Digital Straight Line Segments
IEEE Transactions on Computers
Three-Dimensional Digital Planes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Digital Straight Lines and Convexity of Digital Regions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Three-Dimensional Digital Line Segments
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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A digital straight line segment is defined as the grid-intersect quantization of a straight line segment in the plane. Let S be a set of pixels on a square grid. Rosenfeld [8] showed that S is a digital straight line segment if and only if it is a Digital arc having the chord property. Then Kim and Rosenfeld [3,6] showed that S has the chord properly if and if for every p, q@eS there is a digital straight line segment C @? S such that p and q are the extremities of C. We give a simple proof of these two results based on the Transversal Theorem of Santalo. We show how the underlying methodology can be generalized to the case of (infinite) digital straight lines and to the quantization of hyperplanes in an n-dimensional space for n = 3.