Projective Reconstruction from N Views Having One View in Common

  • M. Urban
  • T. Pajdla
  • V. Hlaváč
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1883)


Projective reconstruction recovers projective coordinates of 3D scene points from their several projections in 2D images. We introduce a method for the projective reconstruction based on concatenation of trifocal constraints around a reference view. This configuration simplifies computations significantly. The method uses only linear estimates which stay “close” to image data. The method requires correspondences only across triplets of views. However, it is not symmetrical with respect to views. The reference view plays a special role. The method can be viewed as a generalization of Hartley”s algorithm [11], or as a particular application of Triggs’ [21] closure relations.


Texture Mapping Projection Matrice Bundle Adjustment Fundamental Matrice Projective Reconstruction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Avidan and A. Shashua. Threading fundamental matrices. In ECCV-98, Frieburg, Germany, June 1998. Springer-Verlag.Google Scholar
  2. 2.
    P. Beardsley, P. Torr, and A. Zisserman. 3D model acquisition from extended image sequences. In Bernard Buxton and Roberto Cippola, editors, ECCV-96. Springer-Verlag, 1996.Google Scholar
  3. 3.
    D. Bondyfalat, B. Mourrain, and V.Y. Pan. Controlled iterative methods for solving polynomials systems. ISSAC’98. ACM Press, 1998.Google Scholar
  4. 4.
    J. Buriánek. Korespondence pro virtualní kameru. Master’s thesis, Czech Technical University, FEL ČVUT, Karlovo náměstí 13, Praha, Czech Republic, 1998. In Czech.Google Scholar
  5. 5.
    O. Faugeras. Three-Dimensional Computer Vision: A Geometric Viewpoint. The MIT Press, 1993.Google Scholar
  6. 6.
    O. Faugeras and T. Papadopoulo. Grassmann-Cayley algebra for modeling systems of cameras and the algebraic equations of the manifold of trifocal tensors. Technical Report 3225, INRIA, Jully 1997.Google Scholar
  7. 7.
    O. Faugeras and B. Mourrain. The geometry and algebra of the point and line correspondences between n images. Technical Report RR-2665, INRIA-Sophia Antipolis, Octobre 1995.Google Scholar
  8. 8.
    Fitzgibbon, A.W. and Cross, G. and Zisserman, A. Automatic 3D Model Construction for Turn-Table Sequences. SMILE98, Freiburg, Germany, Springer-Verlag LNCS 1506, June 1998.Google Scholar
  9. 9.
    R. I. Hartley. Computation of the quadrifocal tensor. In ECCV-98, volume I, pages 20–35. Springer Verlag, 1998.CrossRefGoogle Scholar
  10. 10.
    R. I. Hartley. Projective reconstruction from line correspondences. Technical report, GE-Corporate Research and Development, P.O. Box 8, Schenectady, NY, 12301., 1995.Google Scholar
  11. 11.
    R.I. Hartley. Lines and points in three views and the trifocal tensor. International Journal of Computer Vision, 22(2):125–140, March 1997.Google Scholar
  12. 12.
    A. Heyden. A common framework for multiple view tensors. In ECCV-98, volume I, pages 3–19. Springer Verlag, 1998.CrossRefGoogle Scholar
  13. 13.
    A. Heyden. Reduced multilinear constraints-theory and experiments. International Journal of Computer Vision, 30:5–26, 1998.CrossRefGoogle Scholar
  14. 14.
    R.H. Lewis and P.F. Stiller. Solving the recognition problem for six lines using the Dixon resultant. Preprint submitted to Elsevier Preprint, 1999.Google Scholar
  15. 15.
    M. Pollefeys, R. Koch, and L. VanGool. Self-calibration and metric reconstruction in spite of varying and unknown internal camera parameters. In ICCV98, page Session 1.4, 1998.Google Scholar
  16. 16.
    L. Quan. Invariants of 6 points and projective reconstruction from 3 uncalibrated images. PAMI, 17(1):34–46, January 1995.Google Scholar
  17. 17.
    A. Shashua. Trilinear tensor: The fundamental construct of multiple-view geometry and its applications. In International Workshop on Algebraic Frames For The Perception Action Cycle (AFPAC97), Kiel Germany, September 1997.Google Scholar
  18. 18.
    A. Shashua and S. Avidan. The rank 4 constraint in multiple (⩾3) view geometry. In Bernard Buxton and Roberto Cipolla, editors, ECCV-96, pages 196–206. Springer Verlag, April 1996.Google Scholar
  19. 19.
    A. Shashua and M. Werman. Fundamental tensor: On the geometry of three perspective views. Technical report, Hebrew University of Jerusalem, Institut of Computer Science, 91904 Jerusalem, Israel, 1995.Google Scholar
  20. 20.
    P. Sturm and B. Triggs. A factorization based algorithm for multi-image projective structure and motion. In ECCV-96. Springer-Verlag, 1996.Google Scholar
  21. 21.
    B. Triggs. Linear projective reconstruction from matching tensors. Technical report, Edinburgh, 1996. British Machine Vision Conference.Google Scholar
  22. 22.
    B. Triggs. The geometry of projective reconstruction I: Matching constraints and the joint image. Technical report, 1995. unpublished report.Google Scholar
  23. 23.
    M. Urban, T. Pajdla, and V. Hlaváč. Projective reconstruction from multiple views. Technical Report CTU-CMP-1999-5, CMP, FEL CVUT, Karlovo náměstý 13, Praha, Czech Republic, December 1999.Google Scholar
  24. 24.
    T. Werner, T. Pajdla, and M. Urban. Rec3d: Toolbox for 3d reconstruction from uncalibrated 2d views. Technical Report CTU-CMP-1999-4, Czech Technical University, FEL CVUT, Karlovo náměstí 13, Praha, Czech Republic, December 1999.Google Scholar
  25. 25.
    Zhengyou Zhang. Determining the epipolar geometry and its uncertainty: A review. IJCV, 1997.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • M. Urban
    • 1
  • T. Pajdla
    • 1
  • V. Hlaváč
    • 1
  1. 1.Center for Machine PerceptionCzech Technical University, PraguePragueCzech Republic

Personalised recommendations