A New A Contrario Approach for the Robust Determination of the Fundamental Matrix

  • Ferran Espuny
  • Pascal Monasse
  • Lionel Moisan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8334)


The fundamental matrix is a two-view tensor that plays a central role in Computer Vision geometry. We address its robust estimation given correspondences between image features. We use a non-parametric estimate of the distribution of image features, and then follow a probabilistic approach to select the best possible set of inliers among the given feature correspondences. The use of this perception-based a contrario principle allows us to avoid the selection of a precision threshold as in RANSAC, since we provide a decision criterion that integrates all data and method parameters (total number of points, precision threshold, number of inliers given this threshold). Our proposal is analyzed in simulated and real data experiments; it yields a significant improvement of the ORSA method proposed in 2004, in terms of reprojection error and relative motion estimation, especially in situations of low inlier ratios.


stereovision fundamental matrix feature matching a contrario model outlier detection 


  1. 1.
    Chum, O., Werner, T., Matas, J.: Two-view geometry estimation unaffected by a dominant plane. In: Proc. CVPR (2005)Google Scholar
  2. 2.
    Desolneux, A., Moisan, L., Morel, J.-M.: From Gestalt Theory to Image Analysis. A Probabilistic Approach. Springer-Verlag, collection “Interdisciplinary Applied Mathematics” 34 (2008)Google Scholar
  3. 3.
    Fischler, M.A., Bolles, R.C.: Random sample consensus: A paradigm for model fitting with applications to image analysis and automated cartography. Comm. ACM 24(6), 381–395 (1981)CrossRefMathSciNetGoogle Scholar
  4. 4.
    Frahm, J.-M., Pollefeys, M.: Ransac for (quasi-)degenerate data (QDEGSAC). In: Proc. CVPR (2006)Google Scholar
  5. 5.
    Goshen, L., Shimshoni, I.: Balanced exploration and exploitation model search for eficient epipolar geometry estimations. In: Proc. ECCV (2006)Google Scholar
  6. 6.
    Grosjean, B., Moisan, L.: A-contrario detectability of spots in textured backgrounds. J. Math. Imag. Vis. 33(3), 313–337 (2009)CrossRefMathSciNetGoogle Scholar
  7. 7.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press (2004)Google Scholar
  8. 8.
    Kanatani, K., Sugaya, Y., Niitsuma, H.: Triangulation from two views revisited: Hartley-Sturm vs. optimal correction. In: Proc. BMVC (2008)Google Scholar
  9. 9.
    Kanatani, K., Sugaya, Y.: Fundamental matrix computation: Theory and practice. Memoirs of the Faculty of Engineering, Okayama University 42, 18–35 (2008)Google Scholar
  10. 10.
    Lowe, D.G.: Distinctive image features from scale-invariant keypoints. Int. J. Comput. Vis. 60(2), 91–110 (2004)CrossRefGoogle Scholar
  11. 11.
    Moisan, L., Stival, B.: A probabilistic criterion to detect rigid point matches between two images and estimate the fundamental matrix. Int. J. Comput. Vis. 57(3), 201–218 (2004)CrossRefGoogle Scholar
  12. 12.
    Moisan, L., Moulon, P., Monasse, P.: Automatic Homographic Registration of a Pair of Images, with A Contrario Elimination of Outliers. In: IPOL (2012)Google Scholar
  13. 13.
    Moulon, P., Monasse, P., Marlet, R.: Adaptive structure from motion with a contrario model estimation. In: Lee, K.M., Matsushita, Y., Rehg, J.M., Hu, Z. (eds.) ACCV 2012, Part IV. LNCS, vol. 7727, pp. 257–270. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  14. 14.
    Noury, N., Sur, F., Berger, M.-O.: Fundamental matrix estimation without prior match. In: Proc. ICIP (2007)Google Scholar
  15. 15.
    Sheather, S.J.: Density estimation. Stat. Sci. 19(4), 588–597 (2004)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Sheather, S.J., Jones, M.C.: A reliable data-based bandwidth selection method for kernel density estimation. J. R. Stat. Soc. (Series B) 53, 683–690 (1991)Google Scholar
  17. 17.
    Torr, P.H.S., Zisserman, A.: MLESAC: A new robust estimator with application to estimating image geometry. Comput. Vis. Image Understand 78, 138–156 (2000)CrossRefGoogle Scholar
  18. 18.
    Torr, P.H.S., Zisserman, A., Maybank, S.J.: Robust detection of degenerate configurations while estimating the fundamental matrix. Comput. Vis. Image Understand 71(3), 312–333 (1998)CrossRefGoogle Scholar
  19. 19.
    Zhang, Z.: Determining the epipolar geometry and its uncertainty: a review. Int. J. Comput. Vis. 27(2), 161–195 (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Ferran Espuny
    • 1
  • Pascal Monasse
    • 2
  • Lionel Moisan
    • 3
  1. 1.School of Environmental SciencesUniversity of LiverpoolUK
  2. 2.LIGM (CNRS UMR 8049), Center for Visual Computing, ENPCUniversité Paris-EstMarne-la-ValléeFrance
  3. 3.MAP5 (CNRS UMR 8145)Université Paris DescartesFrance

Personalised recommendations