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Flow Complexity: Fast Polytopal Graph Complexity and 3D Object Clustering

  • Francisco Escolano
  • Daniela Giorgi
  • Edwin R. Hancock
  • Miguel A. Lozano
  • Bianca Falcidieno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5534)

Abstract

In this paper, we introduce a novel descriptor of graph complexity which can be computed in real time and has the same qualitative behavior of polytopal (Birkhoff) complexity, which has been successfully tested in the context of Bioinformatics. We also show how the phase-change point may be characterized in terms of the Laplacian spectrum, by analyzing the derivatives of the complexity function. In addition, the new complexity notion (flow complexity) is applied to cluster a database of Reeb graphs coming from analyzing 3D objects.

Keywords

Heat Kernel Critical Area Geodesic Distance Graph Complexity Graph Permutation 
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 2009

Authors and Affiliations

  • Francisco Escolano
    • 1
  • Daniela Giorgi
    • 2
  • Edwin R. Hancock
    • 3
  • Miguel A. Lozano
    • 1
  • Bianca Falcidieno
    • 2
  1. 1.Departamento de Ciencia de la Computación e Inteligencia ArtificialUniversity of AlicanteSpain
  2. 2.Istituto di Matematica Applicata e Tecnologie Informatiche Consiglio Nazionale delle RicercheItaly
  3. 3.Department of Computer ScienceUniversity of YorkUK

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