Robust Geometry Estimation Using the Generalized Voronoi Covariance Measure

DOI10.1137/140977552zbMath1325.65032arXiv1408.6210OpenAlexW1536847641MaRDI QIDQ3192653

Quentin Mérigot, Louis Cuel, Boris Thibert, Jacques-Olivier Lachaud

Publication date: 13 October 2015

Published in: SIAM Journal on Imaging Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1408.6210

zbMATH Keywords

power diagramcurvature estimationgeometric inferencedistance to a measurenormal estimationsharp feature detectionHausdorff noisenormal and curvature estimationVoronoi covariance measure

Mathematics Subject Classification ID

Numerical aspects of computer graphics, image analysis, and computational geometry (65D18) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (10)

Sparse convolution-based digital derivatives, fast estimation for noisy signals and approximation results ⋮ Corrected curvature measures ⋮ Analysis of noisy digital contours with adaptive tangential cover ⋮ A new lattice-based plane-probing algorithm ⋮ An optimized framework for plane-probing algorithms ⋮ Stochastic distance transform: theory, algorithms and applications ⋮ Inference of Curvature Using Tubular Neighborhoods ⋮ Directional density measure to intrinsically estimate and counteract non-uniformity in point clouds ⋮ Stochastic Distance Transform ⋮ Gaussian Process Landmarking on Manifolds

Uses Software

• CGAL

Cites Work

• Integral invariants for robust geometry processing
• Geometric inference for probability measures
• Boundary measures for geometric inference
• Surface reconstruction by Voronoi filtering
• Witnessed \(k\)-distance
• Estimating differential quantities using polynomial fitting of osculating jets
• The rotation of eigenvectors by a perturbation
• Normal and Feature Approximations from Noisy Point Clouds
• Optimal Transport

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