@misc{LangePolthier2005, author = {Lange, Carsten and Polthier, Konrad}, title = {Anisotropic Smoothing of Point Sets}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-8508}, number = {05-16}, year = {2005}, abstract = {The use of point sets instead of meshes became more popular during the last years. We present a new method for anisotropic fairing of a point sampled surface using an anisotropic geometric mean curvature flow. The main advantage of our approach is that the evolution removes noise from a point set while it detects and enhances geometric features of the surface such as edges and corners. We derive a shape operator, principal curvature properties of a point set, and an anisotropic Laplacian of the surface. This anisotropic Laplacian reflects curvature properties which can be understood as the point set analogue of Taubin's curvature-tensor for polyhedral surfaces. We combine these discrete tools with techniques from geometric diffusion and image processing. Several applications demonstrate the efficiency and accuracy of our method.}, language = {en} }