Research On Subspace Representation Of Face Images

Since the 1990s, the face recognition technology has been greatly promoted by subspace methods such as PCA (Principal Component Analysis) and LDA (Linear Discriminant Analysis), which have become the de facto baseline methods. Two major problems with regard to face recognition by subspace methods are Small Sample Size (SSS) and Great Facial Variations (GFV). This paper is focused on two aspects, namely, on one hand, conducting comparative studies among some existing subspace methods to facilitate future studies, and on the other hand, proposing some effective methods to deal with the aforementioned problems. The major contributions in this paper are that:(1) On PCA, the following four researches are conducted. First, an in-depth analysis is given to 2DPCA (two-dimensional PCA), with the main result being that 2DPCA is indeed PCA subjected to the Kronecker product constraint. Second, the GLRAM (Generalized Low Rank Approximations of Matrices) method is revisited, with the main results being that: (a) some basic properties of GLRAM are revealed, (b) a lower bound of the objective function of GLRAM is derived to answer the two open problems raised by Ye, and (c) when and why GLRAM can obtain good compression (reconstruction) performance is explored. Third, the GLRAM method is extended to its non-iterative version, NIGLRAM (Non-Iterative GLRAM). NIGLRAM constructs and optimizes an approximate objective function of GLRAM, and enjoys an automatic criterion in determining the number of projection vectors. Fourth, a PrPCA (Progressive PCA) method is proposed. PrPCA makes use of the contextual information among the image blocks, and reads face images progressively to compute the principal components(2) On LDA, the following four researches are carried out. First, some properties of DCV (Discriminant Common Vectors), NCA (Neighborhood Component Analysis), LAP (Laplacianfaces) and wMMC (weighted Maximal Margin Criterion) are revealed. Second, efficient algorithms are proposed for RDA (Regularized Discriminant Analysis), wMMC, PLDA (Pseudo-inverse LDA) and KPLDA (Kernelized PLDA). Third, DCV's relationships with NCA, LAP, wMMC and RDA are revealed, with the main results being that: (a) DCV can obtain the optimal result of the objective functions of both NCA and LAP, (b) DCV is a special case of both wMMC and RDA, and (c) when the MSV (Mean Standard Variation) criterion is relatively small, DCV can obtain good classification performance. Fourth, the resampling technique is employed to improve the classification performance of Fisherfaces (or PCA+LDA) and LDA/QR ((LDA via QR decomposition).(3) The FSVDR (Fractional order Singular Value Decomposition Representation) is proposed to alleviate the great facial variations, and to offer an intermediate representation between the original face images and subspace methods. Empirical results show that, FSVD can obviously improve the classification performance of subspace methods such as PCA, DCV and LDA/QR under great facial variations.(4) The SIS (Single Image Subspace) representation is proposed. The core of SIS is to represent each (training, testing) image as a subspace spanned by its synthesized virtual images. To measure the dissimilarity of face images under SIS representation, a new subspace distance that can deal with unequal number of subspace dimensions is developed. To deal with the great facial variations, face images are divided into a set of sub-images, on which SIS is employed. Finally, some new kernels based on SIS are defined.