FACE RECOGNITION USING INDEPENDENT COMPONENT

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1 Chapter 5 FACE RECOGNITION USING INDEPENDENT COMPONENT ANALYSIS OF GABORJET (GABORJET-ICA) 5.1 INTRODUCTION PCA is probably the most widely used subspace projection technique for face recognition. A major disadvantage of appearance based approaches is that they are sensitive to lighting variation and expression changes since they require alignment of uniform-lighted image to take advantage of the correlation among different images. The EBGM [38] method utilizes an attributed relational graph to characterize a face, with facial landmarks (fiducial points) as graph nodes. Gabor wavelet around each fiducial point as node attributes and distances between nodes as edge attributes. Compared to image intensity, Gabor wavelet is less sensitive to illumination changes. However, since Gabor wavelet is a general image processing tool, which is not specifically designed for face recognition, Gabor features do not contain face specific information learned from face training data. Therefore, directly using Gabor features may not be the best approach. It is reasonable to use statistical techniques for better selection of Gabor features in order to integrate the advantages of Gabor wavelet and the statistical techniques. A similar approach has been used in [85], where Gabor feature vector was derived from a set of downsampled Gabor wavelet representations of face images. Dimensionality of the vector was reduced by means of principal component analysis (PCA) and independent component analysis (ICA). We proposed a new face recognition technique based on Independent Component Analysis of GaborJets (GaborJet-ICA). 99

2 5.2 PROPOSED FACE RECOGNITION SYSTEM Instead of deriving Gabor feature from a whole face image as used in [85], we have derived Gabor feature vector from facial landmarks (fiducial points) known as GaborJets as shown in Figure 5.2. GaborJets are a collection of complex Gabor coefficients from the same location in an image. The coefficients are generated using Gabor wavelets of a variety of different sizes, orientations, and frequencies. GaborJets act as feature vectors that describe the landmark from which the jet was taken. We then transform this GaborJet feature vector into the basis space of PCA and ICA as depicted in Figure 5.3. Trained face images are represented as points in this space. In order to identify, GaborJet feature vector of test images are also projected into the basis space of PCA and ICA. 5.3 FEATURE VECTOR EXTRACTION Gabor Wavelet Bidimensional Gabor Filters [38], correspond to a family of bidimensional Gaussian functions modulated by a cosine function (real part) and a sine function (imaginary part). These filters are given by a family of Gabor kernel,, (5.1) where the arguments, x and y specify the position of a image. There are five parameters that control the wavelet (5.2) (5.3) (1) θ specifies the orientation of the wavelet. This parameter rotates the wavelet about its center. This particular set uses eight different orientations over the 100

3 interval 0 to π. Orientations from π to 2π would be redundant due to the even/odd symmetry of the wavelets i.e. θ ϵ (0, π/8, 2π/8, 3π/8, 4π/8, 5π/8, 6π/8, 7π/8) (2) λ Specifies wavelength of the cosine wave, or inversely the frequency of the wavelet. Wavelets with a large wavelength will respond to gradual changes in intensity in the image. Wavelets with short wavelengths will respond to sharp edges and bars. λ ϵ {4,4 2,8,8 2,16} (3) φ specifies phase of the sine wave. Typically Gabor wavelets are either even or odd. Convolution with both phases produces a complex coefficient, i.e. φ ϵ {0, π/2}. Figure 5.1: Family of 80 Gabor wavelet kernals with 8 orientations, 5 frequencies, and 2 phases 101

4 (4) specifies radius of the Gaussian. This parameter is usually proportional to the wavelength, such that wavelets of different size and frequency are scaled versions of each other, i.e. (5) specifies the aspect ratio of the Gaussian. This parameter was included such that the wavelets could also approximate some biological models. The wavelets used here have circular Gaussian, i.e. 1. This yields 8 orientations, 5 frequencies, and 2 phases for a total of 80 different wavelets. Figure 5.1 shows family of all 80 Gabor wavelet kernals. This is known as a wavelet transform because the family of kernels is self-similar, all kernels being generated from one mother wavelet by dilation and rotation. The Gabor wavelet representation captures salient visual properties such as spatial localization, orientation selectivity, and spatial frequency. The Gabor wavelets have been found to be particularly suitable for image decomposition and representation when the goal is the derivation of local and discriminating features. The Gabor decomposition can be considered as a directional microscope with an orientation and scaling sensitivity GaborJet Landmarks (fiducial points) are parts of the face that are easily located and have similar structure across all faces. In our approach we manually choose 5 landmarks namely, left eyeball centre, right eyeball center, nose tip and two mouth corners as shown in Figure 5.2. GaborJet representation,,,,,, at the chosen landmark is the convolution of image with the family of Gabor kernals, obtained around a given pixel 102

5 x, y. We have used Gabor kernals of 5 sizes i.e , 22 22, 32 32, and During convolution, the size of image around pixel, i.e. landmark was chosen same as that of Gabor kernel. In that way, each face image is finally represented by a large GaborJet feature vector of size 400 combining 5 local vectors of size 80 each.,,,,. (5.4) GaborJet describes the behavior of image around the chosen landmark. Therefore, the GaborJet will contain a good description of the local frequency information around the landmark. Face Landmark Localization Gabor Wavelets Convolve GaborJet Feature Vector Figure 5.2: Feature extraction in proposed face recognition system 103

