7.1 INTRODUCTION Wavelet Transform is a popular multiresolution analysis tool in image processing and

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1 Chapter 7 FACE RECOGNITION USING CURVELET 7.1 INTRODUCTION Wavelet Transform is a popular multiresolution analysis tool in image processing and computer vision, because of its ability to capture localized time-frequency information of image extraction. Over the past two decades, following wavelets, other multiresolution tools like contourlets, ridgelets etc. were developed. Curvelet Transform [50] is a recent addition to this list of multiscale transforms. The transform was designed to represent edges and other singularities along curves much more efficiently than traditional transforms, i.e. using many fewer coefficients for a given accuracy of reconstruction. Unlike the wavelet transform, curvelet transform has directional parameters, and the curvelet pyramid contains elements with a very high degree of directional specificity. 7.2 THE PROPOSED ALGORITHM AND EXPERIMENTAL RESULTS Face recognition based on low frequency curvelet coefficients called as curvefaces has been presented in [94]. Statistical measures of curvelet coefficients such as mean, variance and entropy have been used in [54] [95] to extract face image features using curvelet. However we found poor accuracy using these approaches. Motivated by this fact we proposed new face recognition technique based on Independent Component Analysis and curvelet. Our approach is based on thresholding the curvelet coefficients. We extract image features of facial images by applying curvelet transform. Face images are then partially reconstructed by applying inverse curvelet transform to the coefficients after thresholding. These partially reconstructed images 122

2 form the feature vector. We then transformed this feature vector into the basis space of PCA and ICA for dimensionality reduction. Trained face images are represented as points in this space. In order to identify, test images are also projected into this basis space. Euclidean distance measure has been used to estimate the similarity. We then compared the performance in both PCA and ICA subspaces. We resized the face images to size The feature extraction using curvelet is applied to each database image. For image size of , the maximum number of levels possible are 4. Hence each image is decomposed into 4 levels of scales using curvelet transform. The numbers of subbands at different scales are different. For 4 levels of decomposition, there are 1, 16, 32 and 1 subbands at decomposition level 1, 2, 3, and 4 respectively. Therefore, 4 levels decomposition creates 50 (= ) subbands of curvelet coefficients. However, because a curvelet oriented at an angle θ produces the same coefficients as a curvelet oriented at an angle π + θ, only half of the subbands at level 2 and 3 may be used. Figure 7.1, 7.2 and 7.3 shows curvelet coefficients of a sample image for all the 50 subbands. Figure 7.1: (a) Original image (b) Subband at scale 1 (c) Subband at scale 4 123

3 Figure 7.2: 16 Subbands at scale 2 Figure 7.3: 32 Subbands at scale 3 The proposed technique is shown in Figure 7.4. We set a threshold in percentage and consider only above threshold values of coefficients for the partial reconstruction. Remaining small coefficients are set to zero. Figure 7.5 shows partially reconstructed face images taking only 10% coefficients after setting the remaining coefficients to zero. In this experiment we have used frequency wrapping based curvelet toolbox, Curvelet [78]. The partially reconstructed face images are then projected in PCA and ICA subspace for dimensionality reduction. The features extracted can be 124

4 classified by measuring Euclidean distance between mean values of the training images in each class and the testing images. During our experiments we evaluated the recognition accuracy for different threshold values in the range 0.05% to 10%. Figure 7.6 depicts the plot of recognition accuracy vs. percentage coefficients used for thresholding. The results show maximum accuracy of 87.50% and 85.00% for curvelet-ica and curvelet-pca respectively. Whereas accuracy using ICA and PCA alone was 73% and 82.50% respectively. Input Face Image FDCT Thresholding Subbands IFDCT PCA/ICA Classifier PCA/ICA Subspace Recognition Result Figure 7.4: Outline of the proposed method 125

5 Table 7.1: Percentage recognition accuracy using curvelet PCA and curvelet ICA for different values of percentage threshold Threshold in % Recognition accuracy in % Curvelet PCA Curvelet ICA Figure 7.5: Partially reconstructed face images 126

6 Figure 7.6: Recognition accuracy for different values of thresholds 7.3 CONCLUSION We proposed a face recognition system that combined curvelet transform and independent component analysis (ICA). We investigated the possibility of combining curvelet transform with subspace analysis techniques like PCA and ICA. Instead of using statistical measures such as mean and variance for feature extraction we partially reconstructed the face images by thresholding the curvelet coefficients. This approach is found to give better results as curvelets is more effective in capturing curvilinear properties like lines and edges. As depicted in table 7.1 in case of PCA recognition accuracy remains consistently constant after percentage threshold of 3%. This shows only about 3% curvelet coefficients are significant. At 6% and 8% value of the threshold ICA gives better accuracy than PCA. However in case of ICA recognition accuracy does not increase monotonically. This may be because of the fact that ICA is an iterative optimization procedure. 127