Journal
SPATIAL STATISTICS
Volume 2, Issue -, Pages 47-61Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.spasta.2012.10.001
Keywords
Stochastic geometry; Random closed sets; Level sets; Vorob'ev expectation
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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 level or 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 discretisation. The control of discretisation errors is handled with a mild regularity assumption on the boundary of X. Several examples are developed and an application to cosmological data is presented. (C) 2012 Elsevier B.V. All rights reserved.
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