Topology-Preserving Deformations of Fuzzy Digital Pictures

  • Akira Nakamura
  • Azriel Rosenfeld
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 52)


This chapter considers the topology of two-dimensional fuzzy digital pictures, and discusses topology-preserving deformations of these fuzzy pictures that generalize deformations of two-valued digital pictures. It is shown that an arbitrary fuzzy picture can be transformed by this type of deformation into a coherent fuzzy picture. As another application, it is shown that the genus of a fuzzy picture is a linear combination of local property values.


Fuzzy Subset Local Operation Simple Point Local Connectedness Hexagonal Array 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Dyer C.R. and Rosenfeld A., Thinning algorithms for gray-scale pictures,IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 1, pp. 88–89, 1979Google Scholar
  2. 2.
    Nakamura A. and Aizawa K., Connectedness of coherent fuzzy pictures,Information Sciences, Vol. 61, pp. 123–133, 1992Google Scholar
  3. 3.
    Nakamura A. and Rosenfeld A., Deformations of fuzzy pictures,in: “Proceedings of JCIS’97 — Joint Conference on Information Sciences”, Vol. 3, pp. 273276, 1997Google Scholar
  4. 4.
    Rosenfeld A., “Picture Languages”, Academic Press, New York, 1979MATHGoogle Scholar
  5. 5.
    Rosenfeld A., Fuzzy digital topology,Information and Control, Vol. 40, pp. 7687, 1979Google Scholar
  6. 6.
    Rosenfeld A., On connectivity properties of grayscale pictures,Pattern Recognition, Vol. 16, pp. 47–50, 1983Google Scholar
  7. 7.
    Rosenfeld A., Kong T.Y. and A. Nakamura A., Topology-preserving deformations of two-valued digital pictures, Graphical Models and Image Processing, Vol. 60, pp. 24–34, 1998CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Akira Nakamura
    • 1
  • Azriel Rosenfeld
    • 2
  1. 1.Department of Computer ScienceHiroshima-Denki Institute of TechnologyHiroshimaJapan
  2. 2.Center for Automation ResearchUniversity of MarylandCollege ParkUSA

Personalised recommendations