Journal of Mathematical Imaging and Vision

, Volume 23, Issue 2, pp 167–174 | Cite as

Camera Autocalibration and the Calibration Pencil

  • Antonio Valdés
  • José Ignacio Ronda


We study the geometric object given by the set of lines incident with the absolute conic. We see that this object is given by a pencil of quadrics of P5, which is characterized. We describe some of its most relevant properties for the camera autocalibration problem. Finally, we illustrate the applicability of the theory proposing a linear algorithm for the metric upgrading of a projective calibration of a set of ten or more cameras with varying parameters and known skew and aspect ratio.


camera autocalibration line geometry 


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  1. 1.
    D.A. Forsyth, J. Ponce, Computer Vision: A Modern Approach, Prentice Hall: New York, 2002.Google Scholar
  2. 2.
    J. Harris, Algebraic Geometry. A First Course, Graduate Texts in Mathematics vol. 133, Springer-Verlag: New York, 1992.Google Scholar
  3. 3.
    R.I. Hartley, A. Zisserman, Multiple View Geometry in Computer Vision, Cambridge University Press: Cambridge, UK, 2000.Google Scholar
  4. 4.
    F. Kahl, B. Triggs, K. Aastroom, “Critical motions for auto-calibration when some intrinsic parameters can vary,” Journal of Mathematical Imaging and Vision, Vol. 13, pp. 131–146, 2000.CrossRefGoogle Scholar
  5. 5.
    S.J. Maybank, O. Faugeras, “A theory of self-calibration of a moving camera,” The International Journal of Computer Vision, Vol. 8, pp. 123–152, 1992.CrossRefGoogle Scholar
  6. 6.
    J. Ponce, “On computing metric upgrades of projective reconstructions under the rectangular pixel assumption,” in Proc. of the SMILE 2000 Workshop on 3D Structure from Multiple Images of Large-Scale Environments, Springer-Verlag Lecture Notes in Computer Science 2000, Vol. 2018, pp. 52–67.Google Scholar
  7. 7.
    J.G. Semple, G.T. Kneebone, Algebraic Projective Geometry, Oxford University Press, 1998.Google Scholar
  8. 8.
    Y. Seo, A. Heyden, “Auto-calibration from the orthogonality constraints,” in International Conference on Computer Vision, 2000.Google Scholar
  9. 9.
    P. Sturm, “Critical motion sequences for monocular self-calibration and uncalibrated Euclidean reconstruction,” in CVPR—IEEE International Conference on Computer Vision and Pattern Recognition, 1997, pp. 1100–1105.Google Scholar
  10. 10.
    W. Triggs, “Auto-calibration and the absolute quadric,” in Proc. IEEE Conference on Computer Vision and Pattern Recognition, 1997, pp. 609–614.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Antonio Valdés
    • 1
  • José Ignacio Ronda
    • 1
  1. 1.Dep. de Geometría y TopologíaUniversidad Complutense de MadridMadridSpain

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