Research Article Applications of PCA and SVM-PSO Based Real-Time Face Recognition System

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1 Hindawi Publising Corporation atematical Problems in Engineering, Article ID , 12 pages ttp://dx.doi.org/ /2014/ Researc Article Applications of PCA and SV-PSO Based Real-Time Face Recognition System ing-yuan Sie, Juing-Sian Ciou, Yu-Cia Hu, and Kuo-Yang Wang Department of Electrical Engineering, Soutern Taiwan University of Science and Tecnology, Tainan City 710, Taiwan Correspondence sould be addressed to Juing-Sian Ciou; Received 25 February 2014; Accepted 23 April 2014; Publised 13 ay 2014 Academic Editor: Rui u Copyrigt 2014 ing-yuan Sie et al. Tis is an open access article distributed under te Creative Commons Attribution License, wic permits unrestricted use, distribution, and reproduction in any medium, provided te original work is properly cited. Tis paper incorporates principal component analysis (PCA) wit support vector macine-particle swarm optimization (SV- PSO) for developing real-time face recognition systems. Te integrated sceme aims to adopt te SV-PSO metod to improve te validity of PCA based image recognition systems on dynamically visual perception. Te face recognition for most umanrobot interaction applications is accomplised by PCA based metod because of its dimensionality reduction. However, PCA based systems are only suitable for processing te faces wit te same face expressions and/or under te same view directions. Since te facial feature selection process can be considered as a problem of global combinatorial optimization in macine learning, te SV- PSO is usually used as an optimal classifier of te system. In tis paper, te PSO is used to implement a feature selection, and te SVs serve as fitness functions of te PSO for classification problems. Experimental results demonstrate tat te proposed metod simplifies features effectively and obtains iger classification accuracy. 1. Introduction Tere are numerous approaces tat develop useful scemes to detect and recognize te features of uman faces in recent years. Tey are used to filter te background and detect te faces blocks from a digital image firstly, ten to determine teir features and generate caracteristic vectors, to localize te faces continuously, and to recognize te main face finally. In general, te approaces of uman face image processing consist of two fields as face detection and face recognition. For uman-robot interaction, to recognize faces is muc more difficult tan to detect faces. It is because te facial expression and features are cangeable and not easily recognized and predicted. Tere are two standard linear subspace projections of te low-resolution facial images [1],tePCAandtelinear discriminant analysis (LDA) [2], used to distinguis te different styles of images. Te PCA is basically a compression procedure based on linear projection tecniques on a subspace spanned by te principal eigenvectors (tose corresponding to te largest eigenvalues) of te input covariance matrix. Te LDA approac was proposed by Fiser firstly wic identifies directions in space along wic separation of te projections is maximized. Wile te LDA is not always superior to te PCA in terms of recognition accuracy, te PCA + LDA approac as been successfully applied in some face recognition applications. However, te PCA and/or LDA based facial recognition may fail if te facial samples are captured in different directions. Wile te face images are captured from different sigt depts and directions, te accuracy of te PCA based recognition will be reduced eavily. Tere are many face recognition metods provided to overcome suc problems, some focus on te feature extraction. How to use te smallest dimensions to replace te most representation s feature and classificationistemostimportantissueintispaper. Since te facial feature selection process can be considered as a problem of global combinatorial optimization in macine learning, te PSO-SV is usually used as an optimal classifier of te system. In te part of te classification, te PSOisusedtoimplementfeatureselections,andteSVs[3, 4] serve as fitness functions of te PSO for te classification

2 2 atematical Problems in Engineering problem. Te advantage of te SV in te multidimensional spaceistatitcanquicklyandcorrectlyclassifysamplesto findouttebestsupportvector[5]. Te PSO algoritm is a kind of imitation of birds clustering penomenon algoritm [6 9],andintispaper,tePSOwillbeissuedtocorrectte parameters of te SV so tat te image recognition process canbefasterandmorestable. Te rest of tis paper is organized as follows: in Section 2, te image detection sceme is described wic consists of smooting filter, connected position, and ellipse detection. Section 3 describes te face recognition system wic includes te adjustment of te dimensions, te PCA, and te PSO-SV classifier. Section 4, experimental results are presented to demonstrate te feasibility of te proposed sceme. Finally, some conclusions