Geodesic Evolution Laws—A Level-Set Approach

Abstract

Motion of curves governed by geometric evolution laws, such as mean curvature flow and surface diffusion, is the basis for many algorithms in image processing. If the images to be processed are defined on nonplanar surfaces, the geometric evolution laws have to be restricted to the surface and turn into geodesic evolution laws. In this paper we describe efficient algorithms for geodesic mean curvature flow and geodesic surface diffusion within a level-set approach. Thereby we compare approaches with an explicit representation of the surface by a triangulated surface mesh and an implicit surface representation as the zero-level surface of a level-set function. As an application we present the numerical treatment of the classical model of Rudin, Osher, and Fatemi to denoise images on surfaces.