Set Reconstruction by Voronoi Cells

DOI10.1239/aap/1354716584zbMath1280.60013arXiv1111.4169OpenAlexW2963290755MaRDI QIDQ4906502

Matthias Reitzner, Dmitry Zaporozhets, Evgueni Spodarev

Publication date: 28 February 2013

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

Full work available at URL: https://arxiv.org/abs/1111.4169

zbMATH Keywords

Poisson point processperimeterPoisson-Voronoi tessellationPoisson-Voronoi cell

Mathematics Subject Classification ID

Geometric probability and stochastic geometry (60D05) Combinatorial probability (60C05) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55) Random convex sets and integral geometry (aspects of convex geometry) (52A22)

Related Items (9)

Introduction to Stochastic Geometry ⋮ Fold-up derivatives of set-valued functions and the change-set problem: a survey ⋮ Boundary density and Voronoi set estimation for irregular sets ⋮ Extreme values for characteristic radii of a Poisson-Voronoi tessellation ⋮ A central limit theorem for the Poisson-Voronoi approximation ⋮ Surface order scaling in stochastic geometry ⋮ Quantifying Uncertainties on Excursion Sets Under a Gaussian Random Field Prior ⋮ Asymptotic theory for statistics of the Poisson-Voronoi approximation ⋮ Almost sure central limit theorems in stochastic geometry

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Poisson process Fock space representation, chaos expansion and covariance inequalities
• Outer Minkowski content for some classes of closed sets
• Poisson-Voronoi approximation
• Confirmation of Matheron's conjecture on the covariogram of a planar convex body
• Lectures on random Voronoi tessellations
• A new modified logarithmic Sobolev inequality for Poisson point processes and several applications
• A central limit theorem for the Poisson-Voronoi approximation
• Laws of large numbers in stochastic geometry with statistical applications
• COMPUTATION OF THE PERIMETER OF MEASURABLE SETS VIA THEIR COVARIOGRAM. APPLICATIONS TO RANDOM SETS
• Stochastic and Integral Geometry
• On the almost sure coverage property of Voronoi tessellation: the ℝ¹ case
• The two-sample problem in $\Bbb R\sp m$ and measure-valued martingales

This page was built for publication: Set Reconstruction by Voronoi Cells