Level sets estimation and Vorob'ev expectation of random compact sets - Archive ouverte HAL Access content directly
Journal Articles Spatial Statistics Year : 2012

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

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Philippe Heinrich
• Function : Correspondent author
• PersonId : 872598

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Viet Chi Tran

#### Abstract

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.

### Dates and versions

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

### Identifiers

• HAL Id : hal-00495449 , version 2
• ARXIV :
• DOI :

### Cite

Philippe Heinrich, Radu Stoica, Viet Chi Tran. Level sets estimation and Vorob'ev expectation of random compact sets. Spatial Statistics, 2012, 2, pp.47-61. ⟨10.1016/j.spasta.2012.10.001⟩. ⟨hal-00495449v2⟩

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