Optimal covering of a straight line applied to discrete convexity

Jean-Marc Chassery 1 Isabelle Sivignon 1
1 GIPSA-AGPIG - AGPIG
GIPSA-DIS - Département Images et Signal
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.
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17th IAPR International Conference on Discrete Geometry for Computer Imagery (DGCI 2013), Mar 2013, Séville, Spain. 7749, pp.1-10, 2013
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Jean-Marc Chassery, Isabelle Sivignon. Optimal covering of a straight line applied to discrete convexity. 17th IAPR International Conference on Discrete Geometry for Computer Imagery (DGCI 2013), Mar 2013, Séville, Spain. 7749, pp.1-10, 2013. 〈hal-00765865〉

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