Surface reconstruction from point clouds by transforming the medial scaffold

We propose an algorithm for surface reconstruction from unorganized points based on a view of the sampling process as a deformation from the original surface. In the course of this deformation the Medial Scaffold  (MS)(MS) — a graph representation of the 3D Medial Axis  (MA)(MA) — of the original surface undergoes abrupt topological changes (transitions) such that the MSMS of the unorganized point set is significantly different from that of the original surface. The algorithm seeks a sequence of transformations of the MSMS to invert this process. Specifically, some MSMS curves (junctions of 3 MAMA sheets) correspond to triplets of points on the surface and represent candidates for generating a (Delaunay) triangle to mesh that portion of the surface. We devise a greedy algorithm that iteratively transforms the MSMS by “removing” suitable candidate MSMS curves (gap transform) from a rank-ordered list sorted by a combination of properties of the MSMS curve and its neighborhood context. This approach is general and applicable to surfaces which are: non-closed (with boundaries), non-orientable, non-uniformly sampled, non-manifold (with self-intersections), non-smooth (with sharp features: seams, ridges). In addition, the method is comparable in speed and complexity to current popular Voronoi/Delaunay-based algorithms, and is applicable to very large datasets.