Convexity Preserving Contraction of Digital Sets

Lama Tarsissi (1) , David Coeurjolly (2) , Yukiko Kenmochi (3) , Pascal Romon (4)

1 LAMA - Laboratoire de Mathématiques
2 M2DisCo - Geometry Processing and Constrained Optimization
3 LIGM - Laboratoire d'Informatique Gaspard-Monge
4 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

Convexity is one of the useful geometric properties of digital sets in digital image processing. There are various applications which require deforming digital convex sets while preserving their convexity. In this article, we consider the contraction of such digital sets by removing digital points one by one. For this aim, we use some tools of combina-torics on words to detect a set of removable points and to define such convexity-preserving contraction of a digital set as an operation of rewriting its boundary word. In order to chose one of removable points for each contraction step, we present three geometrical strategies, which are related to vertex angle and area changes. We also show experimental results of applying the methods to repair some non-convex digital sets, which are obtained by rotations of convex digital sets.

Domaines: Mathématique discrète [cs.DM]

Lama Tarsissi, David Coeurjolly, Yukiko Kenmochi, Pascal Romon. Convexity Preserving Contraction of Digital Sets. ACPR 2019, Nov 2019, Auckland, New Zealand. ⟨hal-02315084v1⟩