are made in Section Te Face Detection System In order to detect te face from an image, tere are several key steps necessarily processed. Te first is to detect te area of skin color; te second is to reduce te noise; te oters are to distinguis wic one or ones are te face by ellipse detection and to separate te face block from te image background. Figure 1 illustrates te flowcart of te proposed face detection sceme. Te images captured by te webcam in sequence will be sent to te face detection system firstly, and ten te area of te uman face is separated from te complex background by te skin-color detection. ext, te noise is going to be filtered by te noise reduction. Finally, te captured contours will aid in locating te position of te umanface.teblockofteumanfacewillonlyremainin teimageaftertefacedetection Skin-Color Detection. Te RGB image is always wit cromatismbecauseofcangeableilluminationineverycapture. For skin-color detection, a reliable color range defined as te skin-color is principal. Since te color values in RBG are so sensitive to varying illumination, most approaces adopt te color model of YCbCr replacing te RGB because te value Y is relative to luminance and te values of Cb and Cr are relative to croma. YCbCr color space can be regarded as a modified YUV color model. However, YCbCr is not an absolute color space wic is a way of encoding RGB information. In YCbCr color space, Y is te luma component; Cb and Cr represent te blueness and te redness croma components, respectively. Te transform defined in te ITU-R BT.601 standard for digital component video te YCbCr color space can be translated from te RGB color space by Y R 16 [ Cb] = [ ] [ G] + [ 128]. [ Cr] [ ] [ B] [ 128] (1) Te resultant Y is just between 16 and 235 because te values from 0 to 15 are called footroom and te values from 236 to 255 are called eadroom. Besides, in tis paper, te skincolor region of Cb calculated is between 71 and 127; te skincolorregionofcrisbetween130and170fromte150sample images. By te skin-color regions, te uman face block will be easily distinguised from te image according to te values of Cb and Cr. Te low-pass filter (LPF) was used to eliminate te small noises and connect te part of te incomplete image. Te LPFmakesteimageforfilteringbecomemoresmootand uniform. In general, te start of te mask is set to be at te top left pixel of te preprocess image, and it will scan te wole image from left to rigt. It is also referred to te neigboring 8 pixels for processing. Generally te sizes of te masks are 3 3, 5 5,and7 7. Te larger te mask, te larger te filtering effect, but te calculation becomes relatively large. Te 3 3mask was used for low-pass filtering in tis paper. Besides, te opening operation of te morpology is usually used to eliminate noises in an image. Te opening operation included two operands wit erosion and dilation. First, it will use te erosion for te binary image and ten use te dilation for its result. After tis procedure, te noises will be removed from te image. Te opening operation of te morpology can not only remove a part of te noise pixels of te binary image but also make more complete region of te skin-color. After finising te procedure of te noise reduction, te connected component labeling (CCL) was used to find te location of te uman face. Tis metod was mainly used to find te connected pixels of te same object in te image. It marks eac block by different labels and counts size, eigt, and widt of eac independent object in te image. Te 4- connected was used to label pixels in tis paper. It starts to scan te prelabeled binary image from top left. In te coordinates (x, y) of te pixel, determine te presence of 255 on a pixel before cecking te rigt (x + 1, y),left(x 1,y), top (x, y+1),andbottom(x, y 1),foranyoter255values.If yes, it will record its coordinates and te pixel is set to 0. Ten tereisterecursiveprocessofceckingalltepixelsfor presence of 255 valued pixels until none is present. Ten te groupwittemostnumberof255valuedpixelsissearced and labeled. Wile finising te recursive scanning of te image, te group objects for image labeling were calculated. Te biggest areaofteregionwasfoundfromallnumberedregions,tat is, te region of te uman face. Tis region was scanned to find te black background of te facial boundary. Ten te relative coordinates (X min, Y min )and(x max, X max )were employed, to capture te facial region from te original image. Te biggest region for labeling of te binary image is sown in Figure 2. Te Sobel edge detection [10] is used to detect te edge. For face detection, since tere are obvious differences between te background and te region of te skin color in te facial binary image, te edge detection usually employed te first derivative of te image to estimate te regional edge andwasusedtocalculatetesizeoftegradientforimage processing. Te Sobel edge detection employs te gray scale difference at te position of te edge and weigted te top and bottom, or left and rigt, to detect te edge of te object.

