Separation Theorems for Simplicity 26-Surfaces

  • J. C. Ciria
  • E. Domínguez
  • A. R. Francés
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2301)


The main goal of this paper is to prove a Digital Jordan- Brouwer Theorem and an Index Theorem for simplicity 26-surfaces. For this, we follow the approach to Digital Topology introduced in [2], and find a digital space such that the continuous analogue of each simplicity 26-surface is a combinatorial 2-manifold. Thus, the separation theorems quoted above turn out to be an immediate consequence of the general results obtained in [2] and [3] for arbitrary digital n-manifolds.


Digital surface simplicity 26-surface digital separation theorems 


  1. 1.
    R. Ayala, E. Domínguez, A.R. Francés, A. Quintero. Digital Lighting Functions. Lecture Notes in Computer Science. 1347 (1997) 139–150.Google Scholar
  2. 2.
    R. Ayala, E. Domínguez, A.R. Francés, A. Quintero. Weak Lighting Functions and Strong 26-surfaces. To appear in Theoretical Computer Science.Google Scholar
  3. 3.
    R. Ayala, E. Domíguez, A. R. Francés and A. Quintero. A Digital Index Theorem. Int. J. Patter Recog. Art. Intell. 15(7) (2001) 1–22.Google Scholar
  4. 4.
    G. Bertrand, R. Malgouyres. Topological Properties of Discrete Surfaces. Lect. Notes in Comp. Sciences. 1176 (1996) 325–336.Google Scholar
  5. 5.
    M. Couprie, G. Bertrand. Simplicity Surfaces: a new definition of surfaces in ℤ3. SPIE Vision Geometry V. 3454 (1998) 40–51.Google Scholar
  6. 6.
    R. Malgouyres, G. Bertrand. Complete Local Characterization of Strong 26-Surfaces: Continuous Analog for Strong 26-Surfaces. Int. J. Pattern Recog. Art. Intell. 13(4) (1999) 465–484.CrossRefGoogle Scholar
  7. 7.
    T.Y. Kong, A.W. Roscoe. Continuous Analogs of Axiomatized Digital Surfaces. Comput. Vision Graph. Image Process. 29 (1985) 60–86.CrossRefGoogle Scholar
  8. 8.
    T.Y. Kong, A. Rosenfeld. Digital Topology: Introduction and Survey. Comput. Vision Graph. Image Process. 48 (1989) 357–393.CrossRefGoogle Scholar
  9. 9.
    D.G. Morgenthaler, A. Rosenfeld. Surfaces in three-dimensional Digital Images. Inform. Control. 51 (1981) 227–247.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    C.P. Rourke, and B.J. Sanderson. Introduction to Piecewise-Linear Topology. Ergebnisse der Math. 69, Springer 1972.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • J. C. Ciria
    • 1
  • E. Domínguez
    • 1
  • A. R. Francés
    • 1
  1. 1.Dpt. de Informática e Ingeniería de Sistemas. Facultad de CienciasUniversidad de ZaragozaZaragozaSpain

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