Anisotropic Di usion of Noisy Surfaces and Noisy Functions on Surfaces

We present a uni ed anisotropic geometric di usion PDEmodel for smoothing (fairing) out noise both in triangulated 2-manifold surface meshes in IR and functions de ned on these surface meshes, while enhancing curve features on both by careful choice of an anisotropic di usion tensor. We combine the C limit representation of Loop's subdivision for triangular surface meshes and vector functions on the surface mesh with the established di usion model to arrive at a discretized version of the di usion problem in the spatial direction. The time direction discretization then leads to a sparse linear system of equations. Iteratively, solving the sparse linear system, yields a sequence of faired (smoothed) meshes as well as faired functions