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Optimal Covering of a Straight Line Applied to Discrete Convexity

  • Jean-Marc Chassery
  • Isabelle Sivignon
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7749)

Abstract

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.

Keywords

Convex Hull Convex Shape Optimal Covering Digital Space Optimal Radius 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jean-Marc Chassery
    • 1
  • Isabelle Sivignon
    • 1
  1. 1.CNRS, UMR 5216gipsa-labFrance

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