Level sets estimation and Vorob'ev expectation of random compact sets
Probability
2012-11-27 v2 Statistics Theory
Statistics Theory
Abstract
The issue of a "mean shape" of a random set often arises, in particular in image analysis and pattern detection. There is no canonical definition but one possible approach is the so-called Vorob'ev expectation , which is closely linked to quantile sets. In this paper, we propose a consistent and ready to use estimator of built from independent copies of with spatial discretization. The control of discretization errors is handled with a mild regularity assumption on the boundary of : a not too large 'box counting' dimension. Some examples are developed and an application to cosmological data is presented.
Keywords
Cite
@article{arxiv.1006.5135,
title = {Level sets estimation and Vorob'ev expectation of random compact sets},
author = {Philippe Heinrich and Radu Stefan Stoica and Viet Chi Tran},
journal= {arXiv preprint arXiv:1006.5135},
year = {2012}
}