Title :

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

Author(s) :

Heinrich, Philippe [Auteur correspondant]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Stoica, Radu [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Tran, Chi [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Centre de Mathématiques Appliquées de l'Ecole polytechnique [CMAP]

Journal title :

Spatial Statistics

Pages :

47-61

Publisher :

Elsevier

Publication date :

2012-12

ISSN :

2211-6753

English keyword(s) :

Stochastic geometry
Random closed sets
Level sets
Vorob'ev expectation

HAL domain(s) :

Mathématiques [math]/Probabilités [math.PR]
Mathématiques [math]/Statistiques [math.ST]
Statistiques [stat]/Théorie [stat.TH]

English abstract : [en]

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 ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL