Locally Turn-Bounded Curves Are Quasi-Regular

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