Nonlocal Surface Fairing

We propose a new variational model for surface fairing. We extend nonlocal smoothing techniques for image regularization to surface smoothing or fairing, with surfaces represented by triangular meshes. Our method is able to smooth the surfaces and preserve features due to geometric similarities using a mean curvature based local geometric descriptor. We present an efficient two step approach that first smoothes the mean curvature normal map, and then corrects the surface to fit the smoothed normal field. This leads to a fast implementation of a feature preserving fourth order geometric flow. We demonstrate the efficacy of the model with several surface fairing examples.