Human Face Recognition Using Radial Basis Function Neural Network

Transcription

1 Huan Face Recognton Usng Radal Bass Functon eural etwor Javad Haddadna Ph.D Student Departent of Electrcal and Engneerng Arabr Unversty of Technology Hafez Avenue, Tehran, Iran, 594 E-al: FAX: (+98) Kar Faeze Prof. Departent of Electrcal and Engneerng Arabr Unversty of Technology Hafez Avenue, Tehran, Iran, 594 E-al: FAX: (+98) Abstract A neural networ based face recognton syste s presented n ths paper. The syste conssts of two an procedures. The frst one s face features extracton usng Pseudo Zerne Moents (PZM) and the second one s face classfcaton usng Radal Bass Functon (RBF) neural networ. In ths paper, soe new results on face recognton are presented. Sulaton results ndcate that PZM wth RBF neural networ produce hgher detecton and lower ssng rates than several exstng state-of-theart face detecton systes, wth an average false detecton rate. Also experental results show that hgh order degrees of PZM contan very useful nforaton about face recognton process. The proposed syste has been appled on face database of Olvett Research Laboratory (ORL) wth very good results. Introducton Autoatc face recognton has receved sgnfcant attenton fro the countes of coputer vson, neural networ and sgnal processng []. The nterest s otvated by applcatons such as access control systes, odel-based vdeo codng, crnal dentfcaton and authentcaton n secure syste le coputer or ban teller achnes. Although any face recognton by huan bengs and achnes, t s stll dffcult to desgn an autoatc syste for the tas because n real world, llunaton, coplex bacground, vsual angle and facal expresson for face ages are hghly varable [,]. Several ethods have been proposed for face detecton, ncludng graph atchng [3], neural networs [4,5,6], and also geoetrc feature based [7]. Generally n the procedure of achne face recognton two ssues are central: () what features can be used to represent a face under envronent changes?, and () how to classfy a new face age, based on the chosen features, nto one of the possbltes. In frst ssue, any successful face feature extracton procedures have been presented and developed. In ths paper we used PZM based on central oents as face features. The advantages of consderng PZM are that they are shft, rotaton and scalng nvarant and very robust aganst nose. Also sulaton results ndcate that these features are very robust aganst change of face expresson. In the other hand, PZM transfor the nput age nto very low densonal features vector, ths optzaton of feature set allows the desgner to focus on coplex and correct classfer. In second ssue, classfer plays an essental role n the face detecton process. In any face recognton systes, the earest eghbor s wdely used for classfcaton. eural networbased () classfer has been proven to have any advantages for classfcaton such as ncredble generalzaton and good learnng ablty. The approach taes the features vector as nput and tranng a networ to learn a coplex appng for classfcaton and usng of the for classfcaton avods the need for the splfcaton of the classfer. In ths wor, face

