lead to the enormous dmenson as shon n Fg.. Hence, e adopt a specal encodng method to deal th the problem. In addton, n order to keep the resultng code hstogram formatve and compact, enhance the dscrmnant ablty of the descrptor, e apply the dscrmnant analyss technque to the code hstogram. Lnear dscrmnant analyss (LDA) s ell knon as a poerful tool for dscrmnant analyss, and the LDA-based methods have been used very successful n face recognton [8, 9]. LDA constructs a dscrmnant subspace dstngush optmally faces of dfferent persons. In the case of a small tranng data set, hoever, LDA serously suffers from the SSS problem. o date, many approaches have been proposed to tackle ths problem such as PCA+LDA (Fsher faces) [0] and NLDA []. Recently, an exponental dscrmnant analyss (EDA) [2] technque has been presented. Compared th PCA+LDA (Fsher faces) and NLDA, EDA can extract not only the most dscrmnant nformaton ncluded n the null space of the thn-class scatter matrx, lke NLDA, but also the dscrmnant nformaton ncluded n the non-null space of the thn-class scatter matrx, lke PCA + LDA (Fsher faces). Furthermore, the orgnal data can be transformed nto a ne space here LDA crteron s appled, the dstance dffuson mappng strategy can enlarge the margn beteen dfferent classes so that the classfcaton accuracy can be mproved by EDA. In summary, e consder to fuse the LMP and EDA n ths paper. Usng these methods, e obtan a hghly dscrmnatve and compact face representaton. Besdes the representaton, the matchng also plays an mportant role. In most practces, the above face features are typcally fused on the feature layer. Further, the polcy ll eaken the ablty of classfy to varous varatons from uncontrollable condtons. We found that a specfc face feature layer contrbutes dfferently hen the llumnaton combnatons of nput face mages are dfferent. Based on ths observaton, e propose a multple classfer method. Specfcally, e adopt the feature of dfferent layer to recognze respectvely and then fuse them as the fnal decson. Combnng a dscrmnatve mult-scale-based descrptor and a multple classfer method, our combnaton frameork acheves the leadng performance on both ORL and YALE database. he rest of ths paper s organzed as follos: In Secton 2, e brefly ntroduce the LMP method and ts encodng method, and then EDA method s analyzed n Secton 3. In Secton 4, e ntroduce a combnaton frameork th LMP and EDA and present the detals of the proposed frameork. Secton 5 provdes expermental results and dscusson. Secton 6 concludes the paper. 2. Local Multple Pattern 2.. Reve of Local Bnary Pattern he orgnal LBP operator labels the pxels of an mage by threshold the 3 3-neghborhood of each pxel th the center value and consderng the result as a bnary strng. After that, the bnary strng s transformed to a decmal label as shon n the follong equaton. P LBP x, y sg g 2, () PR, c 0 LBP x y s the decmal label of pont x y, P s the number of samplng ponts, here PR,,, R s the radus of a crcle neghborhood, g c s the gray level of central pont x, y, g s the gray level of neghborhood samplng pont around central pont x, y and s X, X 0 0, X Reve of Local Bnary Pattern (2) LBP s bnary patterns only consder the sgn (postve or negatve) evaluated by g g c, hle the contrast nformaton has been gnored. Moreover, contrast characterstc s mportant for recognton by humans. So, t s very necessary to ntroduce contrast to features extracton for classfcaton. As a result, LMP s adopted n ths paper. Frstly, the mddle patterns beteen 0 and have been added by LMP so that t not only can descrbe 93

3 abundant nformaton than LBP but also can be more robust for mage analyss, especally, the analyss of flat areas. Secondly, provdng the nonlnear change of contrast value dos not exceed the range of one layer, the nterference caused by llumnaton varaton can be elmnated. Next, e ll sho ho the LMP s derved. For smplcty, the equdstant dvdng model has been adopted here. h max and h mn are the maxmum and mnmum values of g g c respectvely. L corresponds to the number of dvded patterns, hch separate the nterval [h mn, h max ] nto L parts by L thresholds by the follong formula (3)- (5). u h h h L (3) mn max mn / hl hmn ( hmax hmn )/ Ll h h l l, 2, L u L, X hl L 2, h X h sx ( ), h X h2 0, X h L2 L LMP features value of the center pxel evaluated by the follong formula: (4) (5) g c can be P PR,, c (6) 0 LMP x y s g g L Hoever, t s obvous that the feature dmenson expanson of LMP s enormous, so a specal codng scheme desgned has been used here that splts each multple pattern nto L parts, subsequently treatng these as L separate channels of LBP descrptors. An llustraton of the basc LMP operator s shon n Fg., and L has been set 4 here. Fg. 2 shos the orgnal mages and the correspondng local features extracted by LBP (second column), LP (thrd column), LMP (from fourth column to seventh column). As can be seen, the proposed LMP method has extracted more abundant face nformaton than LBP and LP