# Image Compression Effects on Face Recognition for Images with Reduction in Size

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2 by an integer and is usually in the range between 0 and 255. Hence, the image can be represented by a three matrices of size equal to the size of the image. For example if the image size 200 x 300 pixels, then it can be represented by 3 matrices of size 200 x 300. A gray image will have one matrix representing the pixels. A 2-D image can be transformed to 1D vector by concatenating all rows one after the other into a long thin vector. This operation can also be performed column wise to get a long thin vector. Let there are M vector of size. N is the product of number of rows and number of columns. Each image is represented by and all the images can be averaged to get a mean image. The concept of mean image is only mathematical in the sense and so not carries any physical significance. The centered image with respect to mean image can be found by subtracting mean image from each image and let vectors (1) (2) (3) W is the matrix composed by placing the column side by side. The covariance matrix can be defined by Hence the size of covariance matrix becomes N x N. For example, for the image size of 200 x 300 pixels, the size of the covariance matrix Q becomes x which is huge for solving the covariance matrix for Eigenvalues and Eigenvectors. In order to determine the Eigen values and Eigen vectors of the covariance matrix, one can follow the common theorem proposed in linear algebra. The procedure is mentioned below: Let = Eigen values of =Eigen vectors of = Eigen values of =Eigen vectors of (4) (5) (6) matrix considering the mean image. However, normalization to make to equal to. needs The Eigen vectors can be computed for each no zero Eigen value and they are sorted out in descending order based on the Eigen values. This set of Eigen vector form the orthonormal basis for the subspace within which most image data can be represented, but a with a minimal amount of error. The Eigen vector corresponding to the largest Eigen value is the one with greatest variance among all images and the Eigen vector corresponding to the smallest Eigen value is the one with least variance. 3. EXPERIMENTAL RESULTS Fig. 1 shows the image of 10 people whose images are considered for face recognition in this work. Two expressions of each face is taken as and stored in the database. Hence there are totally 20 images stored in the database which will be compared with the probe image to check if the probe image matches with any of the stored faces. The stored images are considered in 10 different sizes and each size of all the 20 faces are stored in the database at a time for experimentation purpose. Fig.2 shows the image sets of the compressed images from 90% of the original size to 10% of the original size. The left most image represents the original size, the second image is of 90% of the size, third image is 80% of the size and so on; and last one is of 10% of the size. The original size of the image is 180 x 200 pixels and the images shown below are only representative. When the original image is compressed to 10% of its original size, the size of the image becomes 18 x 20. When the probe image, which is 180 x 200 is presented to compare with the store image which is of size 18 x 20, the dimension mis-match occurs for a the PCA algorithm, hence the stored image is reconstructed back to the size 180 x 200. However, though the compressed image is reconstructed back to original size, the original image quality is not recovered as the information is lost when it is compressed and stored at 10% of he original size. In this way, a high quality probe image of size 180 x 200 is compared with the poor quality stored image of size 180 x 200. It is the interest of this work to verify to what level of compression the face recognition is successful and that size of the image can be stored in the databases instead of the original size. Figure 1: Images of persons considered for face recognition By multiplying both the sides by (7) The above equation can be interpreted as the first M-1 Eigen values and Eigen vectors can be derived from and. The M-1 represents the number of degrees of freedom of the Image Set 1 39

3 Image Set 2 Image Set 10 Image Set 3 Image Set 11 Image Set 4 Image Set 12 Image Set 5 Image Set 13 Image Set 6 Image Set 14 Image Set 7 Image Set 15 Image Set 8 Image Set 16 Image Set 9 Image Set 17 40

4 Image Set 18 Image Set 19 Image Set 20 Figure 4: Distribution of Largest Eigen Values for the reconstructed images Fig. 4 shows the distribution of largest Eigen values for the reconstructed images of original and compressed ones. The largest Eigen values of the different compression ratios show very minimal variation up to 20% of size and there is a relatively a dip when the image of 10% size is considered. However, the magnitude does not have much difference and the face recognition is successful. Figure 2: Image sets original and compressed in size from 90% to 10% of the size from left to right. The face recognition is successful when the probe images are presented to compare with the stored images. For all probe images, the face recognition was successful for compression sizes up to 10% of the original size. When the compression is carried out below 10%, the face recognition was not successful for some of the probe images. Hence the cases below 10% compression are not presented here. Fig. 3 shows the distribution of Eigen values for the reconstructed images of original and compressed ones. We can notice that the original and compressed image Eigen values are almost same for all cases. When the compression approaches 10% of the size, there is very small difference in the Eigen values between the original images and 10% of the compressed size of the images. This shows that even if we compress the image to 10% of its size the information is available. Figure 5: Distribution of Second Largest Eigen Values for the reconstructed images Figure 6: Distribution of Third Largest Eigen Values for the reconstructed images Figure 3: Distribution of Eigen Values for the reconstructed images 41