2 classfer s pleented va RBF neural networ to tae advantage of approaches. The organzaton of ths paper s as follow: secton descrbes the face feature extracton ethod. Face classfer technque s presented n secton 3. Experental results are shown n secton 4 for coparng our syste wth other systes. Face features extracton The nvarance propertes of oents of ages have receved consderable attenton n recent years. The ter nvarant denotes an age feature reans unchanged f that age undergoes one or a cobnaton of the changes such as: change of sze (scale), change of poston (translaton), change of orentaton (rotaton), and reflecton. Above propertes of oents, occurred that oents have been proposed as pattern senstve features n classfcaton and recognton applcatons. In ths paper Pseudo Zerne Moents (PZM) s proposed as facal features n face recognton syste. PZM as statstcal features are very ease of use, coputng and extracton, also the advantage of PZM s that they are very robust aganst nose. Also sulaton results ndcates that PZM as face features are very robust aganst change of face expresson.. Pseudo Zerne Polynoals and Moents Zerne and Pseudo Zerne polynoals are well nown and wdely used n the analyss of optcal systes. Pseudo Zerne Polynoals are an orthogonal set of polynoals of followng for: y Vn(x,y) = Rn(x, y)exp(jtan ( )) () x Where Vn(x, y) denotes a coplete set of coplex-valued polynoals, n two real varables x and y, whch are orthogonal n the nteror of the unt crcle, n represents the degree of the polynoals, represents ts angular dependence, Rn (x, y) represents a real-valued set of polynoals nsde the unt crcle as follow: S R n n s n (x,y) Sn,, s(x + y ) n,,s =, n () s= 0 S (n + S)! ( ) S!(n S)!(n S + )! = (3) The Pseudo Zerne Moents are defned as follow: n + * PZMn = f(x,y)v n(x, y) (4) π x y Fro the above equatons, t s obvously * deterned that PZMn, = PZM n, and these oents only coputed for postve value of.. PZM based on Central Moents For reanng shft nvarant property of oents, we used central and radal oents for coputng PZM. Ths done as follows: n+ PZM = π K b ( ) CM n n Sn,, s ( n s) evens, = 0 ( )( ) j + a b, a + b a b n+ + π n a= 0 b= 0 d d ( a )( b ) Sn,, s ( n s) odd, s= 0 a= 0 b= 0 K b ( a )( b )( j ) RMd + a b, a + b (5) Where = (n s ) / and d = (n s + ) /, CM, j s the central oents and RM, j s the radal oents. For each face age these oents are coputed as face features. 3 RBF -based Classfer RBF neural networs have recently attracted extensve research nterests n county of neural networs because: () they are unversal approxatons, () they have very copact topology, (3) ther learnng speed s very fast because of local-tuned neurons, (4) they possess the best approxaton property. In ths paper, RBF neural networ s used as classfer n face detecton syste. 3. Structure of RBF eural etwor Fgure s showed the basc structure of RBF neural networs. x x n w (, ) w (,) Fgure: RBF neural networ y (x) y (x)

3 The output of the th RBF unt s as follow: x c R (x) = R ( ), =,,..., n (6) σ where x s an nput feature vector wth r densonal, c s a r-densonal vector naed center of RBF node, n s the nuber of hdden node. Typcally, R (x) s chosen as a Gaussan functon as follow: x c R (x) exp[ σ = (7) The jth output of RBF neural networ s: j y ( x) = b( j) + R ( x) w ( j, (8) = ] ) Where w ( j, ) s the weght of the th RBF node to the jth output node and b ( j) s the bas of the jth output. The bas s not consdered n ths n order to reduce networ coplexty. Henc: j y ( x) = R ( x) w ( j, (9) = ) 3. Classfer Desgn For desgnng classfer based on RBF neural networ, we set the nuber of nput nodes n nput layer of equal to the nuber of features that deterned based on nuber of PZM. The nuber of nodes n output layer s set to the nuber of age classes. The selectng RBF nodes we do followng steps: ) We ntally set the nuber of RBF nodes equal to outputs. ) For each class s, s=,,,, the center of RBF nodes s selected as the ean value of the saple feature belongng to the class,.e. C p ( r, ) = = (0) where p ( r, ) s the th saple wth r- denton(nuber of PZM s r) belongng to class and s the nuber of age n class. 3) For any class, copute the dstance d fro the ean to the furthest pont p f belongng to class : d = p C () f 4) For any class, copute the dstance dc (, j) between the ean of class and the ean of other classes as follow: j dc(, j) = C C, j=,.s, j Then fnd d n (, l) = n( dc(, j)) and chec the relatonshp between d n (, l) and d, d. If d + d d (, l) then class l l n has no overlappng wth other classes, otherwse class has ovrlappng wth other classes and sclassfcatons ay occur n ths case. 5) For all the tranng data, chec how data are classfed. 6) Repeat step to 5 untll all the tranng saple patterns are classfed satsfactorly. 7) The ean values of the classes are selected as the centers of RBF nodes. In ths paper, a hybrd learnng algorth, whch cobnes the gradent ethod and Lnear Least Squared (LLS) ethod to adjust the paraeters s used that presented n [8]. 4 Sulaton Results Experental Studes are carred out on the ORL (Olvett Research Laboratory) database age of Cabrdge Unversty. In ths database the total nuber of ages for each person s 0. one of the 0 saples are dentcal to each other. They vary n poston, rotaton, scale and expresson. The change n orentaton has been accoplshed by rotatng the person a few degrees (axu 0 degree) n the sae plane, and also each person has changed hs face expresson n each 0 saples. The change n scale has been acheved by changng the dstance between the person and the vdeo caera. Each age was dgtzed and presented by *9 pxel array whose gray levels ranged between 0 and 55. One saple of these ages s shown n fgure. Le the experent of [9] and [0] we also use a database of 400 ages of 40 ndvduals. A total of 00 ages are used to tran and another 00 are used to test, where each person has 5 ages. In feature extracton step wth Pseudo Zerne Moents, sulaton has been done n three step based on degree of the Pseudo Zerne Polynoals (n). Experental results are shown n Table and Table respectvely. In Table tranng data used as tranng ages and testng data as testng ages and n Table testng data used as tranng ages and tranng data as testng ages.

