Digital Circles, Spheres and Hyperspheres: From Morphological Models to Analytical Characterizations and Topological Properties

Jean-Luc Toutant (1) , Eric Andres (2) , Tristan Roussillon (3)

1 ISIT - Image Science for Interventional Techniques
2 XLIM-SIC - SIC
3 M2DisCo - Geometry Processing and Constrained Optimization

In this paper we provide an analytical description of various classes of digital circles, spheres and in some cases hyperspheres, defined in a morphological framework. The topological properties of these objects, especially the separation of the digital space, are discussed according to the shape of the structuring element. The proposed framework is generic enough so that it encompasses most of the digital circle definitions that appear in the literature and extends them to dimension 3 and sometimes dimension n.

Mots clés: Digital geometry; Digital topology; Mathematical morphology; Digital circle and sphere; Analytical characterization

Domaines: Synthèse d'image et réalité virtuelle [cs.GR]; Vision par ordinateur et reconnaissance de formes [cs.CV]

Jean-Luc Toutant, Eric Andres, Tristan Roussillon. Digital Circles, Spheres and Hyperspheres: From Morphological Models to Analytical Characterizations and Topological Properties. Discrete Applied Mathematics, 2013, 161 (16-17), pp.2662-2677. ⟨10.1016/j.dam.2013.06.001⟩. ⟨hal-00857691⟩