Classification of facial images

PROCEEDINGS OF ICETECT 2011 Classification of Facial Images Mrs. Mahananda D. Malkauthekar Assistant Professor in M.C.A. Govt. Engg. College, Karad, Maharashtra, India [email protected] Abstract— This paper consists of development of detection strategies for face recognition tasks and to access its feasibility for forensic analysis using the FERET face database Author has used global feature extraction technique using statistical method for image classification. Facial images of three subjects with different expression and angles are used for classification. Principal Component Analysis has been used for three classes. Mahalanobis distance and Euclidian distance are used as similarity measures and a result of both methods is compared. Keywords— FERET database, Principal Component Analysis, Mahalanobis distance, Euclidian distance, Image Classification, PCA.. I. INTRODUCTION Face recognition is a fairly young technology compared to other biometrics. A facial recognition system is an application, which automatically identifies a person from a digital image. It does that by comparing selected test face image with the facial database. The Face Recognition technique of Biometric-based authentication applications include National ID cards, airport security, workstation, network, and domain access, application logon, data protection, and remote access to resources, transaction security and Web security. In dynamic environment many problems may arise during the development of a face recognition system. Faces are highly dynamic and can vary considerably in their orientation, lighting, scale and facial expression; therefore face recognition is considered a difficult problem to solve. Aging, Occlusions and makeup or cosmetics can also degrade the accuracy of a real time face recognition system [1] [2]. In this paper we present results on variation of reduction in dimensionality with PCA. FERET database is used having face images with different poses and expressions. Euclidean distance and Mahalanobis distance are used for image recognition and Results of two distance measures are compared II. METHODOLOGY produces uncorrelated components [4] [5]. Another representation based on multiple low-dimensional Eigen spaces is proposed in [6]. Principal Component Analysis (PCA) involves a mathematical procedure that transforms a number of possibly correlated variables into a smaller number of uncorrelated variables called principal components. PCA is the simplest of the true eigenvector-based multivariate analyses. Often, its operation can be thought of as revealing the internal structure of the data in a way which best explains the variance in the data. PCA algorithm can be explained as follows. Let a face image Xi be a two-dimensional m by m array of intensity values. Thus, an image may also be considered as a vector of m2 dimension. Denote the training set of n face images by image belongs to one of c classes. Thus defines covariance and we assume that each matrix as follows where Then, the Eigen values and eigenvectors of the covarianc e can be be calculated. Let the r eigenvectors corresponding to the r largest Eigen values. Thus, for a set of original face images , their corresponding Eigen face-based feature can be obtained by projecting X into the Eigen face space as follows: . The eigenvectors corresponding to non-zero Eigen values of the covariance matrix form an orthonormal basis that rotates and/or reflects the images in the N-dimensional space [7] [8] [9]. A. Representation It has been observed that the PCA based representation is used when distance vector measure techniques are used for classification [3]. As for statistical unsupervised techniques, PCA can be computed as an optimal compression scheme that minimizes the mean squared error between an image and its reconstruction. This easy to compute, unsupervised, learning technique is mainly used for dimension reduction and 978-1-4244-7926-9/11/$26.00 ©2011 IEEE B. Recognition Here two distance measures are used for image recognition. 