Level sets estimation and Vorob'ev expectation ...
Document type :
Compte-rendu et recension critique d'ouvrage
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]
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
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]
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 >
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
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