Local Turn-Boundedness, a curvature control for continuous curves with application to digitization

Etienne Le Quentrec (1) , Loïc Mazo (1) , Étienne Baudrier (1) , Mohamed Tajine (1)

1 ICube - Laboratoire des sciences de l'ingénieur, de l'informatique et de l'imagerie

This article 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 satisfied 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 does 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 constrain spatially the continuous curve as a function of its digitization.

Domaines: Traitement des images [eess.IV]; Mathématique discrète [cs.DM]; Mathématiques générales [math.GM]

Etienne Le Quentrec, Loïc Mazo, Étienne Baudrier, Mohamed Tajine. Local Turn-Boundedness, a curvature control for continuous curves with application to digitization. Journal of Mathematical Imaging and Vision, 2020, 62 (5), pp.673-692. ⟨10.1007/s10851-020-00952-x⟩. ⟨hal-02891118⟩