International Journal of Computer Vision

, Volume 112, Issue 1, pp 115–129 | Cite as

Tractable Algorithms for Robust Model Estimation

  • Olof EnqvistEmail author
  • Erik Ask
  • Fredrik Kahl
  • Kalle Åström


What is the computational complexity of geometric model estimation in the presence of noise and outliers? We show that the number of outliers can be minimized in polynomial time with respect to the number of measurements, although exponential in the model dimension. Moreover, for a large class of problems, we prove that the statistically more desirable truncated \(L_2\)-norm can be optimized with the same complexity. In a similar vein, it is also shown how to transform a multi-model estimation problem into a purely combinatorial one—with worst-case complexity that is polynomial in the number of measurements but exponential in the number of models. We apply our framework to a series of hard fitting problems. It gives a practical method for simultaneously dealing with measurement noise and large amounts of outliers in the estimation of low-dimensional models. Experimental results and a comparison to random sampling techniques are presented for the applications rigid registration, triangulation and stitching.


Outliers Geometry Optimization  3D reconstruction Image registration 


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Olof Enqvist
    • 1
    Email author
  • Erik Ask
    • 2
  • Fredrik Kahl
    • 1
    • 2
  • Kalle Åström
    • 2
  1. 1.Chalmers University of TechnologyGöteborgSweden
  2. 2.Lund UniversityLundSweden

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