Manifold Processing from scattered points: applications to surface denoising and thin shell analysis

MARINO ARROYO; DANIEL MILLÁN

Bonn

Workshop; 4th International Workshop Meshfree Methods for Partial Differential Equations; 2007

Institut für Numerische Simulation, Universität Bonn

We present a method for point-based (embedded) manifold processing avoiding any kind of mesh or tessellation. A fundamental difficulty in this endeavor is the absence of an obvious parametric space for general surfaces. In mesh-based processing, the mesh not only provides a geometric description of the surface, but it also provides a support to local parametric spaces and shape functions. This approach is seriously hindered in high dimensions. We apply methods of statistical learning together with maximum entropy approximants to provide a robust method for point-based manifold processing.