3 atematical Problems in Engineering 3 Webcam oise reduction Image binarization Smooting filter Skin-color detection Color space transformation Luminance compensation Skin-color segmentation Face localization Opening operation Connected component labeling Sobel edge detection Yes o Captured te uman face Ellipse detection Figure 1: Face detection system flowcart. Figure 2: Te biggest region for labeling of te binary image. Figure 3: Te result of te Sobel edge detection. Troug te Sobel edge detection processing, te region of tefaceissowninfigure 3. Since te size of a uman face is similar to te elliptical model wit te ratio of te vertical axis and te orizontal axis as approximately 1.2 : 1, tus, an ellipse mask is used to locate te uman face, wic marks a boundary to extract te edge of te image. After te edge detection, te region tat resembles more te sape of an ellipse will provide te position of te face. Te center of te ellipse wit te use of its circumference and te lengt of its axis can elp to determine its position, sape, and size. In order to meet te size of te facial cange, te elliptical model must adjust te ratio of te lengt of te axis to scan te image in real time. Terefore, we designed an elliptical model tat determines te coordinates of te center of te ellipse (x 0,y 0 ) wit x as te radius of te orizontal axis and y fortatofteverticalaxis. Face detection is ten finised after te ellipse detection processing. Te ellipse detection cooperates wit te connected component labeling to find te facial region. Te locations of te detected faces in te original image and te binary image are sown in Figures 3 and 4, respectively. ext, te unnecessary region outside of te elliptical range was

4 4 atematical Problems in Engineering Webcam Figure 4: Face location of te binary image. Image preprocessing Face recognition Face detection Captured face images Image normalization PCA based training Training database Feature extraction Feature weigt vector Database of faces SV classification PSO parameter optimization Recognition results Figure 6: Te sceme of te face recognition system. Figure 5: Te result of te captured facial image. removed. Tis procedure will elp in eliminating te image of te neck and locate te facial region. Te relative coordinate wasusedtocapturetefaceforteoriginalimage.teresult oftecapturedfacialimageissowninfigure Te Face Recognition System 3.1. Description of te Face Recognition System. Te face recognition processing will be executed after finising face detection. However, since te dimensions of te facial images arenottesame,tenormalizationprocessfortefacial image becomes important. Te processed image to be analyzed contains te same information of te environment to make te dimensions of te facial regions te same for eac face. After te image normalization processing, tecapturedimageservesasteinputdataforteface recognition system. And ten, principal component analysis is utilized to calculate te feature. Tis metod could reduce te dimension of te image and save computation time. It could surmount te problems of te canged expression or presence of glasses on te face, because it treats te wole face as a feature. Te weigting vectors of te processed facial image will be calculated by using PCA. All te weigting vectors are collectedtobuildtedatabasefortefacerecognitionsystem. Te user identity could be determined by te support vector macine tat compares te current image wit te image in te database. Tis way is a fast and accurate classifier tat can be applied to classification and comparison applications. It sows tat te velocity and accuracy of te face recognition system can be increased troug te support vector macine processed. At te same time, te particle swarm optimization (PSO) is used to design te parameter of te support vector macine. Tis metod makes te face recognition system complete and quick. Te face recognition system flowcart proposedintispaperisassowninfigure Image ormalization. Acieving ig recognition rate for te face recognition system does not only need a good recognition algoritm but also needs a robust face image for te preprocessing of te image. It could reduce te differenceforeacinputimageandcangedeacimageto te same dimension for te database. Terefore te bilinear interpolation is used to amend te image tat detects te face wit te size of te pixel at Trougtebilinear interpolation processing, feature extraction and recognition are executed for te facial image.

