Advertisement

Another Way of Looking at Plane-Based Calibration: The Centre Circle Constraint

  • Pierre Gurdjos
  • Alain Crouzil
  • René Payrissat
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2353)

Abstract

The plane-based calibration consists in recovering the internal parameters of the camera from the views of a planar pattern with a known geometric structure. The existing direct algorithms use a problem formulation based on the properties of basis vectors. They minimize algebraic distances and may require a ‘good’ choice of system normalization. Our contribution is to put this problem into a more intuitive geometric framework. A solution can be obtained by intersecting circles, called Centre Circles, whose parameters are computed from the world-to-image homographies. The Centre Circle is the camera centre locus when planar figures are in perpective correspondence, in accordance with a Poncelet’s theorem. An interesting aspect of our formulation, using the Centre Circle constraint, is that we can easily transform the cost function into a sum of squared Euclidean distances. The simulations on synthetic data and an application with real images confirm the strong points of our method.

Keywords

Calibration Homography Planar Scene Multiple View Geometry Poncelet 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    O. Faugeras. Three-Dimensional Computer Vision: a Geometric Viewpoint. The MIT Press, Cambridge, Massachusetts, USA. 1993.Google Scholar
  2. 2.
    P. Gurdjos and R. Payrissat. Plane-based Calibration of a Camera with Varying Focal Length: the Centre Line Constraint. In Proc. of the 12th British Machine Vision Conference (BMVC’01), Manchester, UK, pp. 623–632. September 2001.Google Scholar
  3. 3.
  4. 4.
    R. Hartley and A. Zisserman. Multiple View Geometry in Computer Vision. Cambridge University Press, Cambridge, UK. 2000.zbMATHGoogle Scholar
  5. 5.
    S. Van Huffel and J. Vandewalle. The total least squares problem: computational aspects and analysis. Frontiers in Applied Mathematics series, vol. 9, SIAM, Philadelphia, Pennsylvania, USA. 1991.Google Scholar
  6. 6.
    Y. Leedan and P. Meer. Heteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint. International Journal of Computer Vision (IJCV), vol. 37, no. 2, p. 127–150. 2000.zbMATHCrossRefGoogle Scholar
  7. 7.
    D. Liebowitz and A. Zisserman. Combining Scene and Auto-Calibration Constraints. In Proc. of the 7th International Conference on Computer Vision (ICCV’99), Kerkyra, Greece. September 1999.Google Scholar
  8. 8.
    E. Malis and R. Cipolla. Self-Calibration of Zooming Cameras Observing an Unknown Planar Structure. In Proc. of the 15th International Conference on Pattern Recognition (ICPR’00), vol. 1, pp. 85–88, Barcelona, Spain. September 2000.Google Scholar
  9. 9.
    C. Matsunaga and K. Kanatani. Calibration of a Moving Camera Using a Planar Pattern: Optimal Computation, Reliability Evaluation, and Stabilization by Model Selection. In Proc. of the 6th European Conference on Computer Vision (ECCV’00), Dublin, Ireland. July 2000.Google Scholar
  10. 10.
    J.-V. Poncelet. Applications d’Analyse et de Géometrie-Traité des Propriétés Projectives des Figures. Tome I. Imprimerie de Mallet-Bachelier, Paris. 1862.Google Scholar
  11. 11.
    P. Sturm and S. Maybank. On Plane-Based Camera Calibration: a General Algorithm, Singularities, Applications. In Proc. of the Computer Vision and Pattern Recognition Conference (CVPR’99), Fort Collins, Colorado, USA, pp. 432–437. June 1999.Google Scholar
  12. 12.
    P. Sturm. Algorithms for Plane-Based Pose Estimation. In Proc. of the Computer Vision and Pattern Recognition Conference (CVPR’00), Hilton Head, USA, pp. 1010–1017. June 2000.Google Scholar
  13. 13.
    B. Triggs. Autocalibration from Planar Scenes. In Proc. of the 5th European Conference on Computer Vision (ECCV’98), pp. 89–105, Freiburg, Germany. June 1998.Google Scholar
  14. 14.
    Z. Zhang. A Flexible New Technique for Camera Calibration. IEEE Transactions on Pattern Analysis and Machine Intelligence (PAMI), vol. 22, no. 11, pp. 1330–1344. 2000.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Pierre Gurdjos
    • 1
  • Alain Crouzil
    • 1
  • René Payrissat
    • 1
  1. 1.IRIT-TCIUniversité Paul SabatierToulouse Cedex 4France

Personalised recommendations