Robust Geometry Estimation using the Generalized Voronoi Covariance Measure

TL;DR

This paper introduces a generalized Voronoi Covariance Measure that is robust to noise and outliers, improving the estimation of normals and curvature from point clouds.

Contribution

The authors extend the Voronoi Covariance Measure to any distance-like function, enhancing robustness in geometric estimations from noisy data.

Findings

Robust normal and curvature estimation demonstrated

Effective feature detection in noisy point clouds

Resilience to Hausdorff noise and outliers

Abstract

The Voronoi Covariance Measure of a compact set K of R^d is a tensor-valued measure that encodes geometric information on K and which is known to be resilient to Hausdorff noise but sensitive to outliers. In this article, we generalize this notion to any distance-like function delta and define the delta-VCM. We show that the delta-VCM is resilient to Hausdorff noise and to outliers, thus providing a tool to estimate robustly normals from a point cloud approximation. We present experiments showing the robustness of our approach for normal and curvature estimation and sharp feature detection.