5 atematical Problems in Engineering 5 A E B y P 1 x P 2 vertical distance of P 1 corresponding to te four neigboring pixels. If te distance from pixel to pixel is one unit as assumed in tis paper, it can be represented by 0<xand y< 1, ten te adjusted facial dimension is sown in Figure 8. C F D Figure 7: Te diagram of te bilinear interpolation. Te relation of te pixel coordinate between te original imageandfinalimageisnottesameastegeneralimage processing wen te image is zoomed. A pixel of te original image could project into many pixels for te final image, wen te images are zoomed in. Similarly, many pixels of te original image could project onto a pixel for te final image, wen te images are zoomed out. Terefore, te final image must searc for a pixel to substitute te original image. And wit tis in mind, te interpolation process is needed to calculate te pixel of te final image; oterwise te finalimagewouldproducetremendousdistortion.actually te interpolation used discrete samplings to calculate te continuous function wic passes troug te coordinates of tesesamplesandtenemploytisfunctiontofindtevalue of nonsamplings. Te image zooming could define te signal resamplingbecauseteimagewasasignaltatiscomposed of te two-dimensional discrete sampling. Ten te bilinear interpolation adopted te four neigboring pixels to calculate te new pixel. Te diagram of te bilinear interpolation is sown in Figure 7. In order to obtain te pixel P 2 as a projection of te original image, P 2 is supposed to project onto P 1 ;tuste four neigboring pixels (A, B, C, D) were used to calculate te distances between P 1 and te coordinates of four pixels. If te four pixels are closer to P 1 ten te contribution is large for P 2. Conversely te influence is smaller if te distance is farter. Terefore te effect is inversely proportional to te distance. In fact, te bilinear interpolation calculated te linear interpolation continuously for tree times. Te first interpolation was calculated to be te influence between two points (A, B) and P 2 in order to obtain pixel E. Te equation of te first interpolation is expressed in E = (1 x) A +xb. (2) And ten te second interpolation was calculated using teinfluencebetweentwopoints(c,d)andp 2 to obtain pixel F. Te equation of te second interpolation is expressed in 3.3. Principal Component Analysis. After normalization, if te face recognition is directly implemented it would cost a lotofcomputingtime.tisisduetotefacttatallteinformation of te original image is spread in eac pixel; ence, tere is te need to reduce te dimensions of te image. Andten,tesuitablefeaturesarecapturedtoexpressalot of information in lower dimensions. It could reduce many variations for data wit te use of PCA and applying some mutually independent linear combinations to substitute for te original data. Troug te linear combination computing, te difference of te variation was te large influence of te data. Tis analysis made data to display te biggest individual differences. Below is te process for implementing PCA. If tere were facial images as te training samples te original feature parameters were {X 1,X 2,...,X }.Te objective of PCA was order to find te linear transformation matrix P wit a size of n m. It extracts feature parameter X k of te original n dimension to transform te more representative of te feature parameter Z k tat te dimension was m(m n). Te equation of te transformation expressed in Z k =P T X k,,2,...,. (5) Before te transformation computing, te mean vector was X. After te transformation, te mean vector was Z expressed in Z = 1 k = Z 1 P T X k =P T ( 1 X k ) =P T X. (6) Ten te total scatter matrix was used to indicate te dispersion of all feature parameters tat were opposite to te mean vector X. Before te transformation computation, te total scatter matrix was S tx wic as a size of n n.te equation of te total scatter matrix S tx is expressed in S tx = (X k X) (X k X) T. (7) Troug (18) to(20), te total scatter matrix S tz can be obtainedavinga size ofm mafter te transformation. Te equation of te total scatter matrix S tz is expressed in F = (1 x) C +xd. (3) Finally, te tird interpolation was used to calculate te pixel of P 2 for two points (E, F). Te equation of te tird interpolation is expressed in P 2 = (1 y) E +yf, (4) were x represents te relative orizontal distance of P 1 in relation to te four neigboring pixels; y is te relative S tz = = =P T ( (Z k Z) (Z k Z) T (P T X k P T X) (P T X k P T X) T (X k X) (X k X) T )P=P T S tz P. (8)

6 6 atematical Problems in Engineering (a) Te original image (b) Te image after facial dimension adjusting (80 100) Figure 8: Facial dimension adjusting. In order to increase te dispersion between te mean value and te feature parameters of te transformation, te transformation matrix P opt sould be calculated tat could make te maximization of S tz.teequationofte transformation matrix P opt is expressed in P opt = arg max P (PT S tz P). (9) According to te teory of linear algebra, te trace or te determinant can be used to express te element s distribution. Terefore, (9) couldberewrittenas P opt = arg max P tr (P T S tz P). (10) In (10), in order to limit te value of tr (P T S tz P) and avoid te occurrence of infinity, a limit condition as P T P=Iwas added for te transformation matrix P tat as a size of n m: F (P) =P T S tz P λ(p T P 1). (11) As follows, te value of F(P) is maximum wile te first derivative for P is zero: F (P) P =2S t Z P 2λP = 0. (12) Ten, (12) becomes(13) troug simplification using transposition: (S tz λi)p=0. (13) In (13), it needs to compute te eigenvectors of matrix S tz by composing te matrix for P. Te eigenvalues and te eigenvectorsaretespecialforminmatrixalgebraandits elements could be restructured in te matrix. In addition, te important information would be concentrated in te larger eigenvalue tat would correspond to te