Voronoi-Based Curvature and Feature Estimation from Point Clouds

Quentin Mérigot 1 Maks Ovsjanikov 2 Leonidas J. Guibas 2
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We present an efficient and robust method for extracting curvature information, sharp features, and normal directions of a piecewise smooth surface from its point cloud sampling in a unified framework. Our method is integral in nature and uses convolved covariance matrices of Voronoi cells of the point cloud which makes it provably robust in the presence of noise. We show that these matrices contain information related to curvature in the smooth parts of the surface, and information about the directions and angles of sharp edges around the features of a piecewise-smooth surface. Our method is applicable in both two and three dimensions, and can be easily parallelized, making it possible to process arbitrarily large point clouds, which was a challenge for Voronoi-based methods. In addition, we describe a Monte-Carlo version of our method, which is applicable in any dimension. We illustrate the correctness of both principal curvature information and feature extraction in the presence of varying levels of noise and sampling density on a variety of models. As a sample application, we use our feature detection method to segment point cloud samplings of piecewise-smooth surfaces.
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Quentin Mérigot, Maks Ovsjanikov, Leonidas J. Guibas. Voronoi-Based Curvature and Feature Estimation from Point Clouds. IEEE Transactions on Visualization and Computer Graphics, Institute of Electrical and Electronics Engineers, 2011, 17 (6), pp.743 - 756. ⟨10.1109/TVCG.2010.261⟩. ⟨inria-00406575v2⟩

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