A Bibliography on Digital and Computational Convexity (1961-1988)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Lines and Digital Convexity
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
Digital Geometry: Geometric Methods for Digital Picture Analysis
Digital Geometry: Geometric Methods for Digital Picture Analysis
Measuring Concavity on a Rectangular Mosaic
IEEE Transactions on Computers
Digital Straight Lines and Convexity of Digital Regions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Convexity, Straightness, and Convex Polygons
IEEE Transactions on Pattern Analysis and Machine Intelligence
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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.