Optimal Covering of a Straight Line Applied to Discrete Convexity

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.

• Type: Journal
• Year: 2013
• Where: DGCI
• Authors: Jean-Marc Chassery, Isabelle Sivignon
• Keywords: DGCI 2013, Discrete Geometry