DEPARTMENT OF COMPUTER SCIENCE DOCTORAL DISSERTATION DEFENSE Candidate: Hsing-Kuo Kenneth Pao Advisor: Davi Geiger A Continuous Model for Salient Shape Selection and Representation 4:00 p.m., Friday, April 6, 2001 7th floor conference room, 715 Broadway Abstract We propose a new framework for shape representation and salient shape selection. The framework is considered as a low- to middle-level vision process. The framework can be applied to various topics, including figure/ground separation, searching of the shape axis, junction detection and illusory figure finding. The model construction is inspired by the Gestalt studies. They suggest that proximity, convexity, similarity, good continuation, closure, symmetry, etc, are useful for figure/ground separation and visual organization construction. First, we quantify those attributes for (completed or partial) shapes by our distributed systems. The shape will be evaluated and represented by those results. In particular, the shape convexity, rather than other shape attributes like the symmetry axis or size which were well-studied before, will be emphasized in our discussion. Our problem is proposed in a continuous manner. For the shape convexity, unlike the conventional mathematical definition, we are aimed at deriving a definition to describe a shape ``more convex'' or ``less convex'' than the other. To search the shape axis, more than a binary information telling a point on or off any axis, a continuous information will be obtained. We distinguish axes with ``stronger'' or ``weaker'' declarations. An Easy and natural scheme of pruning can be applied by such representation. For the junction detection, we do not assume any artificial threshold. Instead, the transition from low-curvature to high-curvature curves or curves with discontinuities will be shown by our representation. The model is based on a variational approach, provided by the minimization of the data fitting error as well as the neighborhood discrepancy. Two models will be proposed, the decay diffusion process and the orientation diffusion process.