SET RECONSTRUCTION BY VORONOI CELLS

Abstract

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