Level sets estimation and Vorob'ev expectation of random compact sets

Details Level sets estimation and Vorob'ev expectation of random compact sets Level sets estimation and Vorob'ev expectation of random compact sets

2010-06-26

arxiv.org/abs/1006.5135v2

Mathematics

Probability

Scientific paper

The issue of a "mean shape" of a random set $X$ 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 $X$ with spatial discretization. The control of discretization errors is handled with a mild regularity assumption on the boundary of $X$: a not too large 'box counting' dimension. Some examples are developed and an application to cosmological data is presented.

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