Bipartite Polar Classification for Surface Reconstruction

In this paper, we propose bipartite polar classification to augment an input unorganized point set P with two disjoint groups of points distributed around the ambient space of P to assist the task of surface reconstruction. The goal of bipartite polar classification is to obtain a space partitioning of P by assigning pairs of Voronoi poles into two mutually invisible sets lying in the opposite sides of P through direct point set visibility examination. Based on the observation that a pair of Voronoi poles are mutually invisible, spatial classification is accomplished by carving away visible exterior poles with their counterparts simultaneously determined as interior ones. By examining the conflicts of mutual invisibility, holes or boundaries can also be effectively detected, resulting in a hole-aware space carving technique. With the classified poles, the task of surface reconstruction can be facilitated by more robust surface normal estimation with global consistent orientation and off-surface point specification for variational implicit surface reconstruction. We demonstrate the ability of the bipartite polar classification to achieve robust and efficient space carving on unorganized point clouds with holes and complex topology and show its application to surface reconstruction.