Efficient Robust Digital Hyperplane Fitting with Bounded Error

Abstract : We consider the following fitting problem: given an arbitrary set of N points in a bounded grid in dimension d, find a digital hyperplane that contains the largest possible number of points. We first observe that the problem is 3SUM-hard in the plane, so that it probably cannot be solved exactly with computational complexity better than O(N 2), and it is conjectured that optimal computational complexity in dimension d is in fact O(N d ). We therefore propose two approximation methods featuring linear time complexity. As the latter one is easily implemented, we present experimental results that show the runtime in practice.
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https://hal.archives-ouvertes.fr/hal-00790712
Contributor : Yukiko Kenmochi <>
Submitted on : Wednesday, February 20, 2013 - 6:34:18 PM
Last modification on : Thursday, July 5, 2018 - 2:25:51 PM

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Dror Aiger, Yukiko Kenmochi, Hugues Talbot, Lilian Buzer. Efficient Robust Digital Hyperplane Fitting with Bounded Error. 16th International Conference on Discrete Geometry for Computer Imagery, DGCI2011, Apr 2011, Nancy, France. pp.223-234, ⟨10.1007/978-3-642-19867-0_19⟩. ⟨hal-00790712⟩

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