Face Recognition Using Kernel PrincipalComponent Analysis

Transcription

1 Advanes in Vision Computing: An International Journal (AVC Vol., No., Marh 4 Fae Reognition Using Kernel PrinipalComponent Analysis Jayanthi and Dr. Ai S Assistant Professor,Department of Computer Appliations, Mohandas College of Engineering and ehnology, Anad, Nedumangad hiruvananthapuram, India Assistant Professor,Department of Computer Siene,University of Kerala Kariyavattom,hiruvananthapuram, India Abstrat Fae reognition is attrating muh attention in the soiety of network multimedia information aess. Areas suh as network seurity, ontent indexing and retrieval, and video ompression benefits from fae reognition tehnology beause people are the enter of attention in a lot of video. Network aess ontrol via fae reognition not only makes hakers virtually impossible to steal one's password, but also inreases the user-friendliness in human-omputer interation. he data in fae images are distributed in a omplex manner due to the variation of light intensity, faial expression and pose. In this paper the Kernel Prinipal Component Analysis (KPCA is used to reognize the faes. A Gaussian model of skin segmentation method is applied here to exlude the global features suh as beard, eyebrow, moustahe, et. both training and test images are randomly seleted from four different data bases to improve the training. he experimental results show that the proposed framework is effiient for reognizing the humanfaes. Keywords Fae reognition, Kernel prinipal omponent analysis, Feature extration. I. INRODUCION Humans have always had the innate ability to reognize and distinguish between faes. Fae reognition is substantially different from lassial pattern reognition problems, suh as obet reognition. he shapes of the obets are usually different in an obet reognition task, while in fae reognition one always identifies obets with the same basi shape. his is of utmost diffiulty for a fae reognition system when one tries to disriminate faes all of whih have the same shape with minor texture differenes. he fae reognition therefore depends heavily on the partiular hoie of fae representation. he aim of feature seletion in fae representation method is to suppress the variations of fae images and simultaneously provide enhaned disriminatory power. he signifiant growth of visual information apturing tehnology has revolutionized the seurity observations and sientifi inquiry, produing signifiant opportunities and hallenges [][]. his renewed interest has been powered by advanes in omputer vision tehniques and interest in the design of robust and aurate fae reognition systems. he human fae provides the

2 Advanes in Vision Computing: An International Journal (AVC Vol., No., Marh 4 information about the identity, sex, rae, approximate age, and urrent mood of an individual. he advaned trends in the image proessing provide a lear path to identify the human faes in a onsiderable manner. he tehnique presented in this paper reveals the possibilities of biometri appliations in seurity aspets. In this paper a fae reognition tehnique is proposed. here are a bunh of remarkable findings in fae reognition and identifiation using various tehniques and algorithms [3-5] in omputations. he fous here is to identify the human faes. Various statistial models [9][] are used to diserning skin pixels in a olor fae image; among them wehave used the Gaussian skin olor model [7][8]. here will be no dominant features in the skin segmented fae images and these images are used to reognize the faes. KPCA, the powerful extension of PCA used to extrat the feature whih has been suessfully applied in fae reognition. II. SKIN SEGMENAION here are different skin segmentation algorithms working with different olor spae like RGB, HSV, HIS, rgb and YCbCr. he threshold value used in these methods deides the suess of the model. he RGB model deals with the illumination onditions of image. And the method required some defined rules of fixing the threshold. Uniform day light R>9, G>4,B> Max{R,G,B} min{r,g,b} <5 R-G >5, R>G, R>B( Lateral illumination (Flash or any other R>, G>, B>7 R G 5, B < R, R < G ( In the HSV model the segmentation has done through the range value seleted for H, the saturation range and V. hese parameters used to study the nature of dark olors and the effet of light variation in the image. V 4. < S <.6; < H < 5 or 335 < H < 36 ( 3 hese thresholds are having a signifiant role in the segmentation. he HIS method finds some unhanged olor pattern in the skin, intensity, hue and saturation. And we an find the threshold empirially through

3 Advanes in Vision Computing: An International Journal (AVC Vol., No., Marh 4 I (R + 3 I I S I + - I 3 H tan ( 4 I Gomez and Morales [6] produe a onstrutive indution method for skin detetion alled rgb model. he normalized oordinates rgb are obtained through the following expressions R G B r g b ( 5 R + G + B R + G + B R + G + B he YCbCr method tries to exploit the spatial distribution harateristis of human skin olor. A skin olor map is used to detet the skin pixel from the hrominane omponents of the image. Even though they are using a threshold like I G 3 + B; I (R - B; I 3 4 (G - R - B 77 Cb 7 and 33 Cr 73, (6 he authors ould reah an appraisable result. he work presented in www-sstudents.stanford.edu by Henry Chang and Ulises Robles proves the pratial importane of the method. he low-pass filter [3] derived from about 3 skin samples is 9 ( 7 he result of skin-olor distribution in different people is shown in the figure Figure : Skin-olor distribution in different people he histogram shows the possibilities of Gaussian model in representing this partiular olor model. 3

