# Robust Geometry Estimation using the Generalized Voronoi Covariance Measure

arXiv: https://arxiv.org/abs/1408.6210 · HTML: https://mlsanity.com/paper/1408.6210/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Aug 2014.

## Built on by (most cited first, 1 of 1)

- [Robust Estimation of Surface Curvature Information from Point Cloud Data](https://mlsanity.com/paper/2306.00299/) (2023)

## Abstract (arXiv)

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.