Voronoi set approximation

Start: 03/09/2015 - 12:00pm
End  : 03/09/2015 - 1:00pm

Applied Math Seminar

Raphael Lachieze-Rey (Paris Descartes University)


Set approximation consists in the reconstruction of an unknown bounded set K, based on a finite random sampling in the region where K is supposed to lie. We are concerned here with a specific procedure called "Voronoi approximation", where one takes the union of all Voronoi cells whose centers lie in K. We will discuss the quality of this approximation when the number of random sampling points goes to infinity. We will in particular present Berry-Esseen bound on the volume approximation, and an a.s. convergence result for the Hausdorff distance. We are also interested in the minimal regularity assumptions required on the set K, and will show that the results even apply to sets with a possibly fractal boundary, such as the Von Koch flake.

Kravis 100