4 Advanes in Vision Computing: An International Journal (AVC Vol., No., Marh 4 he Gaussian model N(m,, where Mean : m E { x } where x (r,b Covariane : C E {(x - m(x- m } (8 Figure : he Gaussian distribution of Skin-olor he Gaussian distribution of the skin olor in the experiment data set is given in figure. he likelihood of skin pixel an be easily obtained from this Gaussian skin model. Likelihood P(r,b exp[-.5(x- m C (x - m] Where : x (r,b (9 he parameters r &b are the hromati olor value of the pixel. - he gray sale image obtained an be onverted into binary image by applying an appropriate threshold. his binary fae image is used to segment the skin region from a fae image. (a (b Figure 3(a: OriginalImage (b: After skin segmentation A sample olor image and its resulting skin-segmented image are shown in Figure 3. III. FEAURE EXRACION he dimensionality of a fae image is extremely high. If we put all fae images in a dimensional spae, they will not fully fill the whole spae, but will instead only over a very limited volume. his implies many input omponents are orrelated, and the dimensionality an be signifiantly redued. An exellent Feature Seletion method should preserve as muh as possible relevant omponents, and on the other hand, neglets that insignifiant information. Even though the Feature Seletion is task-dependent, there are someunsupervised strategies whih tend to work well in many ases. 4 M

5 Advanes in Vision Computing: An International Journal (AVC Vol., No., Marh 4 A.Prinipal Component Analysis Prinipal omponent analysis measures the variability of an input omponent by its variane. PCA works well for Gaussian distribution data, sine in this ase the eigenvalues of the ovariane matrix indeed quantifies the variability of data along their orresponding diretions. M i i i i N Consider a data set of entered N dimensional reords X, i,,3, M, that is X R and X. he ovariane of the input an be estimated as M M i X i X i o redue the dimensionality of input, we an rank the eigenvetors in the order of magnitude of the eigenvalues and hoose the first d, d < N, eigenvetors as prinipal omponents. In fae images, these eigenvetors are alled eigenfaes that represent the global feature of the training images. ( Figure 4: (a a set of six training fae images. (b hree eigenfaes with highest eigenvalues, that are derived from (a However, when the variations are aused by global fators suh as lighting or perspetive variations, the performane of PCA will be greatly degraded. B. Kernel Prinipal Component Analysis (KPCA he Cover s theorem abstrats that the nonlinearly separable patterns in an input spae will beome linearly separable by transforming the input spae into a high dimensional feature spae. A high order statistis of the input variable an be obtained by applying PCA in the high dimensional feature spae. his fat leads to the origin of KPCA. It is muh diffiult to diretly ompute PCA in the high-dimensional feature spae. Computation of dot produts of vetors with a high dimension is highly omputational expensive. By means of a kernel funtion it is possible to ompute the dot produts in the original low-dimensional input spae. 5

6 Advanes in Vision Computing: An International Journal (AVC Vol., No., Marh 4 Here we would like to present an abstrat review of the first KPCA proposed by ShÄolkopf. he ovariane matrix of a given data set X is E [( ( x E [ ( x ]( ( x E [ ( x ] Where m N i Ni ( ( x i m ( ( x i m, ( N i Ni ( xi is the mean over all N feature vetors in F. Sine KPCA seeks to find the optimal proetion diretions in F, onto whih all patterns are proeted to give the orresponding ovariane matrix with maximum trae, the obetive funtion an be denoted by maximizing the following: Jkpa(v v It an be proved that the eigenvetor v must lie in a spae spanned by { ( x i } in F and thus it an be expressed in the form of the following linear expansion: v ] ( v N i i w i ( x i ( 3 Substituting (3 into (, we obtain an equivalent eigenvalue problem as follows: ( I K ( I w w N N, ( 4 where I is an N x N identity matrix, is an N x N matrix with all terms being one, N N w ( w,..., w,..., w,..., w is the vetor of expansion of oeffiients of a given eigenvetor v, and K is the N x N Gram matrix whih an be further defined as,..., Nh K (K lh l,h,, where K lh (k i i,..., N and ki i ( xl, ( xh l he solution to (4 an be found by solving for the orthonormal eigenvetors w,,w m orresponding to the m largest eigenvalues λ,, λ m, whih are arranged in desending order. hus, the eigenvetors of an be obtained as Φwi (i,,m, where [ ( x,..., ( Φ x,..., ( x,..., ( x N N ]. Furthermore, the orresponding normalized eigenvetors v i (i,,m an be obtained as v i Φwi, sine i (Φw i Φw i λ i. 6

