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arXiv · 1111.4169

Set Reconstruction by Voronoi cells

Matthias Reitzner·Evgeny Spodarev·Dmitry Zaporozhets
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Abstract

For a Borel set $A$ and a homogeneous Poisson point process $η$ in $\R^d$ of intensity $λ>0$, define the Poisson--Voronoi approximation $ A_η$ 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 $\E\Vol(AΔA_η)$ as $λ\to\infty$ where $\Vol$ is the Lebesgue measure. Estimates for all moments of $\Vol(A_η)$ and $\Vol(AΔA_η)$ together with their asymptotics for large $λ$ are obtained as well.

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Matthias Reitzner, Evgeny Spodarev, Dmitry Zaporozhets. 2011-12-22. Set Reconstruction by Voronoi cells. https://arxiv.org/abs/1111.4169

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