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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Chassery, JM., Sivignon, I. (2013). Optimal Covering of a Straight Line Applied to Discrete Convexity. In: Gonzalez-Diaz, R., Jimenez, MJ., Medrano, B. (eds) Discrete Geometry for Computer Imagery. DGCI 2013. Lecture Notes in Computer Science, vol 7749. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37067-0_1
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DOI: https://doi.org/10.1007/978-3-642-37067-0_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37066-3
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