Locally Turn-Bounded Curves Are Quasi-Regular.

The characteristics of a digitization of a Euclidean planar shape depends on the digitization process but also on the shape border regularity. The notion of Local Turn Boundedness (LTB) was introduced by the authors in Le Quentrec, É. et al.: Local Turn-Boundedness: A curvature control for a good digitization, DGCI 2019 so as to have multigrid convergent perimeter estimation on Euclidean shapes. If it was proved that the par-regular curves are locally turn bounded, the relation with the quasi-regularity introduced in Ngo, P.et al.: Convexity-Preserving Rigid Motions of 2D Digital Objects, DGCI 2017 had not yet been explored. Our paper is dedicated to prove that for planar shapes, local turn-boundedness implies quasi-regularity.