Approximation of Vorob'ev expectation for random closed sets - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2010

Approximation of Vorob'ev expectation for random closed sets

Résumé

Random sets appear in many applications, in particular in image analysis. The issue of a "mean shape" often arises since there is no canonical definition. In this paper, we propose a consistent and ready to use estimator for the Vorob'ev expectation of a random set $X$. It is a kind of mean closely linked to quantile-like quantities and built from independent copies of $X$ with spatial discretization. The convergence is established through the Strong Law of Large Numbers of Kovyazin. 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, including Boolean models, are studied.
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Dates et versions

hal-00495449 , version 1 (26-06-2010)
hal-00495449 , version 2 (27-06-2011)

Identifiants

Citer

Philippe Heinrich, Radu Stoica, Viet Chi Tran. Approximation of Vorob'ev expectation for random closed sets. 2010. ⟨hal-00495449v1⟩
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