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Universal Spaces for \((k, \overline{k})-\)Surfaces

  • J. C. Ciria
  • E. Domínguez
  • A. R. Francés
  • A. Quintero
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5810)

Abstract

In the graph–theoretical approach to Digital Topology, the search for a definition of digital surfaces as subsets of voxels is still a work in progress since it was started in the early 1980’s. Despite the interest of the applications in which it is involved (ranging from visualization to image segmentation and graphics), there is not yet a well established general notion of digital surface that naturally extends to higher dimensions (see [5] for a proposal). The fact is that, after the first definition of surface, proposed by Morgenthaler [13] for \({\mathbb Z}^3\) with the usual adjacency pairs (26,6) and (6,26), each new contribution [10,4,9], either increasing the number of surfaces or extendeding the definition to other adjacencies, has still left out some objects considered as surfaces for practical purposes [12].

In this paper we find, for each adjacency pair \((k,{\overline{k}})\), \(k,{\overline{k}}\in\{6, 18, 26\}\) and \((k,{\overline{k}})\neq(6,6)\), a homogeneous \((k,{\overline{k}})\)-connected digital space whose set of digital surfaces is larger than any of those quoted above; moreover, it is the largest set of surfaces within that class of digital spaces as defined in [3]. This is an extension of a previous result for the (26,6)-adjacency in [7].

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • J. C. Ciria
    • 1
  • E. Domínguez
    • 1
  • A. R. Francés
    • 1
  • A. Quintero
    • 2
  1. 1.Dpto. de Informática e Ingeniería de Sistemas, Facultad de CienciasUniversidad de ZaragozaZaragozaSpain
  2. 2.Dpto. de Geometría y Topología, Facultad de MatemáticasUniversidad de SevillaSevillaSpain

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