A plate-based definition of discrete surfaces

  • Authors:
  • J. C. Ciria;E. DomíNguez;A. R. FrancéS;A. Quintero

  • Affiliations:
  • Universidad de Zaragoza, Dpto. Informática e Ingeniería de Sistemas, E-50009 Zaragoza, Spain;Universidad de Zaragoza, Dpto. Informática e Ingeniería de Sistemas, E-50009 Zaragoza, Spain;Universidad de Zaragoza, Dpto. Informática e Ingeniería de Sistemas, E-50009 Zaragoza, Spain;Universidad de Sevilla, Dpto. Geometría y Topología, Sevilla, Spain

  • Venue:
  • Pattern Recognition Letters
  • Year:
  • 2012

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Abstract

By the use of certain discrete plates in the role of polygonal faces we mimic the definition of a combinatorial surface to produce, for each adjacency pair (k,k@?)(6,6), k,k@?@?{6,18,26}, a new family S"k"k"@? of discrete surfaces, termed (k,k@?)-surfaces, in the grid Z^3 that strictly contains several well-known families of surfaces, such as the strong and simplicity surfaces, as well as other objects considered as surfaces in the literature. Moreover, the number of possible configurations in the 26-neighbourhood of a (26,6)-surface voxel is estimated to rise up to 10,580. In addition, we show that S"k"k"@? is the largest set of discrete surfaces that can be defined within the framework for Digital Topology in (Ayala et al., 2002).