Efficient Robust Digital Hyperplane Fitting with Bounded Error

  • Dror Aiger
  • Yukiko Kenmochi
  • Hugues Talbot
  • Lilian Buzer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6607)


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.


fitting digital hyperplane approximation linear programming randomization 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dror Aiger
    • 1
  • Yukiko Kenmochi
    • 1
  • Hugues Talbot
    • 1
  • Lilian Buzer
    • 1
  1. 1.Laboratoire d’Informatique Gaspard-MongeUniversité Paris-EstFrance

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