Local Turn-Boundedness: A Curvature Control for a Good Digitization

  • Étienne Le QuentrecEmail author
  • Loïc Mazo
  • Étienne Baudrier
  • Mohamed Tajine
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11414)


This paper focuses on the classical problem of the control of information loss during the digitization step. The properties proposed in the literature rely on smoothness hypotheses that are not verified by the curves including angular points. The notion of turn introduced by Milnor in the article On the Total Curvature of Knots generalizes the notion of integral curvature to continuous curves. Thanks to the turn, we are able to define the local turn-boundedness. This promising property of curves do not require smoothness hypotheses and shares several properties with the par(r)-regularity, in particular well-composed digitizations. Besides, the local turn-boundedness enables to constraint spatially the continuous curve in function of its digitization.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Étienne Le Quentrec
    • 1
    Email author
  • Loïc Mazo
    • 1
  • Étienne Baudrier
    • 1
  • Mohamed Tajine
    • 1
  1. 1.ICube-UMR 7357, 300 Bd Sébastien Brant - CS 10413Illkirch CedexFrance

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