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Robust Geometry Estimation using the Generalized Voronoi Covariance Measure

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.
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Contributor : Quentin Mérigot <>
Submitted on : Wednesday, November 4, 2015 - 1:33:30 PM
Last modification on : Wednesday, July 28, 2021 - 4:00:55 AM
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Louis Cuel, Jacques-Olivier Lachaud, Quentin Mérigot, Boris Thibert. Robust Geometry Estimation using the Generalized Voronoi Covariance Measure. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2015, 8 (2), pp.1293-1314. ⟨10.1137/140977552⟩. ⟨hal-01058145v2⟩



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