Computation of the quadrifocal tensor

  • Richard I. Hartley
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1406)


This paper gives a practical and accurate algorithm for the computation of the quadrifocal tensor and extraction of camera matrices from it. Previous methods for using the quadrifocal tensor in projective scene reconstruction have not emphasized accuracy of the algorithm in conditions of noise. Methods given in this paper minimize algebraic error either through a non-iterative linear algorithm, or two alternative iterative algorithms. It is shown by experiments with synthetic data that the iterative methods, though minimizing algebraic, rather than more correctly geometric error measured in the image, give almost optimal results.


Calibration and Pose Estimation Stereo and Motion Image Sequence Analysis Algebraic error Quadrifocal tensor 


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  1. 1.
    Richard I. Hartley. Euclidean reconstruction from uncalibrated views. In Applications of Invariance in Computer Vision: Proc. of the Second Joint European — US Workshop, Ponta Delgada, Azores — LNCS-Series Vol. 825, Springer Verlag, pages 237–256, October 1993.Google Scholar
  2. 2.
    Richard I. Hartley. Lines and points in three views and the trifocal tensor. International Journal of Computer Vision, 22(2):125–140, March 1997.CrossRefGoogle Scholar
  3. 3.
    Richard I. Hartley. Minimizing algebraic error in geometric estimation problems. In Proc. International Conference on Computer Vision, 1998.Google Scholar
  4. 4.
    Richard I. Hartley. Multilinear relationships between coordinates of corresponding image points and lines to appear.Google Scholar
  5. 5.
    Anders Heyden. Geometry and Algebra of Multiple Projective Transformations. PhD thesis, Department of Mathematics, Lund University, Sweden, December 1995.Google Scholar
  6. 6.
    Anders Heyden. Reconstruction from multiple images using kinetic depths. International Journal of Computer Vision, to appear.Google Scholar
  7. 7.
    K. Kanatani. Statistical Optimization for Geometric Computation: Theory and Practice. North Holland, Amsterdam, 1996.Google Scholar
  8. 8.
    Bill Triggs. The geometry of projective reconstruction I: Matching constraints and the joint image. unpublished report, 1995.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Richard I. Hartley
    • 1
  1. 1.G.E. Corporate Research and DevelopmentNiskayunaUSA

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