Level sets estimation and Vorob'ev expectation of random compact sets
arXiv:1006.5135 · doi:10.1016/j.spasta.2012.10.001
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 $\E_V(X)$, which is closely linked to quantile sets. In this paper, we propose a consistent and ready to use estimator of $\E_V(X)$ 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.