Camera calibration using multiple images

  • Paul Beardsley
  • David Murray
  • Andrew Zisserman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 588)


This paper describes a method for camera calibration. The system consists of a static camera which takes a sequence of images of a calibration plane rotating around a fixed axis. There is no requirement for any exact positioning of the camera or calibration plane.

From each image of the sequence, the vanishing points and hence the vanishing line of the calibration plane are determined. As the calibration plane rotates, each vanishing point moves along a locus which is a conic section, and the vanishing line generates an envelope which is also a conic section. We describe how such conics can be used to determine the camera's focal length, the principal point (the intersection of the optic axis with the image plane), and the aspect ratio.


  1. [Be91]
    P.A. Beardsley et al. The correction of radial distortion in images. Technical report 1896/91. Department of Engineering Science, University of Oxford.Google Scholar
  2. [Bo79]
    F.L. Bookstein Fitting conic sections to scattered data. Computer Graphics and Image Processing, pages 56–91, 1979.Google Scholar
  3. [CT90]
    B. Caprile and V. Torre Using vanishing points for camera calibration. International Journal of Computer Vision, pages 127–140, 1990.Google Scholar
  4. [FT87]
    O.D. Faugeras and G. Toscani The calibration problem for stereo. In Proc. of IEEE Conf Computer Vision and Pattern Recognition, Miami, 1987.Google Scholar
  5. [Ga84]
    S. Ganapathy. Decomposition of transformation matrices for robot vision. In Proc. of IEEE Conference on Robotics, pages 130–139, 1984.Google Scholar
  6. [Ka92]
    K. Kanatani. Geometric Computation for Machine Vision. Oxford University Press, Due for publication 1992/3.Google Scholar
  7. [LT88]
    R.K. Lenz and R.Y. Tsai. Techniques for calibration of the scale factor and image center for high accuracy 3-D machine vision metrology. In IEEE Transactions Pattern Analysis and Machine Intelligence, pages 713–720, 1988.Google Scholar
  8. [Ph80]
    Manual of Photogrammetry. American Society of Photogrammetry, 1980.Google Scholar
  9. [Pu90]
    P. Puget and T. Skordas An optimal solution for mobile camera calibration. In Proc. First European Conf Computer Vision, pages 187–188, 1990.Google Scholar
  10. [SK52]
    J.G. Semple and G.T. Kneebone. Algebraic Projective Geometry. Oxford University Press, 1952.Google Scholar
  11. [Ts86]
    R.Y. Tsai. An efficient and accurate camera calibration technique for 3D machine vision. In Proc. of IEEE Conf Computer Vision, pages 364–374, 1986.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Paul Beardsley
    • 1
  • David Murray
    • 1
  • Andrew Zisserman
    • 1
  1. 1.Robotics Group, Dept. of Engineering ScienceUniversity of OxfordOxfordUK

Personalised recommendations