Fast and Robust Algorithm for Fundamental Matrix Estimation

  • Ming Zhang
  • Guanghui WangEmail author
  • Haiyang Chao
  • Fuchao Wu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9164)


Fundamental matrix estimation from two views plays an important role in 3D computer vision. In this paper, a fast and robust algorithm is proposed for the fundamental matrix estimation in the presence of outliers. Instead of algebra error, the reprojection error is adopted to evaluate the confidence of the fundamental matrix. Assuming Gaussian image noise, it is proved that the reprojection error can be described by a chi-square distribution, and thus, the outliers can be eliminated using the 3-sigma principle. With this strategy, the inlier set is robustly established in only two steps. Compared to classical RANSAC-based strategies, the proposed algorithm is very efficient with higher accuracy. Experimental evaluations and comparisons with previous methods demonstrate the effectiveness and advantages of the proposed approach.


Fundamental matrix Robust estimation Outlier elimination 



The work is partly supported by the Kansas NASA EPSCoR Program, and the NSFC (61273282).


  1. 1.
    Zhang, Z.: Determining the epipolar geometry and its uncertainty: a review. Int. J. Comput. Vision 27, 161–198 (1998)CrossRefGoogle Scholar
  2. 2.
    Hartley, R.: In defense of the 8-point algorithm. In: Proceedings of the 8th International Conference on Computer Vision, pp. 1064–1070 (1995)Google Scholar
  3. 3.
    Stewart, C.V.: Robust parameter estimation in computer vision. SIAM Rev. 41, 513–537 (1999)zbMATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Armangué, X., Salvi, J.: Overall view regarding fundamental matrix estimation. Image Vis. Comput. 21, 205–220 (2003)CrossRefGoogle Scholar
  5. 5.
    Rousseeuw, P.J., Leroy, A.M.: Robust Regression and Outlier Detection. Wiley, New York (1987)zbMATHCrossRefGoogle Scholar
  6. 6.
    Torr, P.H.S., Murray, D.W.: The development and comparison of robust methods for estimating the fundamental matrix. IJCV 24, 271–300 (1997)CrossRefGoogle Scholar
  7. 7.
    Fischler, M., Bolles, R.: Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography. Commun. ACM 24, 381–385 (1981)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Chum, O., Matas, J.: Matching with PROSAC - progressive sample consensus. In: IEEE Conference on Computer Vision and Pattern Recognition, June 2005Google Scholar
  9. 9.
    Torr, P.H.S., Zisserman, A.: MLESAC: a new robust estimator with application to estimating image geometry. Comput. Vis. Image Underst. 78, 138–156 (2000)CrossRefGoogle Scholar
  10. 10.
    Torr, P.H.S.: Bayesian model estimation and selection for epipolar geometry and generic manifold fitting. Int. J. Comput. Vision 50(1), 35–61 (2002)zbMATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Feng, C.L., Hung, Y.S.: A robust method for estimating the fundamental matrix. In: DICTA, pp. 633–642 (2003)Google Scholar
  12. 12.
    Huang, J.F., Lai, S.H., Cheng, C.M.: Robust fundamental matrix estimation with accurate outlier detection. J. Inf. Sci. Eng. 23(4), 1213–1225 (2007)Google Scholar
  13. 13.
    Carro, A.I., Morros, J.R.: Promeds: an adaptive robust fundamental matrix estimation approach. In: 3DTV-Conference, pp. 1–4. IEEE (2012)Google Scholar
  14. 14.
    Hartley, R.I., Sturm, P.: Triangulation. Comput. Vis. Image Underst. 68(2), 146–157 (1997)CrossRefGoogle Scholar
  15. 15.
    Rousseeuw, P., Leroy, A.: Robust Regression and Outlier Detection. Wiley, New York (1987)zbMATHCrossRefGoogle Scholar
  16. 16.
    Wang, G., Zelek, J., Wu, J., Bajcsy, R.: Robust rank-4 affine factorization for structure from motion. In: IEEE WACV, pp. 180–185 (2013)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Ming Zhang
    • 1
    • 2
  • Guanghui Wang
    • 1
    Email author
  • Haiyang Chao
    • 1
  • Fuchao Wu
    • 2
  1. 1.School of EngineeringUniversity of KansasLawrenceUSA
  2. 2.National Lab of Pattern RecognitionChinese Academy of SciencesBeijingChina

Personalised recommendations