On Making nD Images Well-Composed by a Self-dual Local Interpolation

  • Nicolas Boutry
  • Thierry Géraud
  • Laurent Najman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8668)


Natural and synthetic discrete images are generally not well-composed, leading to many topological issues: connectivities in binary images are not equivalent, the Jordan Separation theorem is not true anymore, and so on. Conversely, making images well-composed solves those problems and then gives access to many powerful tools already known in mathematical morphology as the Tree of Shapes which is of our principal interest. In this paper, we present two main results: a characterization of 3D well-composed gray-valued images; and a counter-example showing that no local self-dual interpolation satisfying a classical set of properties makes well-composed images with one subdivision in 3D, as soon as we choose the mean operator to interpolate in 1D. Then, we briefly discuss various constraints that could be interesting to change to make the problem solvable in nD.


Digital topology gray-level images well-composed sets well-composed images 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Nicolas Boutry
    • 1
    • 2
  • Thierry Géraud
    • 1
  • Laurent Najman
    • 2
  1. 1.EPITA Research and Development Laboratory (LRDE)France
  2. 2.Université Paris-Est, LIGM, Équipe A3SI, ESIEEFrance

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