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Image-based face recognition has attained wide applications during the past decades in commerce and law enforcement areas, such as mug shot database matching, identity authentication, and access control. Existing face recognition techniques (e.g., Eigenface, Fisherface, and Elastic Bunch Graph Matching, etc.), however, do not perform well when the following case inevitably exists. The case is that, due to some variations in imaging conditions, e.g., pose and illumination changes, face images of the same person often have different appearances. These variations make face recognition techniques much challenging. With this concern in mind, the objective of my research is to develop robust face recognition techniques against variations. This thesis addresses two main variation problems in face recognition, i.e., pose and illumination variations. To improve the performance of face recognition systems, the following methods are proposed: (1) a face feature extraction and representation method using non-uniformly selected Gabor convolution features, (2) an illumination normalization method using adaptive region-based image enhancement for face recognition under variable illumination conditions, (3) an eye detection method in gray-scale face images under various illumination conditions, and (4) a virtual pose generation method for pose-invariant face recognition. The details of these proposed methods are explained in this thesis. In addition, we conduct a comprehensive survey of the existing face recognition methods. Future research directions are pointed out.

The goal of this thesis is to gain a deep understanding of inverse problems arising from 2D image and 3D surface reconstruction, and to design effective techniques for solving them. Both computational and theoretical issues are studied and efficient numerical algorithms are proposed. The first part of this thesis is concerned with the recovery of 2D images, e.g., de-noising and de-blurring. We first consider implicit methods that involve solving linear systems at each iteration. An adaptive Huber regularization functional is used to select the most reasonable model and a global convergence result for lagged diffusivity is proved. Two mechanisms---multilevel continuation and multigrid preconditioning---are proposed to improve efficiency for large-scale problems. Next, explicit methods involving the construction of an artificial time-dependent differential equation model followed by forward Euler discretization are analyzed. A rapid, adaptive scheme is then proposed, and additional hybrid algorithms are designed to improve the quality of such processes. We also devise methods for more challenging cases, such as recapturing texture from a noisy input and de-blurring an image in the presence of significant noise. It is well-known that extending image processing methods to 3D triangular surface meshes is far from trivial or automatic. In the second part of this thesis we discuss techniques for faithfully reconstructing such surface models with different features. Some models contain a lot of small yet visually meaningful details, and typically require very fine meshes to represent them well; others consist of large flat regions, long sharp edges (creases) and distinct corners, and the meshes required for their representation can often be much coarser. All of these models may be sampled very irregularly. For models of the first class, we methodically develop a fast multiscale anisotropic Laplacian (MSAL) smoothing algorithm. To reconstruct a piecewise smooth CAD-like model in the second class, we design an efficient hybrid algorithm based on specific vertex classification, which combines K-means clustering and geometric a priori information. Hence, we have a set of algorithms that efficiently handle smoothing and regularization of meshes large and small in a variety of situations.

A novel approach for the analysis of spinal cord deformation based on a combined technique of non-invasive imaging and medical image processing is presented. A sopposed to traditional approaches where animal spinal cords are exposed and directly subjected to mechanical impact in order to be examined, this approach can be used to quantify deformities of the spinal cord in vivo, so that deformations — specifically those of myelopathy-related sustained compression — of the spinal cord can be computed in its original physiological environment. This, then, allows for a more accurate understanding of spinal cord deformations and injuries. Images of rat spinal cord deformations, acquired using magnetic resonance imaging (MRI), were analyzed using a combination of various image processing methods, including image segmentation, a versor-based rigid registration technique, and a B-spline-based non-rigid registration technique. To verify the validity and assess the accuracy of this approach, several validation schemes were implemented to compare the deformation fields computed by the proposed algorithm against known deformation fields. First, validation was performed on a synthetically-generated spinal cord model data warped using synthetic deformations; error levels achieved were consistently below 6% with respect to cord width, even for large degrees of deformation up to half of the dorsal-ventral width of the cord (50% deflection). Then, accuracy was established using in vivo rat spinal cord images warped using those same synthetic deformations; error levels achieved were also consistently below 6% with respect to cord width, in this case for large degrees of deformation up to the entire dorsal-ventral width of the cord (100% deflection). Finally, the accuracy was assessed using data from the Visible Human Project (VHP) warped using simulated deformations obtained from finite element (FE) analysis of the spinal cord; error levels achieved were as low as 3.9% with respect to cord width. This in vivo, non-invasive semi-automated analysis tool provides a new framework through which the causes, mechanisms, and tolerance parameters of myelopathy-related sustained spinal cord compression, as well as the measures used in neuroprotection and regeneration of spinal cord tissue, can be prospectively derived in a manner that ensures the bio-fidelity of the cord.