5 more research is required to understand this behavior, which is under progress. Figure 7: Distribution of Tenth Largest Eigen Values for the reconstructed images Figs. 5 to 7 shows the distribution of second, third and tenth largest Eigen values for the reconstructed images of original and compressed ones. These Eigen values of the different compression ratios show very minimal variation up to 20% of size and there is a relatively a dip when the image of 10% size is considered. However, the magnitude does not have much difference and the face recognition is successful. Figure 8: Coefficients of First Eigen vector Figure 9: Coefficients of Fifth Eigen vector Figs 8 and 9 show the coefficients of the first and fifth Eigen vectors of the reconstructed images. The coefficients have almost same sign as well the nearest magnitudes with respect to the original image. However, it is quite different at 10 of the size, the Eigen values and Eigen vector coefficients vary too much, and 4. CONCLUSION In this work, the face recognition using PCA is tested for various sizes of compression and its suitability to store the images at smaller sizes is evaluated. It is proven that, when the images are compressed up to a size of 10 % of its original size, the face recognition is successful and the compression of images to sizes below 10% is not successful in all cases. By looking at the Eigen values and coefficients of Eigen vectors, it is concluded that, the values start to deviate from the Eigen values and Eigen vectors of original image at 10% of the size. Research is under progress to determine if it is possible to successfully recognize faces by modifying the Eigen values with suitable algorithms. 5. REFERENCES [1] Zhao W., Chellappa R., Rosenfeld A., Phillips P.J., Face Recognition: A Literature Survey, ACM Computing Surveys, Vol. 35, Issue 4, December 2003, pp [2] Delac K., Grgic M., A Survey of Biometric Recognition Methods, Proc. of the 46th International Symposium Electronics in Marine, ELMAR-2004, Zadar, Croatia, June 2004, pp [3] Li S.Z., Jain A.K., ed., Handbook of Face Recognition, Springer, New York, USA, 2005 [4] Delac, K., Grgic, M. (eds.), Face Recognition, I-Tech Education and Publishing, ISBN , Vienna, July 2007, 558 pages [5] Rakshit, S., Monro, D.M., An Evaluation of Image Sampling and Compression for Human Iris Recognition, IEEE Trans. on Information Forensics and Security, Vol. 2, No. 3, 2007, pp [6] Matschitsch, S., Tschinder, M., Uhl, A., Comparison of Compression Algorithms' Impact on Iris Recognition Accuracy, Lecture Notes in Computer Science - Advances in Biometrics, Vol. 4642, 2007, pp [7] Funk, W., Arnold, M., Busch, C., Munde, A., Evaluation of Image Compression Algorithms for Fingerprint and Face Recognition Systems, Proc. from the Sixth Annual IEEE Systems, Man and Cybernetics (SMC) Information Assurance Workshop, 2005, pp [8] Mascher-Kampfer, A., Stoegner, H., Uhl, A., Comparison of Compression Algorithms' Impact on Fingerprint and Face Recognition Accuracy, Visual Communications and Image Processing 2007 (VCIP'07), Proc. of SPIE 6508, 2007, Vol. 6508, , 12 pages [9] Elad, M., Goldenberg, R., Kimmel, R., Low Bit-Rate Compression of Facial Images, IEEE Trans. on Image Processing, Vol. 16, No. 9, 2007, pp [10] Skodras A., Christopoulos C., Ebrahimi T., The JPEG 2000 Still Image Compression Standard, IEEE Signal Processing Magazine, Vol. 18, No. 5, September 2001, pp [11] Wallace G.K., The JPEG Still Picture compression Standard, Communications of the ACM, Vol. 34, Issue 4, April 1991, pp

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