Computational-geometric methods for polygonal approximations of a curve
Computer Vision, Graphics, and Image Processing
Fitting polygonal functions to a set of points in the plane
CVGIP: Graphical Models and Image Processing
On approximating polygonal curves in two and three dimensions
CVGIP: Graphical Models and Image Processing
Approximating monotone polygonal curves using the uniform metric
Proceedings of the twelfth annual symposium on Computational geometry
A new algorithm for fitting a rectilinear x-monotone curve to a set of points in the plane
Pattern Recognition Letters
Approximation of Point Sets by 1-Corner Polygonal Chains
INFORMS Journal on Computing
Weighted rectilinear approximation of points in the plane
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
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We derive algorithms for approximating a set S of n points in the plane by an x-monotone rectilinear polyline with k horizontal segments. The quality of the approximation is measured by the maximum distance from a point in S to the segment above or below it. We consider two types of problems: min-ε, where the goal is to minimize the error for k horizontal segments and min-#, where the goal is to minimize the number of segments for error ε. After O(n) preprocessing time, we solve the latter in O(min{klogn, n}) time per instance. We then solve the former in O(min{n2, nklog n}) time. We also describe an approximation algorithm for the min-ε problem that computes a solution within a factor of 3 of the optimal error for k segments, or with at most the same error as the k-optimal but using 2k–1 segments. Both approximations run in O(nlog n) time.