Two-View Triangulation: A Novel Approach Using Sampson’s Distance

  • Gaurav Verma
  • Shashi Poddar
  • Vipan Kumar
  • Amitava DasEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 1022)


With the increase in the need for video-based navigation, the estimation of 3D coordinates of a point in space, using images, is one of the most challenging tasks in the field of computer vision. In this work, we propose a novel approach to formulate the triangulation problem using Sampson’s distance, and have shown that the approach theoretically converges toward an existing state-of-the-art algorithm. The theoretical formulation required for achieving optimal solution is presented along with its comparison with the existing algorithm. Based on the presented solution, it has been shown that the proposed approach converges closely to Kanatani–Sugaya–Niitsuma algorithm. The purpose of this research is to open a new frontier to view the problem in a novel way and further work on this approach may lead to some new findings to the triangulation problem.


Triangulation Stereovision Monocular vision Fundamental matrix Epipolar geometry 



The authors would like to thank Dr. Peter Lindstrom, Lawrence Livermore National Laboratory, for sharing with us the data set on which he has tested his method in [14].


  1. 1.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision, vol. 2. Cambridge University Press, Cambridge (2000)zbMATHGoogle Scholar
  2. 2.
    Matthies, L., Shafer, S.A.: Error modeling in stereo navigation. IEEE J. Robot. Autom. 3(3), 239–248 (1987)CrossRefGoogle Scholar
  3. 3.
    Scaramuzza, D., Fraundorfer, F.: Visual odometry [tutorial]. IEEE Robot. Autom. Mag. 18(4), 80–92 (2011)CrossRefGoogle Scholar
  4. 4.
    Sünderhauf, N., Protzel, P.: Stereo odometry–a review of approaches. Technical report, Chemnitz University of Technology (2007)Google Scholar
  5. 5.
    Maimone, M., Cheng, Y., Matthies, L.: Two years of visual odometry on the mars exploration rovers. J. Field Robot. 24(3), 169–186 (2007)CrossRefGoogle Scholar
  6. 6.
    Wu, J.J., Sharma, R., Huang, T.S.: Analysis of uncertainty bounds due to quantization for three-dimensional position estimation using multiple cameras. Opt. Eng. 37(1), 280–292 (1998)CrossRefGoogle Scholar
  7. 7.
    Fooladgar, F., Samavi, S., Soroushmehr, S., Shirani, S.: Geometrical analysis of localization error in stereo vision systems (2013)Google Scholar
  8. 8.
    Beardsley, P.A., Zisserman, A., Murray, D.W.: Navigation using affine structure from motion. In: Computer Vision ECCV’94, pp. 85–96. Springer, Berlin (1994)Google Scholar
  9. 9.
    Hartley, R.I., Sturm, P.: Triangulation. Comput. Vis. Image Underst. 68(2), 146–157 (1997)CrossRefGoogle Scholar
  10. 10.
    Vite-Silva, I., Cruz-Cortés, N., Toscano-Pulido, G., de la Fraga, L.G.: Optimal triangulation in 3d computer vision using a multi-objective evolutionary algorithm. In: Applications of Evolutionary Computing, pp. 330–339, Springer, Berlin (2007)Google Scholar
  11. 11.
    Wong, Y.-P., Ng, B.-Y.: 3d reconstruction from multiple views using particle swarm optimization. In: 2010 IEEE Congress on Evolutionary Computation (CEC), pp. 1–8. IEEE (2010)Google Scholar
  12. 12.
    Kanazawa, Y., Kanatani, K.: Reliability of 3-d reconstruction by stereo vision. IEICE Trans. Inf. Syst. 78(10), 1301–1306 (1995)Google Scholar
  13. 13.
    Kanatani, K., Sugaya, Y., Niitsuma, H.: Triangulation from two views revisited: Hartley-sturm vs. optimal correction. In: Practice, vol. 4, p. 5 (2008)Google Scholar
  14. 14.
    Lindstrom, P.: Triangulation made easy. In: 2010 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 1554–1561. IEEE (2010)Google Scholar
  15. 15.
    Kanatani, K., Niitsuma, H.: Optimal two-view planar scene triangulation. In: Computer Vision–ACCV 2010, pp. 242–253. Springer, Berlin (2011)Google Scholar
  16. 16.
    Sampson, P.D.: Fitting conic sections to very scattered data: an iterative refinement of the bookstein algorithm. Comput. Graph. Image Process. 18(1), 97–108 (1982)Google Scholar
  17. 17.
    Zhang, Z.: Determining the epipolar geometry and its uncertainty: a review. Int. J. Comput. Vis. 27(2), 161–195 (1998)CrossRefGoogle Scholar
  18. 18.
    Petersen, K.B., Pedersen, M.S.: The matrix cookbook. Technical University of Denmark, pp. 7–15 (2008)Google Scholar
  19. 19.
    Longuet-Higgins, H.: A computer algorithm for reconstructing a scene from two projections. In: Fischler M.A., Firschein, O. (eds.) Readings in Computer Vision: Issues, Problems, Principles, and Paradigms, pp. 61–62 (1987)Google Scholar
  20. 20.
    Nistér, D.: An efficient solution to the five-point relative pose problem. IEEE Trans. Pattern Anal. Mach. Intell. 26(6), 756–770 (2004)CrossRefGoogle Scholar
  21. 21.
    Stewénius, H., Engels, C., Nistér, D.: Recent developments on direct relative orientation. ISPRS J. Photogramm. Remote. Sens. 60(4), 284–294 (2006)CrossRefGoogle Scholar
  22. 22.
    Szeliski, R.: Computer Vision: Algorithms and Applications. Springer, Berlin (2010)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Gaurav Verma
    • 1
    • 2
  • Shashi Poddar
    • 1
    • 2
  • Vipan Kumar
    • 1
    • 2
  • Amitava Das
    • 1
    • 2
    Email author
  1. 1.CSIR-Central Scientific Instruments Organisation (CSIO)ChandigarhIndia
  2. 2.Academy of Scientific Innovation and Research (AcSIR)ChandigarhIndia

Personalised recommendations