Journal of Mathematical Imaging and Vision

, Volume 44, Issue 3, pp 254–281 | Cite as

Topology on Digital Label Images

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


In digital imaging, after several decades devoted to the study of topological properties of binary images, there is an increasing need of new methods enabling to take into (topological) consideration n-ary images (also called label images). Indeed, while binary images enable to handle one object of interest, label images authorise to simultaneously deal with a plurality of objects, which is a frequent requirement in several application fields. In this context, one of the main purposes is to propose topology-preserving transformation procedures for such label images, thus extending the ones (e.g., growing, reduction, skeletonisation) existing for binary images. In this article, we propose, for a wide range of digital images, a new approach that permits to locally modify a label image, while preserving not only the topology of each label set, but also the topology of any arrangement of the labels understood as the topology of any union of label sets. This approach enables in particular to unify and extend some previous attempts devoted to the same purpose.


Digital imaging Topology Label images Homotopy Simple points 


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Loïc Mazo
    • 1
    • 2
  • Nicolas Passat
    • 1
  • Michel Couprie
    • 2
  • Christian Ronse
    • 1
  1. 1.LSIIT, UMR CNRS 7005Université de StrasbourgStrasbourgFrance
  2. 2.Laboratoire d’Informatique Gaspard-Monge, Équipe A3SI, ESIEEUniversité Paris-EstParisFrance

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