A unified topological framework for digital imaging

Loïc Mazo (1, 2) , Nicolas Passat (2) , Michel Couprie (1) , Christian Ronse (2)

1 LIGM - Laboratoire d'Informatique Gaspard-Monge
2 LSIIT - Laboratoire des Sciences de l'Image, de l'Informatique et de la Télédétection

In this article, a tractable modus operandi is proposed to model a (binary) digital image (i.e., an image defined on Z^n and equipped with a standard pair of adjacencies) as an image defined in the space of cubical complexes (F^n). In particular, it is shown that all the standard pairs of adjacencies in Z^n can then be correctly modelled in F^n. Moreover, it is established that the digital fundamental group of a digital image in Z^n is isomorphic to the fundamental group of its corresponding image in F^n, thus proving the topological correctness of the proposed approach. From these results, it becomes possible to establish links between topology-oriented methods developed either in classical digital spaces (Z^n) or cubical complexes (F^n).

Mots clés: homotopy; digital imaging; digital topology; cubical complexes; fundamental group

Domaines: Traitement des images [eess.IV]; Mathématique discrète [cs.DM]; Topologie géométrique [math.GT]

Loïc Mazo, Nicolas Passat, Michel Couprie, Christian Ronse. A unified topological framework for digital imaging. Discrete Geometry for Computer Imagery (DGCI), 2011, Nancy, France. pp.163-174, ⟨10.1007/978-3-642-19867-0_14⟩. ⟨hal-00728915⟩