method from the orgnal mages. Furthermore, the face space s scale s gettng larger and larger no. In order to get a more compact face descrptor and further mprove the dscrmnatve ablty of the descrptor, the EDA method has been suggested to use. 3. Exponental Dscrmnant Analyss 3.. Reve of Lnear Dscrmnant Analyss he objectve of LDA s to fnd the most dscrmnant feature of the data, hch takes care of class nformaton. Furthermore, t ams at maxmzng the beteen-class scatter hle smultaneously mnmzng the thn-class scatter. he crteron functon of LDA s gven as: W SbW arg max W W S W (7) he optmal projecton matrx W can be attaned by solvng the generalzed egenvalue problem: SW SW (8) b Fg.. Calculatng the LMP code. Fg. 2. Orgnal mages and the correspondng measures extracted by LBP (second column), LP (thrd column), LMP (from fourth column to seventh column). 94

4 3.2. Reve of Exponental Dscrmnant Analyss Recently, an approach to tackle the SSS problem comng from the LDA method has been proposed by Zhang et al. he dea of the approach s to capture lnear combnaton of the mxed central moments ncludng second-order mxed central moments so that the better representaton of data can be attaned. Suppose a tranng sample set nclude C patter classes L, L2, LC and the number of samples n class L s denoted by N. he total number of tranng samples s N and then N N. he beteen-class scatter matrx S b and the thn-class scatter matrx S can be defned as follos: C Sb N m m m m C j j xjx (9) S x m x m, (0) here m s the average of the total tranng samples, m s average of the tranng samples of th class, X s the set of all tranng samples of th class. Defnton : Gven an arbtrary n-order square matrx A, ts exponental s defned as follos: 2 m A A exp( A) I A () 2! m! In EDA, the nput data can be transformed nto a ne space by the exponental of matrx so that t enlarges the dstance beteen classes. Moreover, the LDA crteron s appled n the transformed space resultng n better classfcaton. he crteron of EDA s as follos: W exp( Sb) W JW arg max (2) W W exp( S ) W 4. A Combnaton Frameork of LMP and EDA Methods In ths secton, e propose a combnaton frameork of LMP and EDA. Frst, e ntutvely llustrate the dversty of LMP method, and then present our combnaton frameork. LMP extends LBP from bnary patterns to multple patterns hch ll result n a consderable problem of feature dmenson expanson. Furthermore, the LMP features ll be sparse and eaken the ablty of reflectng texture pattern. As a result, e adopt a specal codng scheme. he advantage of the codng scheme s as follos: Frstly, t contrbutes to extract mult-scale LBP feature. he LMP features from dfferent layers contan dfferent texture nformaton. Fg. 2 shos the dfferent texture nformaton usng LBP, LP and LMP. It s observed that the texture nformaton of LMP n Fg. 2 s dstnctly dfferent. Secondly, e fnd that the feature of dfferent layer contrbutes dfferently for recognton hen the face s under uncontrollable condton. For example, compared th the features of the hgher layer, the features of the loer layer are more robust to dramatc llumnaton changes. Based on ths observaton, the LMP face feature on dfferent layer ll be desgned to recognze ndependently so that a multple classfer system can be attaned. he LMP face feature can acheve promsng result because of ts strong descrptve ablty. But t stll leaves room for us to mprove t. In ths paper, e advse to use exponental dscrmnant analyss method mprove the dscrmnatve ablty of the LMP descrptor so that the resultng face representaton s compact, hghly dscrmnatve and then the ndvdual recognton performance can be mproved effcently. Furthermore, only f the ndvdual classfers are effectve and dverse, combnaton of classfer ould acheve hgher recognton accuracy than ndvdual classfers. Dversty s a very mportant and necessary characterstc n the desgn of multple classfer system [3, 4]. he soluton takes advantage of the fuzzy membershp functon. It represents the degree of beng smlar to the category nstead of YES/NO. In the proposed method, Ch square s used as fuzzy membershp functon hch shos the degree of sample x belongs to class A. Fnally, e can attan the fuzzy recognton results of dfferent layers. he formula s as follos: L c c o, x,, o, c c o, xl,, o, L (3) c L denotes the degree of the test sample belongs to the c-th class o c of face database on the L-th layer. Namely, e can obtan a set of fuzzy recognton results hch represent the degree of the testng samples belong to all classes on dfferent layers by the above step. Fnally, e fuse the recognton results on dfferent layer, and then the nearest neghbor (NN) dstances as classfer has been used to make decson. In summary, e present a LMP dversty matchng method based on EDA as shon n Fg. 3. he man steps of the combnaton frameork are stated as follos: Step: Feature extracton: extract the multple scales LBP feature ncludng LMP, LMP 2, LMP L Step 2: Optmzng feature space: the feature of dfferent layer s strengthened the dscrmnatve ablty by EDA method. Step 3: Matchng: calculate the dstance of feature vector on dfferent layers and classfy respectvely. 95

