Poisson overlapping microballs: self-similarity and X-ray images
Abstract
We study a random field obtained by counting the number of balls containing each point, when overlapping balls are thrown at random according to a Poisson random measure. We are particularly interested in the local asymptotical self-similarity (lass) properties of the field, as well as the action of X-ray transforms. We discover two different lass properties when considering the asymptotic either "in law" or "on the second order moment" and prove a relationship between the lass behavior of the field and the lass behavior of its X-ray transform. We also describe a microscopic process which leads to a multifractional behavior. These results can be exploited to model and analyze granular media, images or connections network.
Cite
@article{arxiv.math/0505635,
title = {Poisson overlapping microballs: self-similarity and X-ray images},
author = {Hermine Biermé and Anne Estrade},
journal= {arXiv preprint arXiv:math/0505635},
year = {2007}
}
Comments
A multifractional case is investigated and reference [10] is added. Former title: "Poisson microballs: self-similarity and directional analysis"