Imposing Euclidean Constraints During Self-Calibration Processes

  • Didier Bondyfalat
  • Sylvain Bougnoux
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1506)


Using Euclidean constraints to model large 3D environments is made possible. This has been a challenging issue for many years. Using such knowledge not only enlarges the number of feasible cases, but it also provides perfect results, unreachable formerly. We deal with a limited set of constraints composed of incidence relations, parallelism, and orthogonality. This knowledge is given manually, processed through a geometric reasoning system, and used during what we call a constraint bundle adjustment. Results are very encouraging, even though the computational time may be prohibitive.


Geometric Reasoning Self-Calibration Euclidean Constraints 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Sylvain Bougnoux. From projective to euclidean space under any practical situation, a criticism of self-calibration. In International Conference on Computer Vision, pages 790–796, 1998.Google Scholar
  2. [2]
    Sylvain Bougnoux and Luc Robert. Totalcalib: a fast and reliable system for off-line calibration of images sequences. In Proceedings of the International Conference on, June 1997. The Demo Session.Google Scholar
  3. [3]
    Shang-Ching Chou and Xio-Shan Gao. Ritt-wu’s decomposition algorithm and geometry theorem proving. In Proc. CADE-10, pages 202–220, Kaiserslautern, Germany, 1990.Google Scholar
  4. [4]
    Shang-Ching Chou, William F. Schelter, and Jin-Gen Tang. Characteristic Sets and Gröbner Bases in Geometry Theorem Proving. Springer, 1989.Google Scholar
  5. [5]
    D. Cox, J. Little, and D. O’Shea. Ideals, Varieties and Algorithms. Undergraduate texts in mathematics. Springer, 1992.Google Scholar
  6. [6]
    P.E. Debevec, C.J. Taylor, and J. Malik. Modeling and rendering architecture from photographs: a hybrid geometry-and image-based approach. In SIGGRAPH, pages 11–20, 1996.Google Scholar
  7. [7]
    O. Faugeras. Three-Dimensional Computer Vision: a Geometric Viewpoint. MIT Press, 1993.Google Scholar
  8. [8]
    Armin Gruen and Horst A. Beyer. System calibration through self-calibration. In Proceedings of the Workshop on Calibration and Orientation of Cameras in Computer Vision, Washington D.C., August 1992.Google Scholar
  9. [9]
    M. Hebert and E. Krotkov. 3D measurements from imaging laser radars. Image and Vision Computing, 10(3), April 1992.Google Scholar
  10. [10]
    F. Leymarie, A. de la Fortelle, J. Koenderink, A. Kappers, M. Stavridi, B. van Ginneken, S. Muller, S. Krake, O. Faugeras, L. Robert, C. Gauclin, S. Laveau, and C. Zeller. Realise: Reconstruction of reality from image sequences. In P. Delogne, editor, International Conference on Image Processing, volume 3, pages 651–654, 1996.Google Scholar
  11. [11]
    Bernard Mourrain. Géométrie et inte’etation générique: un algorithme. comptesrendus du congrés M.E.G.A-90, pages 363–377, 1990.Google Scholar
  12. [12]
    M. Pollefeys, R. Koch, and L. Van Gool. Self-calibration and metric reconstruction in spite of varying and unknown internal camera parameters. In International Conference on Computer Vision, pages 90–95, 1998.Google Scholar
  13. [13]
    Dongming. Wang and Xiaofan. Jin. Mechanical Theorem Proving in Geometries. Texts and Monographie in Symbolic Computation. Springer, 1994.Google Scholar
  14. [14]
    Wen-tsün Wu. Basic principles of mechanical theorem proving in elementary geometries. Journal of automated Reasoning, 2:221–252, 1986.MATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Didier Bondyfalat
    • 1
  • Sylvain Bougnoux
    • 1
  1. 1.INRIASophia-Antipolis CedexFrance

Personalised recommendations