Parameter-Free Connectivity for Point Clouds

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Diana Marin, Stefan Ohrhallinger, Michael Wimmer

Published: 01 Jan 2024, Last Modified: 04 Nov 2025VISIGRAPP (1): GRAPP, HUCAPP, IVAPP 2024EveryoneRevisionsBibTeXCC BY-SA 4.0
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.