Graph-based Conservative Surface Reconstruction

We propose a new approach for reconstructing a 2-manifold from a point sample in R3. Compared to previous algorithms, our approach is novel in that it throws away geometry information early on in the reconstruction process and mainly operates combinatorially on a graph structure. Furthermore, it is very conservative in creating adjacencies between samples in the vicinity of slivers, still we can prove that the resulting reconstruction faithfully resembles the original 2-manifold. While the theoretical proof requires an extremely high sampling density, our prototype implementation of the approach produces surprisingly good results on typical sample sets.