eigenvectors. Te advantages of PCA in face recognition can be divided into tree advantages. First, it could quickly and easily calculateteresult.second,pcacouldretaintelargest information of te projection data in te linear projection. Tird, PCA used te wole face to do feature extraction tat could overcome te presence of glasses and te canges of te facial expression. Below is te operational procedure of PCA. After normalization, number of facial images was trained using PCA. Te size of eac sample was matrix. ext, eac sample is rearranged as te augmented vector Γ wic as te size 2 1assownin(14). Γ 1,Γ 2,...,Γ represent te facial images processed. Eac facial sample corresponded to Γ, and te mean vector Ψ was calculated by te amount of Γ as expressed in Ψ= 1 Γ k. (14) Te mean vector Ψ is te mean face wic indicates te mutual parts of all face. And ten te mutual parts for facial images were deleted to igligt te different parts between tem. Terefore te different image vector of eac image was obtained as sown in φ k =Γ k Ψ,2,3,...,, (15) werein matrix A equals [φ 1,φ 2,φ 3,...,φ ] tat ad te size 2 and te covariance matrix C of all faces was defined as C= 1 φ k φ T k =AAT. (16)

7 atematical Problems in Engineering 7 Te eigenvalue λ k and te eigenvector u k of te matrix C are expressed in Cu k =λ k u k,2,3,..., 2, (17) were λ k = (1/) j=1 (ut k φ j) 2 and φ={φ 1,φ 2,...,φ }. Since te size of matrix A was 2,itmakestesize of matrix C be 2 2. For suc a large matrix calculating te eigenvalues and eigenvectors is time consuming. Tus, if te dimensions of te matrix could be reduced, it could effectively save calculation time. Terefore, te matrix A T A must be calculated first and te dimensions of te matrix must be reduced as to obtain te eigenvector V k wic expressed in A T AV k =μ k V k,2,3,..., 2. (18) Equation (18) multipliesby tematrixa to obtain AA T AV k =μ k AV k, (19) in wic AA T as te same eigenvalue and eigenvector wit A T A, because te matrix C equals AA T.Bycomparing(17) and (19), (20) can be obtained as follows: u k =AV k λ k =μ k. (20) By using (18), te matrix of A T A is used to calculate te eigenvector V k wic determines te eigenvalue u k.itis considered as an eigenface as expressed in u k = j=1 φ j V kj,,2,...,. (21) Te vector Γ 1,Γ 2,...,Γ of te individual facial image combined wit te corresponding eigenvector to build te feature space. And we calculate te weigt vector V from te feature space as expressed in Ω k =u T k (Γ Ψ) =ut k φv=[φ 1,φ 2,φ 3,...,φ ],2,3,...,. (22) Finally, eac training sample Γ i of te face is inputted to substitute te Γ of (22)andcalculateteeigenvectorV i in te feature space. Troug te computation, te matrix V will be taken as te database of te facial images after te training SV Based Classification for Face Recognition. Euclidean distance based metods [11] aim to calculate te difference value of te distance measurement, wic are usually used in pattern recognition system. Te resemblance computation directly calculates te difference between two vectors. Te smaller value means tat te two vectors are closer. It also indicates tat te features of two images are also closer, and tere is te presence of similarity in te images. Te equation of te Euclidean distance is expressed in k (a i1 b i1 ) 2 d 1 d 2 k d 3 = (a i2 b i2 ) 2., (23) [ ] [ d ]. k [ (a i b i ) 2 ] [ ] in wic d 1,d 2,d 3,...,d are te Euclidean distances between te eigenvector of eac image and te eigenvector of te target image; a i is te it element of te input eigenvector; b i is te it element of te eigenvector saved in te database; k is te dimension of te eigenvector; and is te t image saved in te database. In general, if te Euclidean distance metod is directly used in face recognition system, it would require a lot of computation time, because te Euclidean distance applies bubble sort for comparison. For example, if tere are one tousand data in te database, it will require te process to be performed one tousand times and te larger te database te longer te comparison time. Terefore, support vector macine is used to assist suc face recognition problems. Te calculated Euclidean distances are inputted te feature space oftesupportvectormacinetoperformtecomparisonand classification. Te most important goal of face recognition system is ow to raise te accuracy and sorten te computing time oftesystem.infact,principalcomponentanalysiscould indeed raise te accuracy as sown in previous experiments. However, te comparison of te Euclidean distance would require a lot of computing time. Terefore, te design of te supportvectormacineclassificationsortensteprogram s computing time for te face recognition system. Te SV is performed troug te following process. First, te yperplane is designed to classify te Euclidean distance as sown in Figure 9. In te figure, d i denotes te Euclidean distance between te target image and it image of te database. Tere are images in te database wit i = 1,2,3,...,. Besides, d mean indicates te mean value of te Euclidean distance between te target image and all images in te database. Te equation of d mean is expressed in d mean = d i. (24) In tis metod, te training data is sown: (d 1,y 1 ),...,(d,y ), d 1 R n (25),2,..., y i d mean. Ten, consider (w d i ) +b d mean y i =d mean,,2,..., (26)

