On the reconstruction of convex sets from random normal measurements
Abdallah, Hiba; Mérigot, Quentin (2015), On the reconstruction of convex sets from random normal measurements, Discrete and Computational Geometry, 53, 3, p. 569-586. 10.1007/s00454-015-9673-2
TypeArticle accepté pour publication ou publié
Journal nameDiscrete and Computational Geometry
MetadataShow full item record
Laboratoire Jean Kuntzmann [LJK]
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)We study the problem of reconstructing a convex body using only a finite number of measurements of outer normal vectors. More precisely, we suppose that the normal vectors are measured at independent random locations uniformly distributed along the boundary of our convex set. Given a desired Hausdorff error $\eta$, we provide an upper bounds on the number of probes that one has to perform in order to obtain an $\eta$-approximation of this convex set with high probability. Our result rely on the stability theory related to Minkowski's theorem.
Subjects / KeywordsMinkowski problem; surface area measure; random sampling
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