1) The Mahalanobis distance. It is a very useful way of determining the "similarity" of a set of values from an "unknown: sample to a set of values measured from a collection of "known" samples. One of the main reasons the Mahalanobis distance method is used is that 507 it is very sensitive to inter-variable changes in the training data. In addition, since the Mahalanobis distance is measured in terms of standard deviations from the mean of the training samples, the reported matching values give a statistical measure of how well the spectrum of the unknown sample matches (or does not match) the original training spectra. Mahalanobis, distance (Johnson and Wichern, 1998) from x to μ, can be written[3]. Where µk are the mean and xi is the input vector of attributes where Σ is the covariance matrix given by Fig. 1. Three different persons are used and 9 images of each person. Front faces for each class are used for training and all images of faces with different angles and expressions are used for testing. B. Euclidean distance 1) Class1 The Euclidean distance of front face of class1 (Person1) with all images of three classes is shown in table 1, Where I1 to I9 are the images and P1, P2, P3 are the persons. Table 1 I2 I3 I4 I5 I6 I8 I9 P1 I1 0 0.04 0.05 0.06 0.09 0.09 I7 0.1 0.12 0.12 P2 P3 0.13 0.31 0.14 0.31 0.14 0.32 0.15 0.32 0.16 0.32 0.16 0.32 0.17 0.33 0.18 0.33 0.18 0.33 I1 0.4 and the individual covariance values of Σ are computed from the outer product sum given by I2 0.3 I3 I4 0.2 I5 2) Euclidean distance The Euclidean distance formula can be used to account for variation on all six dimensions without aggregating the components and reducing variance. Recall the Euclidean formula for distance in two dimensions: • This formula can be expanded to n dimensions. • All component scores are rescaled 0 to 1. to create a distance • The above formula is divided by measure that ranges from 0 (most similar) to 1 (least similar) [10]. III. RESULTS A. Resizing Size of the images is fixed. Original image size is (768*512*3), which is changed to (60*60). RGB images are converted to grayscale images. Facial images of 3 subjects (9 images for each person, 9*3=27 images) with different expression and angles are used for classification shown below 0.1 I6 0 I7 P1 P2 I8 P3 I9 Graph 1 2) Class2 The Euclidian distance of front face class2 (Person2) with all images of three classes is calculated and shown in table 2. Table 2 I1 I2 I3 I4 I5 I6 I7 I8 I9 P1 0.13 0.14 0.15 0.17 0.19 0.19 0.22 0.25 0.27 P2 0 0.2 0.2 0.22 0.23 0.24 0.26 0.28 0.3 P3 0.34 0.34 0.35 0.36 0.36 0.37 0.38 0.4 0.41 I1 0.5 I2 0.4 I3 0.3 I4 0.2 I5 I6 0.1 I7 0 P1 P2 P3 I8 I9 Graph 2 508 The Mahalanobis distance of front face of class2 (Person2) with all images of three classes is shown in table 5, Where I1 to I9 are the images and P1, P2, P3 are the persons. 3) Class3 The Euclidian distance of front face of class3 (Person3) with all images of three classes is calculated and shown in table 3. Table 3 I1 I2 I3 I4 I5 I6 P1 0.3 0.3 0.4 0 0.6 1 P2 0.3 0.4 0.4 0 0.61 P3 0 0.5 0.5 1 0.68 I7 I8 I9 2 2.5 5.1 1 2 2.5 5.1 1 2 2.5 5.1 Table 5 I2 I3 I4 I5 I6 I7 I8 I9 P1 I1 1 1.1 1.7 0.4 0.5 2.2 0.3 1.2 1.6 P2 0 0.1 2.7 1.4 0.6 1.2 1.4 2.3 0.6 P3 3.5 3.6 0.8 2.1 2.9 4.7 2.1 1.2 4.1 I1 5 I2 4 I1 3 I2 2 I3 1 3 I4 0 2 I5 1 I6 6 5 4 0 P2 P3 I8 I9 Graph 3 C. The Mahalanobis distance 1) Class1 The Mahalanobis distance of front face of class1 (Person1) with all images of three classes is shown in table 4, Where I1 to I9 are the images and P1, P2, P3 are the persons. Table 4 I1 0 1 2.5 I4 I5 I6 I7 P1 P2 I7 P1 P1 P2 P3 I3 I2 1.1 2.1 1.4 I3 0.1 1.2 2.3 I4 3.2 4.2 0.7 I5 1.3 2.3 1.2 I6 0.3 1.4 2.1 I7 1 0 3.5 I8 0.3 0.7 2.7 I9 1.7 2.7 0.8 P3 I8 Graph 5 3) Class3 The Mahalanobis distance of front face of class3 (Person3) with all images of three classes is shown in table 6, Where I1 to I9 are the images and P1, P2, P3 are the persons. Table 6 I1 I2 I3 I4 I5 I6 1 1.2 1.5 2.2 4.5 3.5 0 2.3 2.5 3.2 0 3.5 1.2 1 0.2 P1 2.5 P2 P3 I7 I8 I9 3 0.7 0.4 5.5 4 0.3 1.5 2 0.5 3.2 2 I1 6 I2 5 I3 4 4 3 2 I3 1 I6 I4 0 I5 1 I5 I7 P1 P2 P3 I7 P1 P2 P3 Graph 4 I8 I9 I6 0 2) Class2 3 2 I4 I2 I1 5 Graph 6 I8 IV EXPERIMENTAL ANALYSIS The results of the methods, the Euclidian distance and the Mahalanobis distance are compared. First the recognition rate for all three classes with different types of images is calculated by Euclidian distance method and then result is compared with 509 the recognition rate obtained by Mahalanobis distance method for all three classes for the same types of images as used in Euclidian distance method. The following tables and graphs show the comparative study. A. Recognition rate using Euclidian distance The table 7 shows the recognition rate obtained by Euclidian distance method. Here total images are used 27. 