4 We also defne the average error rate as follow: E = ave = () t Where s the nuber of experental runs, each beng perfored on rando partton of the database nto sets, s the nuber of sclassfcaton for the th run, and t s the nuber of total testng ages for each runs. The coparson wth Convolutonal eural etwor (C) approach [9] and earest Feature Lne (FL) approach [0] usng the sae ORL database n ters of average error rate s shown n Table 3. Table 3: Error rate n dfferent ethods Methods E ave % C 3.83 FL 3.5 Our Method. The lowest error rate acheved by our ethod s based on these condton: =3, uber of PZM s. The way to partton the tranng set and query set s the sae as that of [9] and [0]. For FL ethod, the best error rate s the average of the error rates obtaned on the condton: =4, nuber of features s 40, and query set s the sae as that of [9] and [0]. For FL ethod, the best error rate s the average of the error rates obtaned on the condton: =4, nuber of features s 40, whereas the average error rate obtaned by C n Table 3 s based on =3. 5- References [] R. Chellappa, C.L.Wlson, and S.Srohey,"Huan and Machne Recognton of Faces: A Survey." Proceedng of the IEEE, 83(5): ,May 995. [] J. Daugan, "Face and Gesture Recognton: Overvew." IEEE Trans. on Pattern Analyss and Machne Intellgence, Vol. 9, o. 7, pp , July 997. [3] L. Wsott, J. Fellous,. Kruger and C.Malsburg, "Face Recognton by Elastc Bunch Graph Matchng." IEEE Trans. on Pattern Recognton and Machne Intellgence, Vol 9, o. 7, pp , July 997. [4] S.Z. L and J. Lu, "Face Detecton by eural Learnng." Proceedng of ICICS-99, Sngapore, Dec. 7-0, 999. [5] E. Osuna, R. Freund and F. Gros, "Tranng Support Vector Machnes: An Applcaton to Face Detecton." In CVPR, pp , 997. [6] H. A. Rowley, S. Baluja and T. Kanade, "eural etwor based Face Detecton." IEEE Trans. On Pattern Recognton and Machne Intellgence, Vol. 0, o., pp. 3-8, 998. [7] G.Z. Yang and T. S. Huang, "Huan Face Detecton n Coplex Bacground.", Pattern Recognton, 7: 53-63, 994. [8] J-S. R. Jang, "AFIS: Adaptve- etwor-based Fuzzy Inference Syste," IEEE Trans. Syst. Man. Cybern., Vol. 3, o. 3, pp , 993. [9] S. Lawrence, C. L. Gles, A. C. Tso and A. D. Bac, "Face Recognton: A Convolutonal eural etwors Approach," IEEE Trans. on eural etwors, Specal Issue on eural etwors and Pattern Recognton, Vol. 8, o., pp. 98-3, 997. [0] S. Z. L and J. Lu. "Face Recognton Usng the earest Feature Lne Method," IEEE Trans. eural etwors, Vol. 0, pp , 999.

5 Table : Error rate and paraeter Features Tranng Test o. of Error PZM Order RMSE() PZM Epochs Msclassfcaton rate() 5 0 n 6 30 ~ ~ 0.0 % 4 6 n 8 0 ~ ~ % 9 n 0 5 ~ 0.04 ~ ()RMSE : Root Mean Squared Error () Error rate = uber of sclassfcaton / uber of total testng pattern Table : Error rate and paraeters Features Tranng Test o. of Error PZM Order RMSE() PZM Epochs Msclassfcaton rate 5 0 n 6 50 ~ ~ % 4 6 n 8 45 ~ ~ % 9 n 0 30 ~ ~ % Fgure: Saple of Face ages on ORL database

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