Description of the symmetric convex random closed sets as zonotopes from their Feret diameters

In this paper, the 2-D random closed sets (RACS) are studied by means of the Feret diameter, also known as the caliper diameter. More specifically, it is shown that a 2-D symmetric convex RACS can be approximated as precisely as we want by some random zonotopes (polytopes formed by the Minkowski sum...

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Main Authors:	Saïd Rahmani, Jean-Charles Pinoli, Johan Debayle
Format:	Article
Language:	English
Published:	VTeX 2017-01-01
Series:	Modern Stochastics: Theory and Applications
Subjects:	Zonotopes random closed set the Feret diameter polygonal approximation
Online Access:	https://vmsta.vtex.vmt/doi/10.15559/16-VMSTA70

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spelling	doaj-832c5932f95149a7b27d4acfdfd648442020-11-25T02:01:12ZengVTeXModern Stochastics: Theory and Applications2351-60462351-60542017-01-013432536410.15559/16-VMSTA70Description of the symmetric convex random closed sets as zonotopes from their Feret diametersSaïd Rahmani0Jean-Charles Pinoli1Johan Debayle2École Nationale Supérieure des Mines de Saint-Etienne, SPIN/LGF UMR CNRS 5307, 158 Cours Fauriel, 42023 Saint-Etienne, FranceÉcole Nationale Supérieure des Mines de Saint-Etienne, SPIN/LGF UMR CNRS 5307, 158 Cours Fauriel, 42023 Saint-Etienne, FranceÉcole Nationale Supérieure des Mines de Saint-Etienne, SPIN/LGF UMR CNRS 5307, 158 Cours Fauriel, 42023 Saint-Etienne, FranceIn this paper, the 2-D random closed sets (RACS) are studied by means of the Feret diameter, also known as the caliper diameter. More specifically, it is shown that a 2-D symmetric convex RACS can be approximated as precisely as we want by some random zonotopes (polytopes formed by the Minkowski sum of line segments) in terms of the Hausdorff distance. Such an approximation is fully defined from the Feret diameter of the 2-D convex RACS. Particularly, the moments of the random vector representing the face lengths of the zonotope approximation are related to the moments of the Feret diameter random process of the RACS.https://vmsta.vtex.vmt/doi/10.15559/16-VMSTA70Zonotopesrandom closed setthe Feret diameterpolygonal approximation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Saïd Rahmani Jean-Charles Pinoli Johan Debayle
spellingShingle	Saïd Rahmani Jean-Charles Pinoli Johan Debayle Description of the symmetric convex random closed sets as zonotopes from their Feret diameters Modern Stochastics: Theory and Applications Zonotopes random closed set the Feret diameter polygonal approximation
author_facet	Saïd Rahmani Jean-Charles Pinoli Johan Debayle
author_sort	Saïd Rahmani
title	Description of the symmetric convex random closed sets as zonotopes from their Feret diameters
title_short	Description of the symmetric convex random closed sets as zonotopes from their Feret diameters
title_full	Description of the symmetric convex random closed sets as zonotopes from their Feret diameters
title_fullStr	Description of the symmetric convex random closed sets as zonotopes from their Feret diameters
title_full_unstemmed	Description of the symmetric convex random closed sets as zonotopes from their Feret diameters
title_sort	description of the symmetric convex random closed sets as zonotopes from their feret diameters
publisher	VTeX
series	Modern Stochastics: Theory and Applications
issn	2351-6046 2351-6054
publishDate	2017-01-01
description	In this paper, the 2-D random closed sets (RACS) are studied by means of the Feret diameter, also known as the caliper diameter. More specifically, it is shown that a 2-D symmetric convex RACS can be approximated as precisely as we want by some random zonotopes (polytopes formed by the Minkowski sum of line segments) in terms of the Hausdorff distance. Such an approximation is fully defined from the Feret diameter of the 2-D convex RACS. Particularly, the moments of the random vector representing the face lengths of the zonotope approximation are related to the moments of the Feret diameter random process of the RACS.
topic	Zonotopes random closed set the Feret diameter polygonal approximation
url	https://vmsta.vtex.vmt/doi/10.15559/16-VMSTA70
work_keys_str_mv	AT saidrahmani descriptionofthesymmetricconvexrandomclosedsetsaszonotopesfromtheirferetdiameters AT jeancharlespinoli descriptionofthesymmetricconvexrandomclosedsetsaszonotopesfromtheirferetdiameters AT johandebayle descriptionofthesymmetricconvexrandomclosedsetsaszonotopesfromtheirferetdiameters
_version_	1724958149241208832

Description of the symmetric convex random closed sets as zonotopes from their Feret diameters

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