Digital Imaging: A Unified Topological Framework

  • Authors:

  • Loïc Mazo;Nicolas Passat;Michel Couprie;Christian Ronse

  • Affiliations:

  • Université de Strasbourg, LSIIT, UMR CNRS 7005, Illkirch Cedex, France 67412 and Université Paris-Est, Laboratoire d'Informatique Gaspard-Monge, Équipe A3SI, ESIEE Paris, Noisy le G ...;Université de Strasbourg, LSIIT, UMR CNRS 7005, Illkirch Cedex, France 67412;Université Paris-Est, Laboratoire d'Informatique Gaspard-Monge, Équipe A3SI, ESIEE Paris, Noisy le Grand Cedex, France 93162;Université de Strasbourg, LSIIT, UMR CNRS 7005, Illkirch Cedex, France 67412

  • Venue:
  • Journal of Mathematical Imaging and Vision
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

Abstract

In this article, a tractable modus operandi is proposed to model a (binary) digital image (i.e., an image defined on 驴 n and equipped with a standard pair of adjacencies) as an image defined in the space ( $\mathbb{F}^{n}$ ) of cubical complexes. In particular, it is shown that all the standard pairs of adjacencies (namely the (4,8) and (8,4)-adjacencies in 驴2, the (6,18), (18,6), (6,26), and (26,6)-adjacencies in 驴3, and more generally the (2n,3 n 驴1) and (3 n 驴1,2n)-adjacencies in 驴 n ) can then be correctly modelled in $\mathbb{F}^{n}$ . Moreover, it is established that the digital fundamental group of a digital image in 驴 n is isomorphic to the fundamental group of its corresponding image in $\mathbb{F}^{n}$ , 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 (驴 n ) or cubical complexes ( $\mathbb{F}^{n}$ ), and to potentially unify some of them.