A Concise Characterization of 3D Simple Points

  • Sébastien Fourey
  • Rémy Malgouyres
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1953)


We recall the definition of simple points which uses the digital fundamental group introduced by T. Y. Kong in [Kon89]. Then, we prove that a not less restrictive de.nition can be given. Indeed, we prove that there is no need of considering the fundamental group of the complement of an object in order to characterize its simple points. In order to prove this result, we do not use the fact that “the number of holes of X is equal to the number of holes in X” which is not su.cient for our purpose but we use the linking number de.ned in [FM00]. In so doing, we formalize the proofs of several results stated without proof in the literature (Bertrand, Kong, Morgenthaler).


digital topology linking number simple points 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Sébastien Fourey
    • 1
  • Rémy Malgouyres
    • 1
  1. 1.GREYC, ISMRACaenFrance

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