A Digital Topology-based Method for the Topological Filtering of a Reconstructed Surface

摘要

In this paper, we use concepts from digital topology for the topological filtering of reconstructed surfaces. Given a finite set S of sample points in 3D space, we use the voronoi-based algorithm of Amenta & Bern ~1 to reconstruct a piecewise-linear approximation surface in the form of a triangular mesh with vertex set equal to S. A typical surface obtained by means of this algorithm often contains small holes that can be considered as noise. We propose a method to remove the unwanted holes that works as follows. We first embed the triangulated surface in a volumetric representation. Then, we use the 3D-hole closing algorithm of Aktouf et al.~2 to filter the holes by their size and close the small holes that are in general irrelevant to the surface while the larger holes often represent topological features of the surface. We present some experimental results that show that this method allows to automatically and effectively search and suppress unwanted holes in a 3D surface.