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Building the component tree in quasi-linear time.

Laurent Najman1, Michel Couprie

  • 1Institut Gaspard-Monge, Groupe ESIEE, Laboratoire A2SI, BP99, 93162 Noisy-le-Grand, France. l.najman@esiee.fr

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|November 2, 2006
PubMed
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This study introduces a fast, quasi-linear algorithm for computing component trees on symmetric graphs. The new method improves upon existing O(n ln(n)) algorithms and includes a way to find significant map lobes.

Area of Science:

  • Computational geometry
  • Graph theory
  • Image analysis

Background:

  • Component trees organize connected components of level sets, finding applications in various fields.
  • Existing algorithms for component tree computation have a worst-case complexity of O(n ln(n)).

Purpose of the Study:

  • To develop a more efficient algorithm for computing component trees on symmetric graphs.
  • To introduce a method for identifying the n most significant lobes of a map.

Main Methods:

  • A quasi-linear algorithm based on Tarjan's union-find procedure.
  • Development of a novel algorithm for lobe computation.

Main Results:

  • The proposed algorithm achieves quasi-linear time complexity for component tree computation on symmetric graphs.

Related Experiment Videos

  • An efficient method for computing the n most significant lobes of a map is presented.

    • Conclusions:

    • The new algorithm offers a simpler and faster approach to component tree construction.
    • This work provides valuable tools for applications relying on component tree analysis and lobe identification.