5 Step 4: Fuson: the dverse recognton results on dfferent layers are fused lastly. Step 5: Decson makng: the nearest neghbor (NN) dstances acts as classfer. 5. Expermental Results and Dscusson In ths secton, e evaluate the effectveness of the proposed combnaton frameork by varous experments on both ORL and the Yale B database and summarze several nterestng experment results. It contans three types of experments. Frstly, e compare LMP method th LBP and LP methods to valdate ts strong descrptve poer. hen, e provde the comparson of EDA method th the competng methods ncludng PCA, LDA and PCA+LDA (Fsher faces). Lastly, e valdate the effectveness of the combnaton frameork th ndependent LMP and EDA methods. he experment settng s descrbed as follos. For each database, e randomly select n samples of each ndvdual for tranng, and use the remanng facal mages for testng. For LMP, consderng the spendng of tme and space, e set L=4. For PCA, e reserve 99 % of the prncpal components for recognton. he nearest neghbor (NN) dstances as classfer has been used n ths paper. Fg. 3. Combned frameork of LMP and EDA. 5.. Experments on the ORL Database In ths experment, e use ORL face database to test the performance of the combned frameork n dealng th small lght, expressons, scale and pose varaton. For the ORL database, a random subset th (n =, 3, 5, 7) mages per subject as taken to form the tranng set, and the rest of the mages ere used as the testng set. he frst experment s devsed to valdate the effectveness of LMP operator. able shos that the recognton results of dfferent methods on dfferent reference sets. As can be seen, LMP outperforms LBP and LP methods on all subsets. he recognton accuracy of LMP acheves more than % recognton rate on average, hle LBP and LP methods only reach % and % recognton rate respectvely. herefore, LMP s an effectve method for texture descrpton. he second experment as desgned to compare EDA th the homologous methods such as PCA, LDA, PCA+LDA (Fsher faces). he average recognton results are shon n able 2. As can be seen, EDA method sgnfcantly outperforms the other compettve methods on all the tranng sets. Especally, the LDA and PCA+LDA (Fsher faces) fal to ok hen the tranng subset s one mage th per subject. he reason s that thn-class scatter matrx S becomes a zero matrx hle EDA can deal th the problem successfully. herefore, the above experment result valdate that EDA s effectve compared th the other compettve methods. o evaluate the effcency of the combnaton frameork, e compare the recognton rate of the proposed method th the ndependent LMP method and EDA method. he recognton accuracy under each reference set s shon n Fg. 4. As can be seen, the advsed combnaton frameork almost acheves to 98 % recognton rates on all reference sets, hle another competng methods EDA can reach 98 % recognton rates hen only relatve many mages are selected as reference mage, and LMP obtans only about 92 % recognton rates n ths case. Meanhle, the recognton rates of LMP serously degrade hen the number of reference mages s small. It s obvous that the proposed combnaton frameork s relatve 96

6 robust to the number of reference mage, hle the other competng methods ncludng EDA and LMP are senstve to the number of reference mage. Furthermore, the advsed methods acheve hgher recognton rates on all subsets than LMP and EDA. able. Performance comparson on ORL database hen usng local features. he frst experment s desgned to test LMP s nsenstve to dfferent llumnaton and pose than any other compettve methods such as LBP and LP. he recognton results are shon n able 3. As can be seen, LMP outperforms LBP and LP on all reference sets methods, hch sho that LMP s more sutable for mage analyss, ncludng the analyss of mage under dfferent llumnaton and pose. able 3. Performance comparson on Yale B database hen usng local features. able 2. Performance comparson on ORL database hen usng global features. he second one s desgned to compare EDA th PCA, LDA and PCA+LDA (Fsher faces) methods under dfferent llumnaton and pose. he comparson of results s llustrated n able 4. As shon n the results, EDA outperforms PCA, LDA, and PCA+LDA (Fsher faces) methods on all subsets. As mentoned above, the LDA and PCA+LDA (Fsher faces) fal to ok hen the tranng subset s one mage th per subject agan. herefore, EDA s superor to any other compettve methods. able 4. Performance comparson on Yale B database hen usng global features. Fg. 4. Performance comparson on ORL database usng combned frameork Experments on the Yale B Database For the experments, e chose Yale B database to test face recognton algorthms, hch contans mages of 0 ndvduals n nne poses and 64 llumnatons per pose. In order to valdate the proposed method s robust to reference mage th dfferent llumnaton and pose synchronously, a random subset th (n =, 3, 5, 7) mages per subject as taken to form the tranng set, and the rest of the mages ere used as the testng set. Meanhle, e perform three experments on ths database. Fg. 5. Performance comparson on Yale B database usng combned frameork. 97