8 8 atematical Problems in Engineering yi < dean w y i = dean Bytemetodofsupportvectormacine,d i found to be located between zero and d mean inteyperplaneare retained. Tese data are used to recalculate te d mean and reexecute te classification by te same way. Tis procedure wouldberepeateduntildataareallplottedbeforeterminating te program. Tis data represents te Euclidean distance closest to te target image. Finally, tis data sows te image wic is te recognition results needed. L 1 : w d i +b=d mean L: w d i +b=0 Figure 9: Hyperplane of te Euclidean distance. in wic w is te normal vector of te yperplane and b is te deviation value. In order to find te division of te yperplane te question of quadratic optimization needs to be resolved. Te constraint is expressed in y i (w d i b) d mean,,2,...,. (27) Te minimum value of d(w) = (1/2) w 2 must be determined because te equation above is quadratic wit a linear constraint. Tis is a typical quadratic optimization problem. So, te Lagrange multiplier is resolved to te question of quadratic optimization wit linear constraint to obtain L (w, b, α) = 1 2 w2 α i [y i (w d i +b) d mean ] α i 0. (28) However, te support vector macine still does not produce te optimal solution. Te metod in wic te problem is dealt wit was to address te dual question. Te dual question is expressed in L w =w α i y i d i =0 w= L b = α i y i =0. α i y i d i. (29) And a new equation was left after performing te substitution as expressed in L D = α i 1 2 i,j α i α j y i y j d i d j. (30) After aving determined te optimal solution to te dual question, eac Lagrange modulus α i is mapped onto eac trained data. If α i 0, tis means tat te data is te supportvectoroftisquestionanditislocatedintemargin separating te yperplane. Te final function is expressed in f (d) = sgn [ α i y i (d i d) + b]. (31) 3.5. PSO-SV Classifier. Te particle swarm optimization (PSO) was proposed by [12 15]. Tis metod is a concept of swarm intelligence wic belongs to te territory of te evolutionary searc. Tis algoritm is an evolutionary optimization implementation similar to te genetic algoritm (GA). First, tey could produce te initial solution and apply evolution to find te optimal solution. Te difference is tat PSO does not ave te procedures of crossover and mutation. Itbelongstotesignal-cannelmessaging,andteprocessof searcing update is canged according to te current optimal solution. Terefore, in te general optimal questions, te PSO converges to te optimal solution more quickly tan te GA. Te origin of te PSO is from te concept of te predation on bird populations. Kennedy used tis concept to researc te solution of te optimal question, and tis question is just like a bird wic flies in space, called particle. Tere is a fitness function of te objective function mapping for all particles tat moved in te space. In addition, eac particle as te velocity to determine te direction and te distance of te movement. Te particles flig in te solution space by te individual successful experience and te trajectory of te best particle in te current population. In addition, eac particle could searc independently in te PSO space. Wen te individual particle found te optimization of te function, te best searc variable will be recorded in te individual memory. Tus, eac particle owns te best memory of te searc variable for itself. It would cange te next searc direction by te individual best memory of te searc variable, and tis procedure is called te cognition-only model. Every searc would compare te optimization extent between te individual best searc variable and te best searc variable of te population. Tis procedure would adjust te variable memory of te best function for te population. At te same time, eac particle could cange te searc velocity of te particle for next time according to te best variable memory of te population, and tis process was called te social-only model. Troug te evolutionary computation, te PSO would calculate te optimal solution according to te best fitness value of te particles [16]. Te flowcart of te PSO is sown in Figure 10. In te space of te SV, it requires te design of an important parameter w. Terefore, PSO is applied to optimize tis parameter. Te particle s position in te PSO space was used to substitute te parameter w of te SV space. Troug te evolutionary computation, eac particle wouldupdatetepositionandteparameterw would be updated continually too. By tis procedure, we could find te optimization value of te parameter w.

