Linear Representation Based Robust Face Recognition

As a special biometric recognition technique, face recognition has been a hot re-search topic in pattern recognition for many years. Linear representation based face recognition methods attract a lot of interests recently. These methods are based on the assumption that a high-dimensional probe face image lies on a low-dimensional subspace spanned by the training samples of the same subject. With the representa-tion coefficients obtained by a regression problem, the decision is made by minimizing the residuals of reconstructing the probe face by a linear combination of the training samples. Despite their simplicities, these approaches can achieve excellent results with features of raw pixels in some situations. In practice, however, various potential fa-cial variations (e.g., changes of expression, corruption, occlusions, etc) make the linear subspace assumption not hold. The estimation of the coefficients are largely biased by the noisy points (outliers) in face images, which deteriorates the recognition accura-cies. To solve this problem, in this dissertation, a research has been made on linear representation based robust face recognition. First, fast robust regression methods has been proposed to detect the noisy pixels in face images. Based on that, more accurate coefficients are estimated, which helps to yield better recognition. Second, incorpo-rating locality information from both spatial features and training samples, a linear representation based method is proposed for robust face recognition. Specifically, the highlights and main contributions of this dissertation include:(1) A fast method of approximate least trimmed sum of squares regression (ALTS) is proposed. ALTS converts the original NP hard LTS problem to an SOCP problem, which can be efficiently solved by an off-the-shelf solver. ALTS can effectively detect the outliers in images, which largely improves the robustness of linear representation based face recognition methods.(2) L∞-Minimization is firstly proved to be effective for outlier removal in face re-ognition problems. Then a new method for the minimization of the L∞norm is presented, which provides a speedup of multiple orders of magnitude for data with high dimension. Based on column generation, the L∞norm minimiza-tion problem is broken up into smaller sub-problems, which can then be solved extremely efficiently. Same as ALTS, this method is shown to be very robust against the occlusions or image corruption problem for face recognition.(3) The importance of locality between samples is explored for face recognition. A locality constrained representation and classification method is proposed. The locality constraint makes the linear subspace assumption more reasonable. A Bayesian interpretation is given for this representation model, based on which the relations between locality and sparsity are explored. We show that the locality constraint on the representation coefficients leads to an approximately sparse representation, and locality are more suitable for classification. Different from the sparse representation based classifier with L1-Minimization, the proposed method only needs to solve an efficient ridge regression problem.(4) The proposed locality constrained method is conducted on the spatial pyramid local patches, which are aggregated by a Bayesian based fusion method. This fusion method effectively aggregate the representation residuals with respect to these patches. In addition, a locality based concentration index (LCI) is defined to measure the reliability and discriminant ability of local patches. The algorith-m is shown to outperform the state-of-the-art on several datasets for both the occlusion and single sample per person (SSPP) problems.