A Unified Topological Framework for Digital Imaging

  • Loïc Mazo
  • Nicolas Passat
  • Michel Couprie
  • Christian Ronse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6607)


In this article, a tractable modus operandi is proposed to model a (binary) digital image (i.e., an image defined on \(\mathbb Z^n\) and equipped with a standard pair of adjacencies) as an image defined in the space of cubical complexes (\(\mathbb F^n\)). In particular, it is shown that all the standard pairs of adjacencies in \(\mathbb Z^n\) can then be correctly modelled in \(\mathbb F^n\). Moreover, it is established that the digital fundamental group of a digital image in \(\mathbb Z^n\) 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 (\(\mathbb Z^n\)) or cubical complexes (\(\mathbb{F}^n\)).


digital imaging digital topology cubical complexes homotopy fundamental group 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Loïc Mazo
    • 1
    • 2
  • Nicolas Passat
    • 1
  • Michel Couprie
    • 2
  • Christian Ronse
    • 1
  1. 1.LSIIT, UMR CNRS 7005Université de StrasbourgFrance
  2. 2.Laboratoire d’Informatique Gaspard-Monge, Équipe A3SIUniversité Paris-Est, ESIEEParisFrance

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