Soft Computing Based Range Facial Recognition Using Eigenface

Transcription

1 Soft Computig Based Rage Facial Recogitio Usig Eigeface Yeug-Hak Lee, Chag-Wook Ha, ad Tae-Su Kim School of Electrical Egieerig ad Computer Sciece, Yeugam Uiversity, 4- Dae-dog, Gyogsa, Gyogbuk, South Korea {aaturu, Departmet of Digital Electroic Egieerig, Kyugwoo Uiversity, 55 Iduk-ri, Sadog-myu, Kumi, Kyugbuk, South Korea Abstract. The depth iformatio i the face represets persoal features i detail. I particular, the surface curvatures extracted from the face cotai the most importat persoal facial iformatio. These surface curvature ad eigeface, which reduce the data dimesios with less degradatio of origial iformatio, are collaborated ito the proposed 3D face recogitio algorithm. The pricipal compoets represet the local facial characteristics without loss for the iformatio. Recogitio for the eigeface referred from the maximum ad miimum curvatures is performed. The ormalized facial images are also cosidered to ehace the recogitio rate. To classify the faces, the cascade architectures of fuzzy eural etworks, which ca guaratee a high recogitio rate as well as parsimoious kowledge base, are cosidered. Experimetal results o a 46 perso data set of 3D images demostrate the effectiveess of the proposed method. Itroductio Today s computer eviromets are chagig because of the developmet of itelliget iterface ad multimedia. To recogize the user automatically, people have researched various recogitio methods usig biometric iformatio figerprit, face, iris, voice, vei, etc []. I a biometric idetificatio system, the face recogitio is a challegig area of research, ext to figerpritig, because it is a o-touch style. For visible spectrum imagig, there have bee may studies reported i literature []. But the method has bee foud to be limited i their applicatio. It is iflueced by lightig illumiace ad ecouters difficulties whe the face is agled away from the camera. These factors cause low recogitio. To solve these problems a computer compay has developed a 3D face recogitio system [][3]. To obtai a 3D face, this method uses stereo matchig, laser scaer, etc. Stereo matchig extracts 3D iformatio from the disparity of pictures which are take by cameras. Eve though it ca extract 3D iformatio from ear ad far away, it has may difficulties i practical use because of its low precisio. 3D laser scaers extract more accurate depth iformatio about the face, ad because it uses a filter ad a laser, it has the advatage of ot beig ifluece by the lightig illumiace whe it is agled away from the cam- V.N. Alexadrov et al. (Eds.): ICCS 006, Part IV, LNCS 3994, pp , 006. Spriger-Verlag Berli Heidelberg 006

2 Soft Computig Based Rage Facial Recogitio Usig Eigeface 863 era. A laser scaer ca measure the distace, therefore, a 3D face image ca be reduced by a scalig effect that is caused by the distace betwee the face ad the camera [4][5]. Broadly speakig the two ways to establish recogitio employs the face feature based approach ad the area based approach [5]-[8]. A feature based approach uses feature vectors which are extracted from withi the image as a recogitio parameter. A area based approach extracts a special area from the face ad recogizes it usig the relatioship ad miimum sum of squared differece. Face recogitio research usually uses dimesioal images. Recetly, the 3D system becomes cheaper, smaller ad faster to process tha it used to be. Thus the use of 3D face image is ow beig more readily researched [3][9]-[]. May researchers have used 3D face recogitio usig differetial geometry tools for the computatio of curvature [9]. Hiromi et al. [0] treated 3D shape recogitio problem of rigid freeform surfaces. Each face i the iput images ad model database is represeted as a Exteded Gaussia Image (EGI), costructed by mappig pricipal curvatures ad their directios. Gordo [] preseted a study of face recogitio based o depth ad curvature features. To fid face specific descriptors, he used the curvatures of the face. Compariso of the two faces was made based o the relatioship betwee the spacig of the features. Lee ad Milios [3] extracted the covex regios of the face by segmetig the rage of the images based o the sig of the mea ad Gaussia curvature at each poit. For each of these covex regios, the Exteded Gaussia Image (EGI) was extracted ad the used to match the facial features of the two face images. Oe of the most successful techiques of face recogitio as statistical method is pricipal compoet aalysis (PCA), ad specifically eigefaces [4][5]. I this paper, we itroduce ovel face recogitio for eigefaces usig the curvature that well presetig persoal characteristics ad reducig dimesioal spaces. Moreover, the ormalized facial images are cosidered to improve the recogitio rate. Neural etworks (NNs) have bee successfully applied to face recogitio problems [6]. However, the complexity of the NNs icreases expoetially with the parameter values, i.e. iput umber, output umber, hidde euro umber, etc., ad becomes umaageable [7]. To overcome this curse of dimesioality, the cascade architectures of fuzzy eural etworks (CAFNNs), costructed by the memetic algorithms (hybrid geetic algorithms) [8], are applied to this problem. Face Normalizatio The ose is protruded shape ad located i the middle of the face. So it ca be used as the referece poit, firstly we tried to fid the ose tip usig the iterative selectio method, after extractio of the face from the 3D face image [0]. Usually, face recogitio systems suffer drastic losses i performace whe the face is ot correctly orieted. The ormalizatio process proposed here is a sequetial procedure that aims to put the face shapes i a stadard spatial positio. The processig sequece is paig, rotatio ad tiltig [].

