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How to Make nD Functions Digitally Well-Composed in a Self-dual Way

  • Nicolas Boutry
  • Thierry Géraud
  • Laurent Najman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9082)

Abstract

Latecki et al. introduced the notion of 2D and 3D wellcomposed images, i.e., a class of images free from the “connectivities paradox” of digital topology. Unfortunately natural and synthetic images are not a priori well-composed. In this paper we extend the notion of “digital well-composedness” to nD sets, integer-valued functions (graylevel images), and interval-valued maps. We also prove that the digital well-composedness implies the equivalence of connectivities of the level set components in nD. Contrasting with a previous result stating that it is not possible to obtain a discrete nD self-dual digitally well-composed function with a local interpolation, we then propose and prove a selfdual discrete (non-local) interpolation method whose result is always a digitally well-composed function. This method is based on a sub-part of a quasi-linear algorithm that computes the morphological tree of shapes.

Keywords

Well-composed functions Equivalence of connectivities Cubical grid Digital topology Interpolation Self-duality 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Nicolas Boutry
    • 1
    • 2
  • Thierry Géraud
    • 1
  • Laurent Najman
    • 2
  1. 1.EPITA Research and Development Laboratory (LRDE)ParisFrance
  2. 2.LIGM, Équipe A3SI, ESIEEUniversité Paris-EstParisFrance

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