Study On Some Subspace Methods For Feature Extraction And Their Applications In Face Recognition

Feature extraction is one of the most basic problems in pattern recognition. For image recognition tasks, extracting the effective image features is a crucial step. As one of the most effective feature extraction approaches, subspace methods have received extensive attention owing to their appealing properties. The essence of subspace methods is to reduce a high-dimensional original sample space to a low-dimensional feature subspace that is benefit to classification. Recently, face recognition has been a hot topic in pattern recognition field due to its wide range of applications. In this dissertation, subspace methods for feature extraction are studied deeply. Several methods are proposed and applied to face recognition successfully. The main work and contributions can be summarized as follows:1. As a kind of effective algebraic features to describe images, singular values (SVs) have been used for face recognition by many researchers. However, SVs neglect the character of human faces and contain inadequate information for recognition. To address these problems, this dissertation proposes a new kind of algebraic features named as Combined SVs (CSVs), which is based on the global and local information of an image. CSVs utilize the high discriminatory local regions to recognition, and have the beneficial properties similar to SVs'. The experimental results on face databases indicate CSVs contain more useful information and are effective for recognition. Furthermore, a new robust method based on grayscale mathematical morphology and gray-level projection is also proposed to detect the needed local regions. The detection algorithm can avoid determining the precise locations of features. The experimental results illustrate it is robust for the variations of facial details, pose and expression, and appropriate for extraction of CSVs.2. Incorporating the sample distribution information into the process of feature extraction is beneficial to promote the classification performance of features. According to the idea of fuzzy membership degree, the dissertation proposes a fuzzy class label based canonical correlation analysis (CCA) method for image feature extraction. Firstly, a new fuzzy class labels in the form of membership degrees are designed elaborately to represent the sample distribution. Then the fuzzy labels are embedded in CCA to extract more discriminative features which combine the information about gray level and distribution together. Furthermore, the proposed fuzzy label CCA has been generalized to nonlinear fuzzy label KCCA algorithm by integrating kernel methods. Obviously, the novel algorithm retains all merits of the fuzzy label CCA method, while being able to extract the nonlinear discriminative features. Comprehensive experimental results on face recognition validate the theoretical analysis and demonstrate the effectiveness of the proposed methods.3. CCA often suffers from the small sample size problem when dealing with the high dimensional image data. Some approaches have been proposed to deal with this problem. This dissertation discusses the shortcomings of two existing approaches in detail, and proposes two improved algorithms. First, according to the matrix theory and dual-space idea, an improved method named dual-space fuzzy label CCA is proposed to counteract the effect of small eigenvalues which are poorly estimated due to finite samples. This method can avoid the overfitting problem and take full advantage of the discriminative information in the image space. Second, an enhanced method is presented to solve the problem that the two-dimensional CCA method requires much storage space and runtime. The essence of 2DCCA is first argued, and then a new class membership matrix is constructed by making use of the spectrum representation of images. Subsequently, a modified correlation criterion function is proposed from the angel of favoring classification. Finally, 2DPCA method is used for further dimensional reduction after 2DCCA. The feasibility and effectiveness of two improved methods have been demonstrated through extensive experiments conducted on several face databases.