3 864 Y.-H. Lee, C.-W. Ha, ad T.-S. Kim 3 Surface Curvatures For each data poit o the facial surface, the pricipal, Gaussia ad mea curvatures are calculated ad the sigs of those (positive, egative ad zero) are used to determie the surface type at every poit. The z(x, y) image represets a surface where the idividual Z-values are surface depth iformatio. Here, x ad y is the two spatial coordiates. We ow closely follow the formalism itroduced by Peet ad Sahota [9], ad specify ay poit o the surface by its positio vector: R ( x, y) = xi + yj + z( x, y) k () The first fudametal form of the surface is the expressio for the elemet of arc legth of curves o the surface which pass through the poit uder cosideratio. It is give by: where I + = ds = dr dr = Edx + Fdxdy Gdy () z E = +, x z z F =, x y z G = + (3) y The secod fudametal form arises from the curvature of these curves at the poit of iterest ad i the give directio: where II + = edx + fdxdy gdy (4) ad z z z e = Δ, f = Δ, g = Δ (5) x x y y Δ = ( / EG F ) (6) Castig the above expressio ito matrix form with; V dx = dy, A E F = F G, e f B = f g (7) the two fudametal forms become: t t I = V AV I = V BV (8) The the curvature of the surface i the directio defied by V is give by: t V BV k = (9) t V AV

4 Soft Computig Based Rage Facial Recogitio Usig Eigeface 865 Extreme values of k are give by the solutio to the eigevalue problem: ( B ka) V = 0 (0) or e ke f kf f kf g kg = 0 () which gives the followig expressios for k ad k, the miimum ad maximum curvatures, respectively: k { = ge Ff + Ge [( ge + Ge Ff ) 4( eg f )( EG F )] / }/ ( EG F ) () k { = ge Ff + Ge + [( ge + Ge Ff ) 4( eg f )( EG F )] / }/ ( EG F ) (3) Here we have igored the directioal iformatio related to k ad k, ad chose k to be the larger of the two. For the preset work, however, this has ot bee doe. The two quatities, k ad k, are ivariat uder rigid motios of the surface. This is a desirable property for us sice the cell uclei have o predefied orietatio o the slide (the x y plae). The Gaussia curvature K ad the mea curvature M is defied by K =, ( )/ k k M = k k (4) which gives k ad k, the miimum ad maximum curvatures, respectively. It turs out that the pricipal curvatures, k ad k, ad Gaussia are best suited to the detailed characterizatio for the facial surface, as illustrated i Fig.. For the simple facet model of secod order polyomial of the form, i.e. a 3 by 3 widow implemetatio i our rage images, the local regio aroud the surface is approximated by a quadric z ( x, y) = a + a x + a y + a y + a x + a y + a xy (5) ad the practical calculatio of pricipal ad Gaussia curvatures is extremely simple. 4 Eigeface 4. Computig Eigefaces [4] Cosider face images of size N by N, extracted cotour lie value. These images ca be thought as a vector of dimesio N, or a poit i N dimesioal space. A set of images, therefore, correspods to a set of poits i this high dimesioal space. Sice facial images are similar i structure, these poits will ot be radomly distributed, ad therefore ca be described by a lower dimesioal subspace. Pricipal compoet aalysis gives the basis vectors for this subspace. Each basis vector is of legth N, ad is the eigevector of covariace matrix correspodig to the origial face images.

5 866 Y.-H. Lee, C.-W. Ha, ad T.-S. Kim (a) (b) (c) (d) (e) (f) Fig.. Six possible surface type accordig to the sig of pricipal curvatures for the face surface; (a) cocave (pit), (b) covex (peak), (c) covex saddle, (d) cocave saddle, (e) miimal surface, (f) plae Let Γ, Γ,, Γ be the traiig set of face images. The average face is defied M by M Ψ = Γ (6) M = Each face differs from the average face by the vector Φi = Γ Ψ. The covariace matrix C = M M = Φ Φ has a dimesio of N x N. Determiig the eigevectors of C for typical size of N is itractable task. Oce the eigefaces are created, idetificatio becomes a patter recogitio task. Fortuately, we determie the eigevectors by solvig a M by M matrix istead. 4. Idetificatio The eigefaces spa a M-dimesioal subspace of the origial N image space. The M sigificat eigevectors are chose as those with the largest correspodig eigevalues. A test face image Γ is projected ito face space by the followig operatio: ω = T u ( Γ Ψ), for =,, M, where u is the eigevectors for C. The weights ω T from a vector Ω = [ ω ω... ω M '] which describes the cotributio of each eigeface i represetig the iput face image. This vector ca the be used to fit the test image to a predefied face class. A simple techique is to use the Euclidia distaceε = Ω Ω, where Ω describes the th face class. I this paper, we used the cascade architectures of fuzzy eural etworks to compare with the distace as described ext chapter. 5 Cascade Architectures of Fuzzy Neural Networks (CAFNNs) As origially itroduced i [7], the structure of the CAFNNs is the cascade combiatio of the logic processors (LPs) which cosist of fuzzy euros. The sequece of relevat iput subset ad the coectios were optimized by memetic algorithms i [8] to costruct parsimoious kowledge base, but accurate oe. As illustrated i [8], the memetic algorithms are more effective tha the optimizatio sceario i T (7)

