Shape diagrams for 2D compact sets - Part I: analytic convex sets. Australian Journal ofReportar como inadecuado

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1 CIS-ENSMSE - Centre Ingénierie et Santé 2 DIM-ENSMSE - Département Imagerie et Morphologie 3 LPMG-EMSE - Laboratoire des Procédés en Milieux Granulaires 4 IFRESIS-ENSMSE - Institut Fédératif de Recherche en Sciences et Ingénierie de la Santé

Abstract : Shape diagrams are representations in the Euclidean plane introduced to study 3-dimensional and 2-dimensional compact convex sets. Such a set is represented by a point within a shape diagram whose coordinates are morphometrical functionals defined as normalized ratios of geometrical functionals. Classically, the geometrical functionals are the area, the perimeter, the radii of the inscribed and circumscribed circles, and the minimum and maximum Feret diameters. They allow thirty-one shape diagrams to be built. Most of these shape diagrams can also been applied to more general compact sets than compact convex sets. Starting from these six classical geometrical functionals, a detailed comparative study has been performed in order to analyze the representation relevance and discrimination power of these thirty-one shape diagrams. The purpose of this paper is to present the first part of this study, by focusing on analytic compact convex sets. A set will be called analytic if its boundary is piecewise defined by explicit functions in such a way that the six geometrical functionals can be straightforwardly calculated. The second and third part of the comparative study are published in two following papers 19, 20. They are focused on analytic simply connected sets and convexity discrimination for analytic and discretized simply connected sets, respectively.

Keywords : Shape discrimination Analytic compact convex sets Geometrical and morphometrical functionals Shape diagrams Shape discrimination.

Autor: Séverine Rivollier - Johan Debayle - Jean-Charles Pinoli -



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