Migration processes

Optimization processes based on "active models" play central roles in many areas of computational vision as well as computational geometry. However, current models usually require highly complex and sophisticated mathematical machinery and at the same time they also 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, is presented. The processes are based on iterated averaging over neighborhoods defined by constant geodesic distance. It is demonstrated that the migration process model combines a number of advantages of different active models. The processes can be applied to derive natural solutions to a variety of optimization problems which include: defining (minimal) surface patches given their boundary curves; finding shortest paths joining set of points; and decomposing objects into "primitive" parts.