6 Soft Computig Based Rage Facial Recogitio Usig Eigeface 867 [7]. Therefore, the optimizatio sceario i [8] will be cosidered i this approach. For more details about the CAFNNs ad its optimizatio, please refer to [7][8]. To apply the CAFNNs to classificatio problems, the output (class) should be fuzzified as biary. For example, if we assume that there are 5 classes (5 persos) i the data sets, the umber of output crisp set should be 5 that are distributed uiformly. If the perso belogs to the d-class, the Boolea output ca be discretized as I this classificatio problem, the wier-take-all method is used to decide the class of the testig data set. This meas that the testig data are classified as the class which has the biggest membership degree. 6 Experimetal Results I this study, we used a 3D laser scaer made by a 4D culture to obtai a 3D face image. First, a laser lie beam was used to strip the face for 3 secods, thereby obtaiig a laser profile image, that is, 80 pieces ad o glasses. The obtaied image size was extracted by usig the extractio algorithm of lie of ceter, which is 640 by 480. Next, calibratio was performed i order to process the height value, resamplig ad iterpolatio. Fially, the 3D face images for this experimet were extracted, at 30 by 30. A database is used to compare the differet strategies ad is composed of 9 images (two images of 46 persos). Of the two pictures available, the secod photos were take at a time iterval of 30 miutes. Table. The compariso of the recogitio rate (%) Best Best5 Best0 Best5 k k CAFNN( ormalized) CAFNN k-nn CAFNN (ormalized) CAFNN k-nn From these 3D face images, fidig the ose tip poit, usig cotour lie threshold values (for which the fiducial poit is ose tip), we extract images aroud the ose area. To perform recogitio experimets for extracted area we first eed to create two sets of images, i.e. traiig ad testig. For each of the two views, 46 ormalexpressio images were used as the traiig set. Traiig images were used to geerate a orthogoal basis, as described i sectio 3, ito which each 3D image i traiig data set is projected i sectio 4. Testig images are a set of 3D images extracted local area we wish to idetify.

7 868 Y.-H. Lee, C.-W. Ha, ad T.-S. Kim Oce the data sets have bee extracted with the aid of eigeface, the developmet procedure of the CAFNNs should be followed for the face recogitio. The used parameter values are the same as [8]. Sice a geetic algorithm is a stochastic optimizatio method, te times idepedet simulatios were performed to compare the results with the covetioal classificatio methods, as described i Table ad Fig.. I Table ad Fig., the results of the CAFNN are averaged over te times idepedet simulatios, ad subsequetly compared with the results of the covetioal method (k-earest eighborhood: k-nn). Also, the ormalized facial images were cosidered to geerate the curvature-based data set. As ca be see from Table ad Fig., the recogitio rate is improved by usig ormalized facial images. 00 k 00 k Recogitio rate (%) CAFNN (ormalized) 50 CAFNN k-nn Raked best Recogitio rate (%) Raked best CAFNN (ormalized) CAFNN k-nn Fig.. The recogitio results usig eigefaces for each area: (a) k, (b) k 7 Coclusios The surface curvatures extracted from the face cotai the most importat persoal facial iformatio. We have itroduced, i this paper, a ew practical implemetatio of a perso verificatio system usig the local shape of 3D face images based o eigefaces ad CAFNNs. The uderlyig motivatios for our approach origiate from the observatio that the curvature of face has differet characteristic for each perso. We foud the exact ose tip poit by usig a iterative selectio method. The lowdimesioal eigefaces represeted were robust for the local area of the face. The ormalized facial images were also cosidered to improve the recogitio rate. To classify the faces, the CAFNNs were used. The CAFNNs have reduced the dimesioality problem by selectig the most relevat iput subspaces too. Experimetal results o a group of face images (9 images) demostrated that our approach produces excellet recogitio results for the local eigefaces. From the experimetal results, we proved that the process of face recogitio may use low dimesio, less parameters, calculatios ad less same perso images (used oly two) tha earlier suggested. We cosider that there are may future experimets that could be doe to exted this study.

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