6 images are facing frontally, 9 images are angle changed, 3 are of changed expressions and 9 images are of changed complexions. Table 7 Euclidean Distance Measure No. of images Recognize d Images Recognitio n rate Recognition rate by Euclidean distance with PCA Changed Front Change Changed Complexion faces d angle Expressio ns changed, 3 are of changed expressions and 9 images are of changed complexions. Table 8 Mahalano bis distance Measure No. of images Recognize d Images Recognitio n rate Recognition rate by Mahalanobis distance with PCA Changed Front Change Changed Complexion faces d angle Expressio ns 6 9 3 9 6 6 1 8 100 66.66 33.33 88.88 Recognition rate by Mahalanobis distance w ith dim ensionality reduction 6 9 3 9 120 4 6 0 1 100 66.66 66.66 0 11.11 80 60 40 20 No. of images 0 Complexion 70 60 50 40 30 20 10 0 Expressions Recognition Rate Reognition of images w ith Euclidean Distance FrontChanged Changed Changed No. of images Recogni zed Images Recogni tion rate Front Changed ChangedChanged f aces angle Recognit ion rat e by M ahalanobis dist ance wit h dimensionalit y reduct ion Recogn ized images Recogn ition rate T yp es o f imag es Graph 8 Recognition rate by Types of im ages Graph 7 C. Comparative study B. Recognition rate using Mahalanobis distance Table 9 shows the comparative study of two methods Euclidian distance and the Mahalanobis distance. The table 8 shows the recognition rate obtained by Mahalanobis distance method. Here total images are used 27. 6 images are facing frontally, 9 images are angle It is observed from the graph 9 that the Mahalanobis distance gives better results than Euclidian distance method. 510 Table 9 Comparison PCA test with EuclideanDistance Measure on only front face images used for training PCA test with Mahalanobisdistance Measure on only front face images used for training REFERENCES Recognition rate by Euclidean distance & Mahalanobis distance Measure with PCA Front faces Changed angle 66.66 66.66 100 [1] Gregory Williams, “More than pretty face, Biometrics and smart card Tokens” 2001. Changed Expressions Changed Complexion 0 11.11 66.66 33.33 88.88 [2] Erum Naz, Umar Farooq, Tabbasum Naz, “Analysis of Principal Component Analysis-Based and Fisher Discriminant Analysis-Based Face Recognition Algorithms”, IEEE--ICET 2006 2nd International Conference on Emerging Technologies. [3] Supriya Kapoor, Shruti Khanna, Rahul Bhatia,”Facial Gesture recognition using correlation and Mahalanobis distance”, Vol. 7, _o. 2, 2010. [4] A. Leonardis, H. Bischof, J. Maver, “Multiple eigenspaces, Pattern Recognition “,35 (11) (2002) 2613–2627. [5] M. Turk, A. Pentland, “Eigenfaces for recognition”, J. Cognitive Neurosci. 3 (1) (1991) 71–86. [6] B. Moghaddam, “Principal manifolds and probabilistic subspaces for visual recognition”, IEEE Trans. Pattern Anal. Machine Intell. 24 (6) (2002) 780–788. Comparison 120 [7] Li, Zhi-Yun Liu “A Novel Method Of Face Recognition Based On The Fusion Of Classifiers “Ming School of Computer and Communication, Lanzhou University of Technology, Lanzhou, 730050, China. 100 80 60 [8] Haitao Zhao, Pong Chi Yuen, James T. Kwok,”A Novel Incremental Principal Component Analysis and It Application for Face Recognition”, IEEE 40 20 0 Recognition rate by [9] Kresimir Delac 1, Mislav Grgic 2, Panos Liatsis3,”Appearance–based Statistical Methods for Face Recognition”. [10] Curtis M. Bell,“Toward a Multi-Dimensional Measure of Regime Similarity”, Graduate Student, Department of Political Science, University of Colorado at Boulder. Graph 9 V CONCLUSION In this paper a total subjects are taken three. Each person with 9 variant images. Hence total images taken are 27. The second person as shown in fig 1 consists of some images with not close up and the third person consists of images with different color complexions. It is observed that the Euclidian distance method does not take into account the variability of the values in all dimensions, and is therefore not an optimum discriminant analysis algorithm for this case. The Mahalanobis distance, however, does take the sample variability into account. Instead of treating all values equally when calculating the distance from the mean point, it weights the differences by the range of variability in the direction of the sample point. VI FUTURE SCOPE Here only FERET database facial images are used. Other database facial images, Cat & Dog images can be used. Also different similarity measures L1 norm, L2 norm, correlation can be used and comparison can be done. 511