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An Abstract Theoretical Foundation of the Geometry of Digital Spaces

  • Gabor T. Herman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2301)

Abstract

Two approaches to providing an abstract theoretical foundation to the geometry of digital spaces are presented and illustrated. They are critically compared and the possibility of combining them into a single theory is discussed. Such a theory allows us to state and prove results regarding geometrical concepts as they occur in a digital environment independently of the specifics of that environment. In particular, versions of the Jordan Curve Theorem are discussed in this general digital setting.

References

  1. 1.
    Herman, G.T.: Geometry of Digital Spaces. Birkhäuser, Boston Basel Berlin (1998)zbMATHGoogle Scholar
  2. 2.
    Fourey, S., Kong, T.Y., Herman, G.T.: Generic Axiomatized Digital Surface-Structures, submitted for publication in Disc. Appl. Math. (preliminary version appeared in Electronic Notes in Theoretical Computer Science 46 (2001) see http://www.elsevier.nl/gej-ng/31/29/23/86/27/show/Products/notes/index.htt)

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Gabor T. Herman
    • 1
  1. 1.Department of Computer Science, The Graduate CenterCity University of New YorkNew YorkUSA

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