Implicit curve/surface evolution with application to the image segmentation problem

This dissertation deals with variational shape modeling and its applications in image analysis, in particular image segmentation. Shapes are modeled by their boundaries (contours/surfaces). In the image domain various degradations may obscure the correct object boundary due to pose, orientation changes from 3D to 2D, and due to various errors in the image capturing process that may alter or camouflage the true object boundary. Over three decades of work in the literature (1960--1990) has been devoted to gradient-based and statistical-based approaches for detection and linking of objects' boundaries. These approaches have a mixed record of success due to the ill-posed nature of the problem, and they do not easily adapt to fusion of a priori information about the objects or the imaging sensors. Variational approaches have been common in the past decade and they provide an alternate view to purely gradient-based and statistical-based methods. Variational approaches extract the objects' boundaries through an energy minimization framework that controls the propagation of a parametric curve/surface (sometimes called front) inside the objects of interest. Two techniques have been proposed for controlling the curve propagation: active contours (snakes), introduced in 1987 by Kass et al. and the level sets approach introduced in 1988 by Osher and co-workers. These two approaches have been examined thoroughly in the computer vision literature during the past decade. At the heart of the active contours and the level set approaches is an energy formulation that implicitly describes the curve/surface propagation in terms of a set of partial differential equations that can be solved numerically to determine the steady state position of the front. The level set methods have proven to be more efficient and flexible than active contours and it is the subject of this dissertation.; The problem under investigation is this: given a multimodal image (i.e., an image with distinct but not necessarily well-defined objects), it is required to produce the outlines of the objects in the image using the intrinsic information in the image (e.g., its intensity statistics, edge information, and other salient characteristics) and whatever known (a priori) shape information about the objects in the image. The proposed solution is to cast the objects' boundaries as a level set function that is able to capture the complicated topology of the objects. The process of curve/surface propagation with level sets is controlled by a new energy model that incorporates the traditional statistical information about the image and a well-defined a priori shape model. The theoretical foundation of the curve/surface propagation is developed using a new level set function in a vector form, and an automatic approach for the initialization of the propagation process. This theory is implemented for tracing contours of various objects and shown to be robust for challenging classes of objects including low resolution images, color images, objects with missing parts due to occlusion or camouflage, and objects that have intrinsic characteristics that may indeed be represented by more than one contour.; On the practical side, the approaches developed in this dissertation have been shown to lend benefits to challenging problems in medical imaging and other computer vision applications. Specifically, the theory is applied in this dissertation for segmentation of T1-weighted magnetic resonance images (MRI) of normal and autistic/dyslexic individuals in order to extract white and gray matter tissues, brain ventricles and the corpus callosum. This step is the basic step in quantifying the changes at the cortical surface between the two groups and volumetric as well as the topological changes in the ventricles and the corpus callosum. Quantification of these changes may lend credence to the hypothesis that the minicolumns networking is different in normal and autistic/dyslexic individuals,...