Initializing 3-D Reconstruction from Three Views Using Three Fundamental Matrices

  • Yasushi Kanazawa
  • Yasuyuki Sugaya
  • Kenichi Kanatani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8334)


This paper focuses on initializing 3-D reconstruction from scratch without any prior scene information. Traditionally, this has been done from two-view matching, which is prone to the degeneracy called “imaginary focal lengths”. We overcome this difficulty by using three images, but we do not require three-view matching; all we need is three fundamental matrices separately computed from image pairs. We exploit the redundancy of the three fundamental matrices to optimize the camera parameters and the 3-D structure. We do numerical simulation to show that imaginary focal lengths are less likely to occur, resulting in higher accuracy than two-view reconstruction. We also test the degeneracy tolerance capability of our method by using endoscopic intestine tract images, for which the camera configuration is almost always nearly degenerate. We demonstrate that our method allows us to obtain more detailed intestine structures than two-view reconstruction and hence leads to new medical applications to endoscopic image analysis.


Initialization of 3-D reconstruction imaginary focal length degeneracy three views three fundamental matrices 


  1. 1.
    Bougnoux, S.: From projective to Euclidean space under any practical situation, a criticism of self-calibration. In: Proc. 6th Int. Conf. Comput. Vis., pp. 790–796 (January 1998)Google Scholar
  2. 2.
    Goldberger, J.: Reconstructing camera projection matrices from multiple pairwise overlapping views. Comput. Vis. Image Understanding 97, 283–296 (2005)CrossRefGoogle Scholar
  3. 3.
    Hartley, R.: Estimation of relative camera positions for uncalibrated cameras. In: Proc. 2nd European Conf. Comput. Vis., Santa Margehrita Ligure, Italy, pp. 579–587 (May 1992)Google Scholar
  4. 4.
    Hartley, R., Silpa-Anan, C.: Reconstruction from two views using approximate calibration. In: Proc. 5th Asian Conf. Comput. Vis., Melbourne, Australia, pp. 338–343 (January 2002)Google Scholar
  5. 5.
    Hartley, R., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press, Cambridge (2004)CrossRefzbMATHGoogle Scholar
  6. 6.
    Hirai, K., Kanazawa, Y., Sagawa, R., Yagi, Y.: Endoscopic image matching for reconstructing the 3-D structure of the intestines. Med. Imag. Tech. 29(1), 36–46 (2011)Google Scholar
  7. 7.
    Kanatani, K.: Geometric Computation for Machine Vision. Oxford University Press, Oxford (1993)zbMATHGoogle Scholar
  8. 8.
    Kanatani, K., Matsunaga, C.: Closed-form expression for focal lengths from the fundamental matrix. In: Proc. 4th Asian Conf. Comput. Vis., Taipei, Taiwan, vol. 1, pp. 128–133 (January 2000)Google Scholar
  9. 9.
    Kanatani, K., Nakatsuji, A., Sugaya, Y.: Stabilizing the focal length computation for 3-D reconstruction from two uncalibrated views. Int. J. Comput. Vis. 66(2), 109–122 (2006)Google Scholar
  10. 10.
    Kanatani, K., Sugaya, Y.: Compact fundamental matrix computation. IPSJ Trans. Comput. Vis. Appl. 2, 59–70 (2010)Google Scholar
  11. 11.
    Kanatani, K., Sugaya, Y., Kanazawa, Y.: Latest algorithms for 3-D reconstruction from two views. In: Chen, C.H. (ed.) Handbook of Pattern Recognition and Computer Vision, 4th edn., pp. 201–234. World Scientific Publishing (2009)Google Scholar
  12. 12.
    Kanatani, K., Sugaya, Y., Niitsuma, H.: Triangulation from two views revisited: Hartley-Sturm vs. optimal correction. In: Proc. 19th British Machine Vis. Conf., Leeds, U.K., pp. 173–182 (September 2008)Google Scholar
  13. 13.
    Lourakis, M.I.A., Argyros, A.A.: SBA: A software package for generic sparse bundle adjustment. ACM Trans. Math. Software 36(1), 2:1–2:30 (2009)Google Scholar
  14. 14.
    Pollefeys, M., Koch, R., Cool, L.V.: Self-calibration and metric reconstruction in spite of varying and unknown intrinsic camera parameters. Int. J. Comput. Vis. 32, 7–25 (1999)Google Scholar
  15. 15.
    Snavely, N., Seitz, S., Szeliski, R.: Photo tourism: Exploring photo collections in 3d. ACM Trans. Graphics 25(8), 835–846 (1995)Google Scholar
  16. 16.
    Snavely, N., Seitz, S., Szeliski, R.: Modeling the world from Internet photo collections. Int. J. Comput. Vis. 80(2), 189–210 (2008)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Yasushi Kanazawa
    • 1
  • Yasuyuki Sugaya
    • 1
  • Kenichi Kanatani
    • 2
  1. 1.Department of Computer Science and EngineeringToyohashi University of TechnologyAichiJapan
  2. 2.Okayama UniversityOkayamaJapan

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