Robust Geometry Estimation Using the Generalized Voronoi Covariance Measure

The Voronoi covariance measure (VCM) of a compact set K of $\mathbb{R}^d$ is a tensor-valued measure that encodes geometrical information on K and which is known to be resilient to Hausdorff noise but sensitive to outliers. In this paper, we generalize this notion to any distance-like function δ and define the δ-VCM. Combining the VCM with the distance to a measure and also with the witnessed-k-distance, we get a provably good tool for normal estimation that is resilient to Hausdorff noise and to outliers. We present experiments showing the robustness of our approach for normal and curvature estimation and sharp feature detection.

SIAM Journal on Imaging Sciences, 8(2): 1293-1314, 2015