Consistent digital line segments
Proceedings of the twenty-sixth annual symposium on Computational geometry
Maximum weight digital regions decomposable into digital star-shaped regions
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Algorithms for computing the maximum weight region decomposable into elementary shapes
Computer Vision and Image Understanding
On maximum weight objects decomposable into based rectilinear convex objects
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
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Given a fixed origin o in the d-dimensional grid, we give a novel definition of digital rays dig(op) from o to each grid point p. Each digital ray dig(op) approximates the Euclidean line segment $\overline {op}$between o and p. The set of all digital rays satisfies a set of axioms analogous to the Euclidean axioms. We measure the approximation quality by the maximum Hausdorff distance between a digital ray and its Euclidean counterpart and establish an asymptotically tight Θ(log n) bound in the n×n grid. The proof of the bound is based on discrepancy theory and a simple construction algorithm. Without a monotonicity property for digital rays the bound is improved to O(1). Digital rays enable us to define the family of digital star-shaped regions centered at o, which we use to design efficient algorithms for image processing problems.