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Robust Fitting for Multiple View Geometry

  • Olof Enqvist
  • Erik Ask
  • Fredrik Kahl
  • Kalle Åström
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7572)

Abstract

How hard are geometric vision problems with outliers? We show that for most fitting problems, a solution that minimizes the number of outliers can be found with an algorithm that has polynomial time-complexity in the number of points (independent of the rate of outliers). Further, and perhaps more interestingly, other cost functions such as the truncated L2-norm can also be handled within the same framework with the same time complexity.

We apply our framework to triangulation, relative pose problems and stitching, and give several other examples that fulfill the required conditions. Based on efficient polynomial equation solvers, it is experimentally demonstrated that these problems can be solved reliably, in particular for low-dimensional models. Comparisons to standard random sampling solvers are also given.

Keywords

Computer Vision Loss Function Active Constraint Residual Function Point Correspondence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Fischler, M.A., Bolles, R.C.: Random sample consensus: a paradigm for model fitting with application to image analysis and automated cartography. Commun. Assoc. Comp. Mach. (1981)Google Scholar
  2. 2.
    Chum, O., Matas, J.: Optimal randomized ransac. Trans. Pattern Analysis and Machine Intelligence (2008)Google Scholar
  3. 3.
    Hartley, R., Sturm, P.: Triangulation. Computer Vision and Image Understanding (1997)Google Scholar
  4. 4.
    Kahl, F., Hartley, R.: Multiple view geometry under the L ∞ -norm. Trans. Pattern Analysis and Machine Intelligence (2008)Google Scholar
  5. 5.
    Ke, Q., Kanade, T.: Quasiconvex optimization for robust geometric reconstruction. Trans. Pattern Analysis and Machine Intelligence (2007)Google Scholar
  6. 6.
    Sim, K., Hartley, R.: Removing outliers using the L ∞ -norm. In: Conf. Computer Vision and Pattern Recognition (2006)Google Scholar
  7. 7.
    Olsson, C., Eriksson, A., Hartley, R.: Outlier removal using duality. In: Conf. Computer Vision and Pattern Recognition (2010)Google Scholar
  8. 8.
    Yu, J., Eriksson, A., Chin, T.J., Suter, D.: An adversarial optimization approach to efficient outlier removal. In: Int. Conf. Computer Vision (2011)Google Scholar
  9. 9.
    Breuel, T.: Implementation techniques for geometric branch-and-bound matching methods. Computer Vision and Image Understanding (2003)Google Scholar
  10. 10.
    Li, H.: Consensus set maximization with guaranteed global optimality for robust geometry estimation. In: Int. Conf. Computer Vision (2009)Google Scholar
  11. 11.
    Cass, T.: Polynomial-time geometric matching for object recognition. Int. Journal of Computer Vision (1999)Google Scholar
  12. 12.
    Li, H.: A practical algorithm for L ∞  triangulation with outliers. In: Conf. Computer Vision and Pattern Recognition (2007)Google Scholar
  13. 13.
    Olsson, C., Enqvist, O., Kahl, F.: A polynomial-time bound for matching and registration with outliers. In: Conf. Computer Vision and Pattern Recognition (2008)Google Scholar
  14. 14.
    Bazaraa, M., Sherali, H., Shetty, C.: Nonlinear Programming: Theory and Algorithms. Wiley (1993)Google Scholar
  15. 15.
    Byröd, M., Josephson, K., Åström, K.: Fast and stable polynomial equation solving and its application to computer vision. Int. Journal of Computer Vision (2009)Google Scholar
  16. 16.
    Källén, H., Ardö, H., Enqvist, O.: Tracking and reconstruction of vehicles for accurate position estimation. In: W. on Applications of Computer Vision (2011)Google Scholar
  17. 17.
    Hartley, R., Kahl, F.: Global optimization through rotation space search. Int. Journal of Computer Vision (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Olof Enqvist
    • 1
  • Erik Ask
    • 1
  • Fredrik Kahl
    • 1
  • Kalle Åström
    • 1
  1. 1.Centre for Mathematical SciencesLund UniversitySweden

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