Advances in Applied Probability

Set reconstruction by Voronoi cells

M. Reitzner, E. Spodarev, and D. Zaporozhets

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Abstract

For a Borel set A and a homogeneous Poisson point process η in ∝d of intensity λ>0, define the Poisson--Voronoi approximation Aη of A as a union of all Voronoi cells with nuclei from η lying in A. If A has a finite volume and perimeter, we find an exact asymptotic of E Vol(AΔ Aη) as λ→∞, where Vol is the Lebesgue measure. Estimates for all moments of Vol(Aη) and Vol(AΔ Aη) together with their asymptotics for large λ are obtained as well.

Article information

Source
Adv. in Appl. Probab. Volume 44, Number 4 (2012), 938-953.

Dates
First available in Project Euclid: 5 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.aap/1354716584

Digital Object Identifier
doi:10.1239/aap/1354716584

Mathematical Reviews number (MathSciNet)
MR3052844

Zentralblatt MATH identifier
1280.60013

Subjects
Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65]
Secondary: 60G55: Point processes 52A22: Random convex sets and integral geometry [See also 53C65, 60D05] 60C05: Combinatorial probability

Keywords
Poisson point process Poisson--Voronoi cell Poisson--Voronoi tessellation perimeter

Citation

Reitzner, M.; Spodarev, E.; Zaporozhets, D. Set reconstruction by Voronoi cells. Adv. in Appl. Probab. 44 (2012), no. 4, 938--953. doi:10.1239/aap/1354716584. https://projecteuclid.org/euclid.aap/1354716584


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