Homotopy in 2-dimensional digital images

  • Rémy Malgouyres
From Principles to Applications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1347)


We recall the basic definitions concerning homotopy in 2D Digital Topology, and we set and prove several results concerning homotopy of subsets. Then we introduce an explicit isomorphism between the fundamental group and a free group. As a consequence, we provide an algorithm for deciding whether two closed path are homotopic.

Key words

Digital topology homotopy fundamental group 


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    T. Y. Kong, Polyhedral Analogs of Locally Finite Topological Spaces R. M. Shortt editor, General Topology and Applications: Proceedings of the 1988 Northeast Conference, Middletown, CT (USA), Lecture Notes in Pure and Applied Mathematics, 123, pp, 153–164, 1990.Google Scholar
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    A. Tarski, Indecidability of group theory, Journal of Symbolic Logic, 14, pp 76–77, 1949.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Rémy Malgouyres
    • 1
  1. 1.GREYC, ISMRACAEN cedexFrance

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