Level sets estimation and Vorob’ev expectation of random compact sets
نویسندگان
چکیده
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 EV (X), which is closely linked to quantile sets. In this paper, we propose a consistent and ready to use estimator of EV (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. keywords: Stochastic geometry ; Random closed sets ; Level sets ; Vorob’ev expectation AMS codes: Primary 60D05 ; Secondary 60F15 ; 28A80
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