### Set reconstruction by Voronoi cells

#### 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

https://projecteuclid.org/euclid.aap/1354716584

Digital Object Identifier
doi:10.1239/aap/1354716584

Mathematical Reviews number (MathSciNet)
MR3052844

Zentralblatt MATH identifier
1280.60013

#### 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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