Topology-Preserving Thinning in 2-D Pseudomanifolds

  • Nicolas Passat
  • Michel Couprie
  • Loïc Mazo
  • Gilles Bertrand
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)

Abstract

Preserving topological properties of objects during thinning procedures is an important issue in the field of image analysis. In the case of 2-D digital images (i.e. images defined on ℤ2) such procedures are usually based on the notion of simple point. By opposition to the case of spaces of higher dimensions (i.e. n , n ≥ 3), it was proved in the 80’s that the exclusive use of simple points in ℤ2 was indeed sufficient to develop thinning procedures providing an output that is minimal with respect to the topological characteristics of the object. Based on the recently introduced notion of minimal simple set (generalising the notion of simple point), we establish new properties related to topology-preserving thinning in 2-D spaces which extend, in particular, this classical result to more general spaces (the 2-D pseudomanifolds) and objects (the 2-D cubical complexes).

Keywords

Topology preservation simple points simple sets cubical complexes collapse confluence pseudomanifolds 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Nicolas Passat
    • 1
  • Michel Couprie
    • 2
  • Loïc Mazo
    • 1
    • 2
  • Gilles Bertrand
    • 2
  1. 1.LSIIT, UMR CNRS 7005Université de StrasbourgStrasbourgFrance
  2. 2.Laboratoire d’Informatique Gaspard-Monge, Équipe A3SI, ESIEE ParisUniversité Paris-EstFrance

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