Restricted delaunay triangulations and normal cycle
Proceedings of the nineteenth annual symposium on Computational geometry
Estimating the tensor of curvature of a surface from a polyhedral approximation
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
ACM SIGGRAPH 2004 Papers
Robust Estimation of Adaptive Tensors of Curvature by Tensor Voting
IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimating differential quantities using polynomial fitting of osculating jets
Computer Aided Geometric Design
Robust moving least-squares fitting with sharp features
ACM SIGGRAPH 2005 Papers
A Sampling Framework for Accurate Curvature Estimation in Discrete Surfaces
IEEE Transactions on Visualization and Computer Graphics
Anisotropic smoothing of point sets
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Computer Vision and Image Understanding
Voronoi-based variational reconstruction of unoriented point sets
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Data-dependent MLS for faithful surface approximation
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Discovering structural regularity in 3D geometry
ACM SIGGRAPH 2008 papers
4-points congruent sets for robust pairwise surface registration
ACM SIGGRAPH 2008 papers
Spline-based feature curves from point-sampled geometry
The Visual Computer: International Journal of Computer Graphics
Integral invariants for robust geometry processing
Computer Aided Geometric Design
Delaunay properties of digital straight segments
DGCI'11 Proceedings of the 16th IAPR international conference on Discrete geometry for computer imagery
Curvature estimation for meshes based on vertex normal triangles
Computer-Aided Design
Feature-Preserving Reconstruction of Singular Surfaces
Computer Graphics Forum
Edge-aware point set resampling
ACM Transactions on Graphics (TOG)
Feature-Preserving Surface Reconstruction and Simplification from Defect-Laden Point Sets
Journal of Mathematical Imaging and Vision
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Many algorithms for shape analysis and shape processing rely on accurate estimates of differential information such as normals and curvature. In most settings, however, care must be taken around non-smooth areas of the shape where these quantities are not easily defined. This problem is particularly prominent with point-cloud data, which are discontinuous everywhere. In this paper we present an efficient and robust method for extracting principal curvatures, sharp features and normal directions of a piecewise smooth surface from its point cloud sampling, with theoretical guarantees. 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 analytically that our method recovers correct principal curvatures and principal curvature directions in smooth parts of the shape, and correct feature directions and feature angles at the sharp edges of a piecewise smooth surface, with the error bounded by the Hausdorff distance between the point cloud and the underlying surface. Using the same analysis we provide theoretical guarantees for a modification of a previously proposed normal estimation technique. 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.