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A Quasi-linear Algorithm to Compute the Tree of Shapes of nD Images

  • Thierry Géraud
  • Edwin Carlinet
  • Sébastien Crozet
  • Laurent Najman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7883)

Abstract

To compute the morphological self-dual representation of images, namely the tree of shapes, the state-of-the-art algorithms do not have a satisfactory time complexity. Furthermore the proposed algorithms are only effective for 2D images and they are far from being simple to implement. That is really penalizing since a self-dual representation of images is a structure that gives rise to many powerful operators and applications, and that could be very useful for 3D images. In this paper we propose a simple-to-write algorithm to compute the tree of shapes; it works for nD images and has a quasi-linear complexity when data quantization is low, typically 12 bits or less. To get that result, this paper introduces a novel representation of images that has some amazing properties of continuity, while remaining discrete.

Keywords

Parent Function Image Representation Cubical Complex Morphological Tree Canonical Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Thierry Géraud
    • 1
    • 2
  • Edwin Carlinet
    • 1
    • 2
  • Sébastien Crozet
    • 1
  • Laurent Najman
    • 2
  1. 1.EPITA Research and Development Laboratory (LRDE)France
  2. 2.LIGM, Équipe A3SI, ESIEEUniversité Paris-EstFrance

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