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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Aiger, D., Kenmochi, Y., Talbot, H., Buzer, L. (2011). Efficient Robust Digital Hyperplane Fitting with Bounded Error. In: Debled-Rennesson, I., Domenjoud, E., Kerautret, B., Even, P. (eds) Discrete Geometry for Computer Imagery. DGCI 2011. Lecture Notes in Computer Science, vol 6607. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19867-0_19
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DOI: https://doi.org/10.1007/978-3-642-19867-0_19
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