Retrieving convex bodies from restricted covariogram functions

DOI10.1239/aap/1189518630zbMath1127.52004arXivmath/0702892OpenAlexW2023163707MaRDI QIDQ5426461

Gabriele Bianchi, Gennadiy Averkov

Publication date: 12 November 2007

Published in: Advances in Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0702892

zbMATH Keywords

convex polytopeconvex bodyquasicrystalgeometric tomographyset covariancegenericity result

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Length, area, volume and convex sets (aspects of convex geometry) (52A38) Convex sets in (n) dimensions (including convex hypersurfaces) (52A20) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (8)

Investigation of convex bodies in \(\mathbb R^3\) by support planes ⋮ On the reconstruction of planar lattice-convex sets from the covariogram ⋮ On variances of partial volumes of the typical cell of a Poisson-Voronoi tessellation and large-dimensional volume degeneracy ⋮ Retrieving convex bodies from restricted covariogram functions ⋮ The covariogram determines three-dimensional convex polytopes ⋮ The cross covariogram of a pair of polygons determines both polygons, with a few exceptions ⋮ On convex bodies that are characterizable by volume function. ``Old and recent problems for a new generation: a survey ⋮ Confirmation of Matheron's conjecture on the covariogram of a planar convex body

Cites Work

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• Linear-Intercept distributions do not characterize plane sets

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