7 With v i Advanes in Vision Computing: An International Journal (AVC Vol., No., Marh 4 Φwi (I,, m onstituting the m orthonormal proetion diretions in F, any i novel input vetor x an obtain its low-dimensional feature representation y (y,,y m in F as: y (v,, v m φ(x, (5 with eah KPCA feature y i (i,,m expanded further as y i v i φ(x i w i Φφ(x N [ (,,..., (,,..., ( N w k x x k x x k x, x,..., k ( x i, x KPCA is superior to PCA in extrating more powerful features, whih are espeially essential when reognizing the human faes. IV. EXPERIMENAL RESULS here are a ouple good faial databases available for evaluating the algorithms in fae reognition and analysis. In order to give a wide spetrum of fae features, we have used four databases for preparing the training and testing images. he database (FERE,ORL, UMIS,and A& that wehave seleted has different feature speifi parameters like lighting, pose, expressions, age and other global features suh as spetales, beard, et. As part of experiments wehave seleted three sets of different faes from eah database. After image preproessing [], the fae regions of 8 pixels are ropped in a generalized resolution by using the fats that all the databases that wehave seleted are fae entered profiles. he seond phase of our experiment was to segment the skin regions in the training images. his has done using the Gaussian model as explained in the previous setions. In the third phase, we extrated the kernel eigenfaes of both male and female sets of data separately. he orrelation between the proeted data sets of mean fae of the training images and test images reveals the approximation of the algorithm. Using KPCA wehave extrated the,, prinipal omponents from the male and female sets of training images. he Fig. 5 shows the variation of auray along different number of prinipal omponents used in FERE and UMIS databases. It is quite easy to understand that the rate of auray is inreasing with inrease of prinipal omponents, whih shows the feature vetors orresponding to large prinipal omponents should be stressed with more weights. ] ( 6 7

8 Advanes in Vision Computing: An International Journal (AVC Vol., No., Marh % of auray FERE Prinipal Components UMIS % of auray Prinipal Components Figure 5: Influene of number prinipal omponents and Rate of Reognition A set of randomly seleted fae images from different databases is used for testing purpose. An auray of perentages has obtained in almost all test ases. It is noted that the FERE and A& databases shows a onsisteny in reognition in the last ouple of prinipal omponents. he following figure shows the reognition rate of both PCA and KPCA in different fae databases. (a (b ( 8 (d KPCA PCA 4 6 Figure 6: Rate of Reognition in PCA and KPCA methods. he Experimental results with the test images from (a FERE database (b ORL database ( UMIS database (d A& database From the results displayed in able- we notie that the KPCA tehnique gives a omparatively better rate of identifiation in all databases onsidering the ordinary PCA. 8

9 Advanes in Vision Computing: An International Journal (AVC Vol., No., Marh 4 able : A study of the rate of fae reognition in different fae databases using PCA and KPCA. KPCA PCA FERE ORL UMIS A& V. CONCLUSION In this paper, we proposed a KPCA method for fae reognition. he experimental results show that the KPCA method is effiient in extrating low level feature of fae images whih are the most supreme omponents of fae reognition problem. Randomly seleted images from four different databases are used as training faes. In almost all databases the KPCA method gives almost 8-9 perentage auray. he test images taken from the databases show almost onsistent result even though it is having different light intensities and fae expressions. we hope that this work provides a new effetive approah of non-intrusive biometri reognition. REFERENCES [] P.J. Phillips, H. Moon, P. Rizvi, and P. Rauss. he FERE evaluation method for fae reognition algorithms. IEEE ransations on Pattern Analysis and Mahine Learning, :9-4,. [] P.J. Phillips, P.J. Flynn,. Sruggs, K.W. Bowyer, J. Chang, K. Hoffman, J. Marques, J. Min, and W. Worek. Overview of the fae reognition grand hallenge. Pro. IEEE Computer Vision & Pattern Reognition, : , 5. [3] M. urk, A. Pentland, Eigenfaes for Reognition, Journal of Cognitive Neurosiene, Vol. 3, No., 99, pp [4] Lu, K.N. Plataniotis, A.N. Venetsanopoulos, Fae Reognition Using LDA-Based Algorithms, IEEE rans. on Neural Networks, Vol. 4, No., January 3, pp. 95- [5] Liu, H. Wehsler, Fae Reognition Using Evolutionary Pursuit, Pro. of the Fifth European Conferene on Computer Vision, ECCV'98, Vol II, -6 June 998, Freiburg, Germany, pp [6] G.Gomez and E.F Morales, Automati feature onstrution and simple rule indution algorithm for skin detetion, Pro, of the ICML workshop on Mahine Leariunging in omputer Vission, A Sowmya, Zrime eds, 3-38( [7] MKenna, S.J., Gong, S.G., Raa, Y., Modelling faial olour and identity with Gaussian mixtures, PR(3, No., Deember 998, pp [8] Yu, Z.W., Wong, H.S., Fast Gaussian Mixture Clustering for Skin Detetion, ICIP7(IV: [9] Jones, M.J., Rehg, J.M., Statistial Color Models with Appliation to Skin Detetion, IJCV(46, No., January, pp [] Ren, J.C., Jiang, J.M., Statistial Classifiation of Skin Color Pixels from MPEG Videos, ACIVS7 ( [] Avena, G.C., Riotta, C., Volpe, F., he influene of prinipal omponent analysis on the spatial struture of a multispetral dataset, JRS(, No. 7, November 999, pp [] Jin Zhou; Yang Liu; Yuehui Chen, Fae Reognition Using Kernel PCA and Hierarhial RBF Network,CISIM apos;7-8-3 June 7 pp [3] Henry Chang, Ulises Robles, Fae Detetion, EE368 Final Proet Report - Spring, 9