7 In order to further analyze the recognton rates of the advsed combnaton frameork s robust versus dfferent lghtng and pose condtons, the thrd experment has been devsed. he recognton accuracy under each reference set s shon n Fg. 5. As can be seen, the combnaton frameork acheves closely to 00 % recognton rates on all reference sets, hle the other competng method EDA s neffectve ths tme. Furthermore, LMP method can reach 00 % recognton rates hen only relatve many mages are selected as reference mage. Hence, the advsed combnaton frameork s superor than LMP and EDA methods Dscusson Several experments on dfferent databases have been performed. It s orthhle to hghlght several nterestng expermental results of the combnaton frameork as follos. Frstly, Comparng th Fg. 4 and Fg. 5, the expermental results sho that LMP outperforms EDA hen the database ncludes llumnaton varaton, because the local features are more robust n uncontrolled envronment. Instead, EDA attans the hgher recognton rate than LMP hen the database s normal. Furthermore, the advsed combnaton frameork attans the perfect results on to databases. he reason s as follos: the method makes good use of the strong descrptve ablty of LMP, and then the multple classfer system can guarantee the recognton result s dverse. It s the most mportant thng s that the ablty of ndvdual classfer has been strengthened by EDA. he expermental results have justfed ths pont. Secondly, as can be seen from Fg. 4 and Fg. 5, the proposed combnaton frameork s not only robust to the number of reference mage but also can attan the perfect result on all reference sets. Hoever, the LMP and EDA have been affected by the number of reference mage on to bases. Especally, the Phenomena become more evdent on YALE B database. In practcal applcatons, sometmes, there mght be only a small number of tranng samples that s avalable for each subject or the tranng sample s under uncontrollable condtons ncludng pose, llumnaton, and expresson varaton. In ths case, the EDA and LMP methods ll be neffcent, hle the proposed combnaton frameork can ork better. 6. Conclusons In ths ork, e have bult the dversty matchng scheme by the local multple pattern, and then EDA has been suggested to apply n every LMP feature space respectvely, hch s helpful n mprovng classfcaton accuracy. o face databases, the ORL and the Yale B, are used to evaluate the combnaton frameork. Expermental results sho our method acheves the leadng performance on varous database n recognton accuracy. Furthermore, t s robust to the number of reference mage. In the future, e ll contnue our ork by further nvestgatng some related ssues such as hether the 3D feature can be combned? and hether the combned frameork s effectve to deal th the problem of agng? Acknoledgements hs ork s supported by the Program for Natural Scence Foundaton of Chna (No. 6004, 67329, , 67060, ), the Specalzed Research Fund for the Doctoral Program of Hgher Educaton of Chna (No ), the Natural Scence Foundaton Project of CQ CSC (CSC202JJA699) and the Fundamental Research Funds for the Central Unverstes (No. CDJXS08226). References []. H. Gang and A. Amr, A robust elastc and partal matchng metrc for face recognton, n Proceedngs of the 2 th Internatonal Conference on Computer Vson, September 2009, Kyoto, Japan, pp [2]. X. Wang and X. ang, A unfed frameork for subspace face recognton, IEEE ransactons on Pattern Analyss and Machne Intellgence, Vol. 26, No. 9, 2004, pp [3]. C. R. Rao, he utlzaton of multple measurements n problems of bologcal classfcaton, Journal of the Royal Statstcal Socety Seres b-statstcal Methodology, Vol. 0, 948, pp [4].. Ahonen, A. Hadd and M. Petkanen, Face descrpton th local bnary patterns: applcaton to face recognton, IEEE ransactons on Pattern Analyss and Machne Intellgence, Vol. 28, No. 2, 2006, pp [5]. C. G. Zhu and R. S. Wang, Local multple patterns based multre soluton gray-scale and rotaton nvarant texture classfcaton, Informaton Scences, Vol. 87, 202, pp [6]. X. an and B. rggs, Enhanced local texture feature sets for face recognton under dffcult lghtng condtons, IEEE ransactons on Image Processng, Vol. 9, No. 6, 200, pp [7]. H. Chen, Y. Y. ang and B. Fang, A mult-layers contrast analyss method for texture classfcaton based on LBP, Internatonal Journal of Pattern Recognton and Artfcal Intellgence, Vol. 25, No., 20, pp [8]. J. Lu, K. N. Platanots and A. N. Venetsanopoulos, Face recognton usng LDA-based algorthms, IEEE ransactons on Neural Netorks, Vol. 4, No., 2003, pp [9]. H. Yu and J. Yang, A drect LDA algorthm for hghdmensonal data: Wth applcaton to face recognton, Pattern Recognton, Vol. 34, No. 0, 200, pp

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