An EA-Based Method for Estimating the Fundamental Matrix

  • Daniel BarraganEmail author
  • Maria Trujillo
  • Ivan Cabezas
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9423)


The camera calibration problem consists in estimating intrinsic and extrinsic parameters. It can be solved by computing a 3x3 matrix enclosing such parameters - the fundamental matrix -, which can be obtained from a set of corresponding points. Nevertheless, in practice, corresponding points may be falsely matched or badly located, due to occlusion and ambiguity. Moreover, if the set of corresponding points does not include information on existing scene depth, the estimated fundamental matrix may not be able to correctly recover the epipolar geometry. In this paper, an EA-based method for accurately selecting estimated corresponding points is introduced. It considers geometric issues that were ignored in previous EA-based approaches. Two selection operators were evaluated and obtained similar results. Additionally, a mutation operator is designed to tackle bad located points by shifting disparity vectors. An inter-technique comparison is performed against a standard camera calibration method. The qualitative evaluation is conducted by analysing obtained epipolar lines, regarding expected appearance, based on a-priori knowledge of camera systems during the capturing process. The quantitative evaluation of the proposed method is based on residuals. Experimental results shown the proposed method is able to correctly reconstruct the epipolar geometry.


Camera calibration Corresponding points Evolutionary algorithms Inverse problems Fundamental matrix 


  1. 1.
    Abellard, A., Bouchouicha, M., Ben Khelifa, M. M.: A genetic algorithm application to stereo calibration. In: Proceedings 2005 IEEE International Symposium on Computational Intelligence in Robotics and Automation, CIRA 2005, pp 285–290 (2005)Google Scholar
  2. 2.
    Chai, J., De Ma, S.: Robust epipolar geometry estimation using genetic algorithm. Pattern Recogn. Lett. 19(9), 829–838 (1998)CrossRefGoogle Scholar
  3. 3.
    Robotics Research Group Visual Geometry Group. Multi-view and oxford colleges building reconstruction (2011)
  4. 4.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision. Cambridge books online,Cambridge University Press(2003)Google Scholar
  5. 5.
    M.F.A. Hassan, I. Ma’arof, and A.M. Samad. Assessment of camera calibration towards accuracy requirement. In: 2014 IEEE 10th International Colloquium on Signal Processing its Applications (CSPA), pp 123–128, March 2014Google Scholar
  6. 6.
    Hati, S., Sengupta, S.: Robust camera parameter estimation using genetic algorithm. In: Proceedings 1999 IEEE International Conference on Systems, Man, and Cybernetics, SMC1999, vol. 4, pp. 943–947. IEEE (1999)Google Scholar
  7. 7.
    Hu, M., Dodds, G., Yuan, B., Tang, X.: Robust camera calibration with epipolar constraints. In: Proceedings 2004 7th International Conference on Signal Processing, ICSP 2004, vol. 2, pp. 1115–1118, August 2004Google Scholar
  8. 8.
    Ju Jeong, Y., Hwang, H., Nam, D., Jay Kuo, C.C.: Uncalibrated multiview synthesis based on epipolar geometry approximation. In: 2015 IEEE International Conference on Consumer Electronics (ICCE), pp. 542–543, January 2015Google Scholar
  9. 9.
    Kovesi, P.D.: MATLAB and Octave functions for computer vision and image processing. Centre for Exploration Targeting, School of Earth and Environment, The University of Western Australia.
  10. 10.
    Kumar, S.,Thakur, M., Raman, B.,Sukavanam, N.: Stereo camera calibration using real coded genetic algorithm. In: TENCON 2008–2008 IEEE Region 10 Conference, pp. 1–5, November 2008Google Scholar
  11. 11.
    Liu, J., Li, Y., Chen, S.: Robust camera calibration by optimal localization of spatial control points. IEEE Transactions on Instrumentation and Measurement 63(12), 3076–3087 (2014)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Merras, M., El Akkad, N., Saaidi, A., Nazih, A.G., Satori, K.: Camera self calibration with varying parameters by an unknown three dimensional scene using the improved genetic algorithm. 3D. Research 6(1), 39: 1–39: 14 (2015)Google Scholar
  13. 13.
    QiShen, L., Li-Cai, L., ZeTao, J.: A camera self-calibration method based on hybrid optimization algorithm. In: Second International Symposium on Electronic Commerce and Security, ISECS 2009, vol. 2, pp. 60–64, May 2009Google Scholar
  14. 14.
    Shi, J., Tomasi, C.: Good features to track. In: Proceeding of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR1994), pp. 593–600 (1994)Google Scholar
  15. 15.
    Song, L., Wu, W., Guo, J., Li, X.: Survey on camera calibration technique. In: 2013 5th International Conference on Intelligent Human-Machine Systems and Cybernetics (IHMSC), vol. 2, pp. 389–392, August 2013Google Scholar
  16. 16.
    Sonnberger, H.: Robust regression and outlier detection. Journal of Applied Econometrics 4(3), 309–311 (1989)CrossRefGoogle Scholar
  17. 17.
    Y. Zhang and Q. Ji. Camera calibration with genetic algorithms. In Robotics and Automation, 2001. Proceedings 2001 ICRA. IEEE International Conference on, volume 3, pages 2177–2182 vol. 3, 2001Google Scholar
  18. 18.
    Zhang, Z., Kanade, T.: Determining the epipolar geometry and its uncertainty: A review. Int. J. Comput. Vision 27, 161–195 (1998)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Universidad del ValleCaliColombia
  2. 2.Universidad de San BuenaventuraCaliColombia

Personalised recommendations