Robust Geometry Estimation using the Generalized Voronoi Covariance Measure

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

Robust Estimation of Surface Curvature Information from Point Cloud Data

This paper surveys and evaluates some popular state of the art methods for algorithmic curvature and normal estimation. In addition to surveying existing methods we also propose a new method for robust curvature estimation and evaluate it against existing methods thus demonstrating its superiority to existing methods in the case of significant data noise. Throughout this paper we are concerned with computation in low dimensional spaces (N < 10) and primarily focus on the computation of the Weingarten map and quantities that may be derived from this; however, the algorithms discussed are theoretically applicable in any dimension. One thing that is common to all these methods is their basis in an estimated graph structure. For any of these methods to work the local geometry of the manifold must be exploited; however, in the case of point cloud data it is often difficult to discover a robust manifold structure underlying the data, even in simple cases, which can greatly influence the results of these algorithms. We hope that in pushing these algorithms to their limits we are able to discover, and perhaps resolve, many major pitfalls that may affect potential users and future researchers hoping to improve these methodsComment: 16 pages, 13 figure

Piecewise smooth reconstruction of normal vector field on digital data

International audienceWe propose a novel method to regularize a normal vector field defined on a digital surface (boundary of a set of voxels). When the digital surface is a digitization of a piecewise smooth manifold, our method localizes sharp features (edges) while regularizing the input normal vector field at the same time. It relies on the optimisation of a variant of the Ambrosio-Tortorelli functional, originally defined for denoising and contour extraction in image processing [AT90]. We reformulate this functional to digital surface processing thanks to discrete calculus operators. Experiments show that the output normal field is very robust to digitization artifacts or noise, and also fairly independent of the sampling resolution. The method allows the user to choose independently the amount of smoothing and the length of the set of discontinuities. Sharp and vanishing features are correctly delineated even on extremely damaged data. Finally, our method can be used to enhance considerably the output of state-of- the-art normal field estimators like Voronoi Covariance Measure [MOG11] or Randomized Hough Transform [BM12]