#### Abstract

Edge detection is cast as a problem in cost minimization. This is achieved by the formulation of two cost functions which evaluate the quality of edge configurations. The first is a comparative cost function (CCF), which is a linear sum of weighted cost factors. It is heuristic in nature and can be applied only to pairs of similar edge configurations. It measures the relative quality between the configurations. The detection of edges is accomplished by a heuristic iterative search algorithm which uses the CCF to evaluate edge quality. The second cost function is the absolute cost function (ACF), which is also a linear sum of weighted cost factors. The cost factors capture desirable characteristics of edges such as accuracy in localization, thinness, and continuity. Edges are detected by finding the edge configurations that minimize the ACF. We have analyzed the function in terms of the characteristics of the edges in minimum cost configurations. These characteristics are directly dependent of the associated weight of each cost factor. Through the analysis of the ACF, we provide guidelines on the choice of weights to achieve certain characteristics of the detected edges. Minimizing the ACF is accomplished by the use of Simulated Annealing. We have developed a set of strategies for generating next states for the annealing process. The method of generating next states allows the annealing process to be executed largely in parallel. Experimental results are shown which verify the usefulness of the CCF and ACF techniques for edge detection. In comparison, the ACF technique produces better edges than the CCF or other current detection techniques.

#### Date of this Version

12-1-1988