On the reconstruction of convex sets from random normal measurements

DOI10.1007/s00454-015-9673-2zbMath1352.52006arXiv1402.5010OpenAlexW2058188161MaRDI QIDQ2349857

Hiba Abdallah, Quentin Mérigot

Publication date: 18 June 2015

Published in: Discrete \& Computational Geometry, Proceedings of the thirtieth annual symposium on Computational geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.5010

zbMATH Keywords

surface reconstructionMinkowski problemsurface area measure

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Mixed volumes and related topics in convex geometry (52A39) Convex sets in (3) dimensions (including convex surfaces) (52A15) Approximation by convex sets (52A27) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20)

Related Items (1)

On length measures of planar closed curves and the comparison of convex shapes

Cites Work

• Surface reconstruction via geodesic interpolation
• The equivalence of weak, strong, and complete convergence in \(L_ 1\) for kernel density estimates
• Stability of the solution of the Minkowski equations
• Convergence of algorithms for reconstructing convex bodies and directional measures
• Bounds for the discrepancy between convex bodies in terms of the isoperimetric difference
• On the Algorithmic Complexity of Minkowski's Reconstruction Theorem
• On the regularity of the solution of then-dimensional Minkowski problem
• Real Analysis and Probability
• Minimizing within Convex Bodies Using a Convex Hull Method
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