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Set Reconstruction by Voronoi Cells
- Part of
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- Journal:
- Advances in Applied Probability / Volume 44 / Issue 4 / December 2012
- Published online by Cambridge University Press:
- 04 January 2016, pp. 938-953
- Print publication:
- December 2012
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- Article
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For a Borel set A and a homogeneous Poisson point process η in
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.
of intensity λ>0, define the Poisson–Voronoi approximation 