Geodesic Evolution Laws---A Level-Set Approach

9 years 5 months ago
Geodesic Evolution Laws---A Level-Set Approach
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. Key words. image denoising, PDEs on surfaces, higher order equations, geodesic evolution laws, level-set method, finite elements, adaptivity AMS subject classifications. 35K55, 53C44, 53D25 DOI. 10...
Christina Stöcker, Axel Voigt
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2008
Authors Christina Stöcker, Axel Voigt
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