6 Train Images Feature vector Projection Matrix PCA/ICA Database of Projections of Train Images... Test Image Feature Project onto Subspace Similarity Measure Recognition Result Figure 5.3: Matching phase of proposed face recognition system 5.4 SUBSPACE PROJECTION AND MATCHING PHASE We then transform this GaborJet feature vector into the basis space of PCA and ICA. Trained face images are represented as points in this space. In order to identify, GaborJet feature vector of test images are also projected into the basis space of PCA and ICA. Euclidean distance was used to estimate the similarity. We then compared the performance in both PCA and ICA. PCA decorrelates the input data using secondorder statistics and thereby generates compressed data with minimum mean-squared 104

7 reprojection error. ICA minimizes both second order and higher order dependencies in the input. ICA can be viewed as a generalization of PCA. Independent Component Analysis (ICA) uses face image as input data, then it should be aligned well and should not include some in-plane and in-depth rotation. The face region should be extracted from the original image and the brightness and contrast should be stable. This makes ICA difficult to use in real application. We tried to overcome these shortcomings by keeping the basic concept that the most distinctive features act as a basis axis in the space. The GaborJet feature vector has useful characteristics. It provides robustness against varying brightness and contrast in the image. Since the characteristics of the local face area can be represented, it is more effective than using the original face image directly. To overcome the shortcomings mentioned above, we used GaborJet feature vector as input of ICA. Let the number of fiducial points that can get the GaborJet are, with 80 Gabor kernals we construct the 80 dimensional array. If we use gallery images, a 80 by matrix could be constructed. Basis vectors could be calculated from matrix.we then transform this GaborJet feature vector into the basis space of PCA and ICA. Dimensionality of GaborJet feature vector is first reduced by PCA and then Independent GaborJet features are derived. Trained face images are represented as points in this space. In order to identify, GaborJet feature vector of test images are also projected onto the basis space of PCA and ICA. Euclidean distance was used to estimate the similarity. 105

8 5.5 EXPERIMENTAL RESULTS AND DISCUSSION The experiment is performed using ORL face database from AT&T (Olivetti) Research Laboratories [24], Cambridge. The database contains 40 individuals with each person having ten frontal images. Figure 5.4 shows some of the sample face images from this database. There are variations in facial expressions such as open or closed eyes, smiling or non-smiling, and glasses or no glasses. All images are 8-bits Figure 5.4: Sample face images from ORL face database [24] Figure 5.5: Locating 5 fiducial points grayscale of size 112x92 pixels. We select 200 samples (5 for each individual) for training. The remaining 200 samples are used as the test set. As described in Figure 5.2, we first manually located 5 fiducial points namely, left eyeball centre, right eyeball center, nose tip and two mouth corners as shown in Figure 5.5. Geometric normalization [89] was performed on these images. With 5 fiducial points for each face image we made a 400 dimensional GaborJet feature 106

9 vector using 80 Gabor wavelet kernels. As the total number of individuals in database was 40, a large GaborJet feature vector of 40 by 400 matrixes was constructed. We then transform this GaborJet feature vector into the basis space of PCA and ICA. Trained face images are represented as points in this space. In order to identify, GaborJet feature vector of test images are also projected into the basis space of PCA and ICA. Euclidean distance was used to estimate the similarity. We compared the performance with GaborJet-PCA and GaborJet-ICA. In face recognition experiments of GaborJet-PCA we evaluated the performance of the system by varying principal components from 2 to 100. Table 5.1 depicts some of sample results for GaborJet-PCA. Figure 5.6 shows plot of number of principal components vs recognition accuracy. Beyond principal component 40, consistent accuracy of 82.25% was obtained in case of GaborJet-PCA. We experimented then with the GaborJet-ICA. Dimensionality of GaborJet feature vector was first reduced using PCA and then Independent GaborJet features were derived. During our experiments we varied number of subspace dimensions from 2 to 40 and number of independent components derived, were in the range 1 to 200. Table 5.2 depicts some of the sample results and Figure 5.7 shows plot of number of independent components vs recognition rate for various values of subspace dimensions. Corresponding to subspace dimension of 40 and independent component of beyond 40 a maximum accuracy of 84.5% was obtained for GaborJet-ICA. This proves that difference in performance of 2.25% between ICA and PCA is insignificant. 107

10 Table 5.1: Recognition accuracy for GaborJet-PCA Number of principal components Accuracy in % to Figure 5.6: Plot number of principal components vs. recognition accuracy. 108

11 Table 5.2: Recognition accuracy for GaborJet-ICA Recognition Accuracy Independent Dimension Dimension Dimension Dimension Component

12 Figure 5.7: Number of independent components vs. recognition rate for various values of subspace dimensions. 5.6 CONCLUSION Gabor wavelet representation captures salient visual properties such as spatial localization, orientation selectivity, and spatial frequency. By their very nature, Gabor wavelet representations are to some extent insensitive to variations of lighting and local distortions caused by face position and expression. However, since Gabor wavelet is a general image processing tool, which is not specifically designed for face recognition, Gabor features do not contain face specific information learned from face training data. Therefore, directly using Gabor features may not be the best approach. In this thesis we proposed a face recognition scheme that combined GaborJet features and ICA named as GaborJet-ICA technique. Instead of deriving Gabor feature from a whole face image as used in [90], we have derived Gabor feature vector from facial landmarks (fiducial points) known as GaborJets. This makes the system 110

13 computationally efficient. This approach can show potential direction in face recognition. PCA/ICA reduces redundancy and represents decorrelated/independent features explicitly. As the literature on PCA and ICA in face recognition is contradictory, we compared the recognition performances of GaborJet-PCA and GaborJet-ICA for various values of PCA dimensions and independent components. We found maximum accuracy of 82.25% and 84.5% for GaborJet-PCA and GaborJet- ICA respectively. This proves that difference in performance of 2.25% between ICA and PCA is insignificant. The results of this experiment are complex because the recognition rate does not increase monotonically with the number of dimensions. 111

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