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

Autor:	Saïd Rahmani, Jean-Charles Pinoli, Johan Debayle
Jazyk:	angličtina
Rok vydání:	2017
Předmět:	Zonotopes random closed set the Feret diameter polygonal approximation Applied mathematics. Quantitative methods T57-57.97 Mathematics QA1-939
Zdroj:	Modern Stochastics: Theory and Applications, Vol 3, Iss 4, Pp 325-364 (2017)
Druh dokumentu:	article
ISSN:	2351-6046 2351-6054
DOI:	10.15559/16-VMSTA70
Popis:	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.
Databáze:	Directory of Open Access Journals
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