9 atematical Problems in Engineering 9 Start Setup te parameters and te quantity of te particles Record te individual best memory and te best memory of te population for te particles (p g x,pg y ); terefore te parameter wg of te SV could be calculated by (p g w g = x )2 +(p g y ) (32) If te set p g wit particles is called te population in te gt generation, it can be expressed in Produce te initial velocity ( o ) and position (s o ) of eac particle randomly Estimate te fitness function of eac particle y o Update te position and velocity for eac particle Satisfy te termination condition? End Figure 10: Te flowcart of te PSO. p g+1 Yes p g =(p g 1,pg 2,...,pg,...,pg ). (33) Te velocity vector and position vector of te t particle ( [1,2,3,...,])integt generation (g [1,2,3,...,G]) are expressed in (34)and(35), respectively, as follows: V g = (Vg 1, Vg 2,...,Vg,...,Vg ), (34) p g = (pg 1,pg 2,...,pg,...,pg ), (35) in wic te position of te t particle in te gt generation is p g. Also, te processes of te PSO could be explained as follows. Step 1. Te initialization of te PSO was set to g=1, F pbest 1 = F pbest 2 = =F pbest =0.Tenumberofteparticles(), te number of te generation (G), and four parameters of C 1, C 2, γ max,andγ min are given. Step 2. Te initial velocity V 1 =(V1 1, V1 2,...,V1,...,V1 ) and te initial position p 1 = (p1 1,p1 2,...,p1,...,p1 ) of particles are created. g g+1 Gbest Step 3. Te fitness value of eac particle in te gt generation is calculated by using (36). fit( ) is te fitness function wic is expressed by te reciprocal computing time of te recognition system: p g Pbest Figure 11: Te PSO searc in te space. Te PSO produces te particles of te initial population randomly and troug te evolutionary computation to find te optimal solution for te function. In eac evolution, te particle would cange te individual searc direction by two searc memories. Te first searc is te optimal individual variable memory Pbest and te oter is te optimal variable memory of te population Gbest. After te computation, te PSO would calculate te optimal solution according to te optimal variable memory. Figure 11 sows te PSO searc in aparticularspace. Having a range of x [0, 20] and y [0, 20], it is supposed tat te coordinate of particle s position was x Step 4. Te F Pbest F(p g )=fit (pg ), =1,2,...,. (36) and p Pbest for eac particle were deter- is expressed in (37), and te is expressed in (38) as follows: mined and te equation of F Pbest equation of p Pbest F Pbest ={ Fg F Pbest p Pbest ={ pg p Pbest, if FPbest, oterwise, F g, if FPbest, oterwise, F g {1,2,...,}, (37) {1,2,...,}, (38) were, p Pbest was te individual optimal fitness value F Pbest form te starting to te current generation. Step 5. Te index q ofteparticlewitteigestfitness function is designed by q=arg max {1,2,...,} FPbest. (39)

10 10 atematical Problems in Engineering And ten, F Gbest and p Gbest are determined by F Gbest =F Pbest q = max {1,2,...,} FPbest, p Gbest =p Pbest q, (40) in wic p Gbest is te position vector of te particle wit te global optimal fitness value F Gbest from te starting to te current generation. Step 6. If g = G,andtengotoStep 10, oterwisegoto Step 7. Step 7. Te velocity vector is updated for eac particle by V g+1 =γ V g +c 1 rand1 () (p Pbest p g ) +c 2 rand2 () (p Gbest p g ), (41) were V g is te current velocity vector of te t particle in te gt generation. V g+1 is te next velocity vector of te t particle in te (g + 1)t generation. rand1() and rand2() are two uniformly distributed random numbers in [0, 1]. C 1 and C 2 are te constant values tat are set to 2. γ was te weigt value wic is defined by γ=γ max γ max γ min g, (42) G were γ min and γ max are, respectively, te minimum value and temaximumvalueofγ,andteγ min is set to 0.4; te γ max is set to 0.9. Step 8. Ten te position vector is updated for eac particle by p g+1 =p g + Vg+1, (43) were p g is te current position vector of te t particle in te gt generation. p g+1 is te next position vector of te t particle in te (g+1)t generation. Step 9. Let g=g+1and go to Step 3. Step 10. Teoptimalpositionvectorofteparticlep Gbest wit te optimal fitness value F Gbest is determined. After te above procedures, te particle moves in te generation tat would create te new parameter w for te SV. Te computing time of te face recognition system is compared for eac parameter w, and te best w in current generation is searced for. It projects te space of te PSO to be te optimal global solution for te next generation. Troug tis metod, te best parameter w of te SV could be found to reduce te computing time of te face recognition system. 4. Experimental Results 4.1. Actual Experiments. In te experiments of te face recognitionsystem,tefacialdatabaseusedcontainedten Table 1: Te comparison wit te experiments wit fifty samples. PCA + ED PCA + SV PCA + SV + PSO Sample numbers Test times Successful numbers Success rate 93% 95% 95% Average training time s s s Average computing time s s s Table 2: Te comparison wit te experiments wit one undred samples. PCA + ED PCA + SV PCA + SV + PSO Sample numbers Test times Successful numbers Success rate 89% 91% 93% Average training time s s s Average computing time s s s people as training samples. Eac person as ten facial images usedasteinputsamples,andtentereareoneundredtest samples in te real-time face recognition system. Troug te real-time detection, te current facial image is captured to be te test face. Te PCA-SV-PSO algoritm is used to execute te face recognition system. Te Euclidean distance between te test face and te samples of te facial database wouldbeclassified,andtenitwouldfindtesampleinte face database in wic te Euclidean distance is closer to te test face to be te result. Te