# Human face recognition

 Author: Wong, Wai-tak Title: Human face recognition Degree: M.Sc. Year: 2007 Subject: Hong Kong Polytechnic University -- Dissertations.Human face recognition (Computer science)Discriminant analysis. Department: Dept. of Electronic and Information Engineering Pages: 74 leaves : ill. ; 30 cm. Language: English InnoPac Record: http://library.polyu.edu.hk/record=b2115931 URI: http://theses.lib.polyu.edu.hk/handle/200/2623 Abstract: The small sample size (sss) problem is often encountered in Linear Discriminant Analysis (LDA) for pattern recognition. This problem results in the singularity of the within-class scatter matrix, so the optimal projection vectors for separating the different classes cannot be solved. In this project, we will first study Principal Component Analysis (PCA), and then three different methods for LDA to solve the sss problem for face recognition. PCA is applied to reduce the dimensionality of an original sample space. In this method, a number of principal components or eigenvectors are derived based on the training samples; this number is usually much smaller than the dimension of the feature vectors. Images represented in the form of vectors are projected onto these eigenvectors to form small-dimensional feature vectors for face recognition. To validate a testing sample, two different approaches are evaluated. The first one is to measure the distance between the testing sample and all the training samples in the eigenspace. The other one is to reconstruct the projected testing image from the eigenspace and then compare it to the training images. The mean squared difference is used as a similarity measure for comparing two face images. For LDA, three different approaches are investigated to solve the sss problem. For all of these approaches, the face vectors are first projected onto the eigenvectors so as to reduce their dimension. The first approach considers only those eigenvectors in the null space of the within-class scatter matrix, because they can minimize the within-class scatter matrix. However, this approach does not guarantee that the between-class scatter matrix is maximized in the meantime. Thus, the eigenvectors corresponding to the largest eigenvalues are selected to maximize the ratio of between-class to within-class scattering. Another method is that a small perturbation is added to the within-class scatter matrix in order to prevent it being a singular matrix due to the small sample size. A random small number is added to each element in the matrix. It is found that the singularity problem can be effectively eliminated, but the corresponding eigenvectors are found to be very sensitive to the perturbation. Hence, iteration processes have to be performed to find the most appropriate perturbation for a high recognition rate. Moreover, a total scatter matrix, which is the sum of the within-class scatter matrix and the between-class scatter matrix, can be used instead of the within-class scatter matrix to solve the sss problem. Due to the high dimensionality of a face, the within-class scatter matrix is probably singular. Although experimental results show that this approach cannot totally eliminate the singularity problem, at least it does improve the recognition rate, which is higher than that when using PCA. The last approach investigated in this project is a null space approach. As the within-class scatter matrix is singular due to the small sample size, the eigenvectors of the inverse of the matrix are selected to form a null space. When the within-class scatter matrix is projected onto these eigenvectors, a zero matrix is obtained. This guarantees that the projections can produce the best discriminant power. After forming the null space, those eigenvectors corresponding to the largest eigenvalues are selected to form the most discriminant projection vectors for face recognition. Experimental results show that the recognition rate based on the null space approach is higher than that of other methods. Furthermore, the LDA approach outperforms the PCA approach. All the experiments are conducted to evaluate the relative performance of the different algorithms. The performance of each algorithm will be evaluated and discussed.

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