| This thesis research is concerned with image segmentation, a classical problem in image processing. The first part of this thesis is focused on a graph-theoretic approach to low-level image segmentation. Two important outstanding problems were addressed: (a) selection of a cost function, whose optima provide an unbiased image segmentation along the image edge, and (b) an efficient optimization algorithm. This thesis presents a satisfactory solution to both problems. Specifically, a novel cost function, cut ratio, is proposed, whose minima correspond to finding image-partitioning boundaries with maximal average edge-likelihood. In addition, a polynomial-time ratio-cut algorithm is developed to find the global optimum of this cost function.; The second part of this thesis is focused on using prior geometric information to improve the reliability and accuracy of image segmentation. Specifically, a new shape-deformation method is proposed to incorporate prior template shape information into image segmentation by deforming a given template shape to fit the detected low-level edge features in a target image. Combining the support vector machine and thin-plate splines, this method increases the robustness to the detection noise as well as the reliability to preserve the template shape topology. In addition, an efficient algorithm is developed to optimize the deformation cost function using quadratic programming. |