experiments of te real-time face recognition system are sown in Figure Experimental Comparison. Intepartoftecomparison wit te experiments, te main comparisons made are on te training time, computing time, and recognition rate for tree ways. Te first way is using PCA and Euclidean distance wit te bubble sort to te face recognition system. Te second is toapplytepcaandsvbasedclassificationtoteface recognition system. Te tird is to adopt PSO as a parameter adjusted sceme for SV based classification. Tere are fifty samples and one undred samples used in te analyses of experimental results. Table 1 expresses te comparison wit te experiments wit fifty samples. Table 2 summarizes te comparison wit te experiments wit one undred samples, in wic ED denotes te Euclidean distance wit te bubble sort. From te results in Tables 1 and 2, onecanseetat te proposed algoritm as really raised te recognition

11 atematical Problems in Engineering 11 (a) (b) (c) (d) Figure 12: Te experimental results of te real-time face recognition system. rate and reduced te computing time for te real-time face recognition system. For te metod of combining PCA and Euclidean distance wit bubble sort, wen te number of samples is doubled from 50 to 100, te average computing time also increases almost linearly from s to s. It is noted tat te time needed for te way of te PCA combined SV-PSO only increases by 40% correspondingly. Based on suc view, one can say tat te proposed algoritm is clearly superior for large-sample-size cases. It also concludes tat te proposed metod is faster and more efficient tan oter common metods for face recognition. Conflict of Interests 5. Conclusions References A real-time face recognition system is designed by using a combination of PCA and ybrid biology algoritm face recognition system application and tis metod as effectively reduced te computing time. Tere is a time savings of 60% after doubling samples from 50 to 100 samples as compared to oter metods. Furtermore, te SV-PSO sceme is designed to speed up te recognition and also enances te performance of te face recognition. In te future, te result of te face recognition system can be furter developed in a cip of an embedded system. Te autors declare tat tere is no conflict of interests regarding te publication of tis paper. Acknowledgment Tis work is supported by te ational Science Council, Taiwan, under Grant nos. SC E and SC E Y3. [1].. Desibi and A. Bastanfard, A new algoritm for age recognition from facial images, Signal Processing, vol. 90, no. 8, pp , [2] W.-J. Zeng, X.-L. Li, X.-D. Zang, and E. Ceng, Kernel-based nonlinear discriminant analysis using minimum squared errors criterion for multiclass and undersampled problems, Signal Processing, vol. 90, no. 8, pp , [3] J. Zang and L. Ye, Local aggregation function learning based on support vector macines, Signal Processing, vol. 89, no. 11, pp , 2009.

12 12 atematical Problems in Engineering [4]Y.E.Sao,C.-J.Lu,andY.-C.Wang, AybridICA-SV approac for determining te quality variables at fault in a multivariate process, atematical Problems in Engineering, vol.2012,articleid284910,12pages,2012. [5] J.-S. Ciou and K.-Y. Wang, Application of a ybrid controller toamobilerobot, Simulation odelling Practice and Teory, vol.16,no.7,pp ,2008. [6] C.-C. Wong, H.-Y. Wang, and S.-A. Li, PSO-based motion fuzzy controller design for mobile robots, International Journal of Fuzzy Systems,vol.10,no.1,pp ,2008. [7]Y.LiuandB.iu, AnovelPSOmodelbasedonsimulating uman social communication beavior, Discrete Dynamics in ature and Society, vol. 2012, Article ID , 21 pages, [8]W.Zou,Y.Zu,H.Cen,andX.Sui, Aclusteringapproac using cooperative artificial bee colony algoritm, Discrete Dynamics in ature and Society, vol. 2010, Article ID , 16 pages, [9] P. Umapaty, C. Venkatasesaia, and. S. Arumugam, Particle swarm optimization wit various inertia weigt variants for optimal power flow solution, Discrete Dynamics in ature and Society,vol.2010,ArticleID462145,15pages,2010. [10]. Kazakova,. argala, and. G. Durdle, Sobel edge detection processor for a real-time volume rendering system, in Proceedings of te IEEE International Symposium on Cirquits and Systems, vol. 2, pp. II913 II916, ay [11] R. O. Duda, P. E. Hart, and D. G. Stork, Pattern Classification, Jon Wiley & Sons, [12] C.-Y. Lee, J.-J. Leou, and H.-H. Hsiao, Saliency-directed color image segmentation using modified particle swarm optimization, Signal Processing,vol.92,no.1,pp.1 18,2012. [13] H.-Y. Cen and J.-J. Leou, Saliency-directed image interpolation using particle swarm optimization, Signal Processing, vol. 90, no. 5, pp , [14] R. Eberart and J. Kennedy, ew optimizer using particle swarm teory, in Proceedings of te 6t International Symposium on icro acine and Human Science,pp.39 43,October [15] J. Kennedy and R. Eberart, Particle swarm optimization, in Proceedings of te IEEE International Conference on eural etworks, pp , December [16] D. Srinivasan, W. H. Loo, and R. L. Ceu, Traffic incident detection using oarticle swarm optimization, in Proceedings of IEEE Swarm Intelligence Symposium, pp , 2003.

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