Discrete active models and applications

Abstract

Optimization processes based on “active models” play central roles in many areas of computational vision as well as computational geometry. Unfortunately, current models usually require highly complex and sophisticated mathematical machinery and at the same time they suffer from a number of limitations which impose restrictions on their applicability. In this paper a simple class of discrete active models, called migration processes (MPs), is presented. The processes are based on iterated averaging over neighborhoods defined by constant geodesic distance. It is demonstrated that the MP model-a system of self-organizing active particles—has a number of advantages over previous models, both parametric active models (“snakes”) and implicit (contour evolution) models. Due to the generality of the MP model, the process can be applied to derive natural solutions to a variety of optimization problems,including defining (minimal) surface patches given their boundary curves; finding shortest paths joining sets of points; and decomposing objects into “primitive” parts.