Optimal covering of a straight line applied to discrete convexity

Jean-Marc Chassery (1) , Isabelle Sivignon (1)

1 GIPSA-AGPIG - GIPSA - Architecture, Géométrie, Perception, Images, Gestes

The relation between a straight line and its digitization as a digital straight line is often expressed using a notion of proximity. In this contribution, we consider the covering of the straight line by a set of balls centered on the digital straight line pixels. We prove that the optimal radius of the balls is strictly less than one, and can be expressed as a function of the slope of the straight line. This property is used to define discrete convexity in concordance with previous works on convexity.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Jean-Marc Chassery, Isabelle Sivignon. Optimal covering of a straight line applied to discrete convexity. DGCI 2013 - 17th IAPR International Conference on Discrete Geometry for Computer Imagery, Mar 2013, Séville, Spain. pp.1-10. ⟨hal-00765865⟩