Face Recognition Approaches Based On Linear Subspace And Circularly Symmetrical Gabor Transforms

This work involves in the research on robust approaches for face recognition. The research is conducted in two phases. One is on such linear feature subspaces as principal component analysis (PCA) and linear discriminant analysis (LDA) based approaches. The other is on approaches based on circular symmetric Gabor transforms (CSGT). The main objective is to increase the robustness of face recognition approaches to the variable factors in the imaging process of face images, which include variation in illumination and shooting angles determined by the imaging condition, variation in expression and poses and the rotation and translation in face images.The main works we have done include what follows. Studies are conducted to the face recognition approaches based on linear feature subspaces both in theory and in algorithms, including PCA and LDA. On this basis, four new approaches are proposed, which are weighted PCA space based face recognition, generalized PCA combining image correction and bit plane fusion, Eigenblock approach and PCA plus Fractional LDA (F-LDA). Furthermore, through the study on Gabor transform (GT) based approaches, a completely new method using CSGT is presented. Experiments on ORL, AR, Yale and UMIST databases are conducted and it is verified that the new approaches are superior to existing ones.The main innovations of this work lie in the following new approaches proposed in this thesis.1) Weighted PCA space based face recognitionIn the study of the traditional PCA approach, the different effects of different features, e.g. eigenfaces in the eigenface space are observed and analyzed by theoretical analysis and experimental observation. It is proposed to perform face recognition in a weighted PCA space.By weighting the traditional PCA space according to the eigenvalue matrix, equal variances are obtained for each feature component. Thus the traditional PCA space is converted to a normalized weighted PCA space and the discriminant performance is improved. Some good characteristics are theoretically proven. It is pointed out that classification by Euclidian distances in the new space is equivalent to that by Mahalanobis distances in the traditional PCA space. Thus, the reason behind the performance improvement of the new approach is given in theory. In addition, when used for reconstruction purpose, the reconstruction error is the same with that of the traditional PCA space if the transform matrix is formed by eigenvectors corresponding to bigger eigenvalues in the weighted PCA space.In the experiment, distributions of the feature components in the traditional PCA space and in the weighted PCA space respectively are demonstrated and analyzed. It is indicated that, in the traditional PCA space, some features with big values but not significant to classification dictate the computation of the distance metrics. While the role of some other features with small values but indeed significant to classification is submerged. Experiment results also indicate that, even in the weighted PCA space, features should be selected in a descending order of eigenvalues as in the traditional PCA space. The proposed approach is superior to the traditional PCA in recognition accuracy in the experiments. 2) Generalized PCA combining image correction and bit plane fusionAccording to the symmetry of human faces, an image correction approach is given to complement the variable illumination existed in the images. Primary correction and complementation is carried out from the image preprocessing phases to the illumination variance existed in the imaging process caused bias light sources. Meanwhile, images are decomposed into bit planes and different characteristics and contributions to image structure and textures of different planes are analyzed. This is further related to the within-class scatter and the between-class scatter. We argue that after histogram equalization, the planes 0, 1, 5, 6 and 7 mainly show structural characteristics, while plane 2, 3 and 4 mainly textural characteristics. Structural characteristics contribute to common properties of all the different images from the same subject, that is, between-class scatter. While textural characteristics emphasize the differences between different image from the same subject, that is, within-class scatter. Based on the analysis, we propose a face recognition approach of combining image correction and bit plane fusion. In the training stage, a class mark mainly composed of structural information from the samples of the same class is established. Together with the texture information, the samples are thus mapped to a complex space to form virtual samples. Finally, effective feature extraction is achieved using generalized PCA in the complex space and in this way, the invariance of the algorithm to variable illumination and expression is increased.3) Eigenblock approach for face recognitionComputation between big matrices and vectors is inevitable due to the big size of face images in traditional PCA. At the same time, as a whole image based approach, traditional PCA is sensitive to local distortion such as occlusion and expression variance in images. To cope with this problem, we propose to partition the face images into blocks first and then perform PCA on the basis of the position sensitive blocks, which we call eigenblock approach. In the experiment, the algorithm is speeded up and its robustness to occlusion is increased by using the block based matching criterion specifically designed for the new approach.4) PCA plus F-LDA approachLDA is carefully studied and two main problems are analyzed. One is the small sample size (SSS) problem, that is, when the number of training samples is less than that of the pixels in the face image, the within-class scatter matrix is singular and thus the generalized eigenequation has no solution in the LDA. The other is that, because in the classical definition of the between-class scatter matrix, the contribution differences of different classes are ignored and this leads to the problem that the criterion function is not directly related to the recognition accuracy in the conventional LDA.One of the effective approaches to cope with above two problems is to apply an modified criterion function based on weighted between-class scatter matrix. However, it is found in research that, the performance of such face recognition systems is greatly dependant on the choice of the weigh functions. To solve the problem, we combine F-LDA, which was proposed recently to solve the problem of choosing weight functions for the weighted Fisher criterion function with PCA dimension reduction technique to propose a new PCA plus F-LDA approach. In this way, the problem of applying F-LDA to high dimensional face images is solve. Better results than existing approaches are achieved in the experiment. 5) Circularly symmetric Gabor transform based face recognitionBecause its good locality both in spatial and frequency domains and good agreement with the mammalian visual characteristics, GT is widely used in face recognition.Research is conducted on GT based face recognition. Two principal feature selection methods are analyzed. One is to sub-sample the transform domain and then form augmented feature vectors. The other is to extract key points or fiducial points. As a helpful exploration, we propose to use CSGT in face recognition. On the basis of complete analysis and discussion to the definition, concept and properties of CSGT, we examined the characteristics of faces in CSGT domain both in theory and in experiment. By comparing to the traditional GT with the help of experiment in locating eyes in face images, it is found that the former is remarkably superior in rotation invariance and data redundancy.We carry out a complete study to the problem of applying CSGT to face recognition based on above-mentioned research. Technical route of determine the fiducial points according to local extremes in the transform domain is proposed and a conceptual block diagram of face recognition based on CSGT is presented. Moreover, three algorithms are designed for face recognition, which include single channel recognition algorithm using ordered local extremes in image blocks, multiple channel feature fusion algorithm using ordered local extremes and multiple channel classifier fusion algorithm. In the experiments on ORL database, recognition rate of up to 98.5% is achieved, which is significantly higher than existing GT based approaches.