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Article Dans Une Revue Australian Journal of Mathematical Analysis and Applications Année : 2010

Shape diagrams for 2D compact sets - Part III: convexity discrimination for analytic and discretized simply connected sets.

Résumé

Shape diagrams are representations in the Euclidean plane introduced to study 3-dimensional and 2-dimensional compact convex sets. However, they can also been applied to more general compact sets than compact convex sets. A compact 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 twenty-two shape diagrams to be built. 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 twenty-two shape diagrams. The two first parts of this study are published in previous papers [8, 9]. They focus on analytic compact convex sets and analytic simply connected compact sets, respectively. The purpose of this paper is to present the third part, by focusing on the convexity discrimination for analytic and discretized simply connected compact sets.
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Dates et versions

hal-00550951 , version 1 (18-01-2011)

Identifiants

  • HAL Id : hal-00550951 , version 1

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Séverine Rivollier, Johan Debayle, Jean-Charles Pinoli. Shape diagrams for 2D compact sets - Part III: convexity discrimination for analytic and discretized simply connected sets.. Australian Journal of Mathematical Analysis and Applications, 2010, 7 (2), Article 5, pp. 1-18. ⟨hal-00550951⟩
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