In this article, we propose algorithms for pixelwise deformations of digital convex sets preserving their convexity using the combinatorics on words to identify digital convex sets via their boundary words, namely Lyndon and Christoffel words. The notion of removable and insertable points are used with a geometric strategy for choosing one of those pixels for each deformation step. The worst-case time complexity of each deflation and inflation step, which is the atomic deformation, is also analysed.
@inproceedings{tarsissiDGMM22,
author = {Lama Tarsissi and Yukiko Kenmochi and Hadjer Djerroumi and David Coeurjolly and Pascal Romon and Jean-Pierre Borel},
booktitle = {IAPR Second International Conference on Discrete
Geometry and Mathematical Morphology},
editor = {Étienne Baudrier and Benoît Naegel and Adrien
Krähenbühl and Mohamed Tajine},
month = {October},
publisher = {Springer, LNCS},
title = {Algorithms for pixelwise shape deformations preserving digital convexity},
year = {2022}
}