Parameter-free connectivity for point clouds

Abstract

Determining connectivity in unstructured point clouds is a long-standing problem that has still not been addressed satisfactorily. In this paper, we analyze an alternative to the often-used k-nearest neighborhood (kNN) graph - the Spheres of Influence Graph (SIG). We show that the edges that are neighboring each vertex are spatially bounded, which allows for fast computation of SIG. Our approach shows a better encoding of the ground truth connectivity compared to the kNN for a wide range of k, and additionally, it is parameter-free. Our result for this fundamental task offers potential for many applications relying on kNN, e.g., parameter-free normal estimation, and consequently, surface reconstruction, motion planning, simulations, and many more.