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Connectivity Forests for Homological Analysis of Digital Volumes

  • Pedro Real
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5517)

Abstract

In this paper, we provide a graph-based representation of the homology (information related to the different “holes” the object has) of a binary digital volume. We analyze the digital volume AT-model representation [8] from this point of view and the cellular version of the AT-model [5] is precisely described here as three forests (connectivity forests), from which, for instance, we can straightforwardly determine representative curves of “tunnels” and “holes”, classify cycles in the complex, computing higher (co)homology operations,... Depending of the order in which we gradually construct these trees, tools so important in Computer Vision and Digital Image Processing as Reeb graphs and topological skeletons appear as results of pruning these graphs.

Keywords

digital volume cell complex chain homotopy graph tree forest homology cohomology 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Pedro Real
    • 1
  1. 1.Dpto. Matematica Aplicada I, E.T.S.I. InformaticaUniversidad de SevillaSevillaSpain

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