Shape representation and analysis of 2D compact sets by shape diagrams

Shape diagrams are shape representations in the Euclidean plane introduced for studying 3D and 2D compact sets. A compact set is represented by a point within a shape diagram whose coordinates are morphological functionals defined from geometrical functionals and inequalities. Classically, the geometrical functionals for 2D sets are the area, the perimeter, the radii of the inscribed and circumscribed circles, and the minimum and maximum Feret diameters. The purpose of this paper is to present a particular shape diagram for which mathematical properties have been well-defined and to analyse the shape of several families of 2D sets for the discrimination of convex and non convex sets as well as the discrimination of similar sets.