Skip to main content

Towards a Guaranteed Solution to Plane-Based Self-calibration

  • Conference paper
Computer Vision – ACCV 2006 (ACCV 2006)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3851))

Included in the following conference series:

Abstract

We investigate the problem of self-calibrating a camera, from multiple views of a planar scene. By self-calibrating, we refer to the problem of simultaneously estimate the camera intrinsic parameters and the Euclidean structure of one 3D plane. A solution is usually obtained by solving a non-linear system via local optimization, with the critical issue of parameter initialization, especially the focal length. Arguing that these five parameters are inter-dependent, we propose an alternate problem formulation, with only three d.o.f., corresponding to three parameters to estimate. In the light of this, we are concerned with global optimization in order to get a guaranteed solution, with the shortest response time. Interval analysis provides an efficient numerical framework, that reveals to be highly performant, with regard to both estimation accuracy and time-consuming.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Hartley, R., Zisserman, A.: Multiple View Geometry, 2nd edn. Cambridge University Press, Cambridge (2003)

    Google Scholar 

  2. Semple, J., Kneebone, G.: Algebraic Projective Geometry. Oxford Classic Series. Clarendon Press (1952) (reprinted, 1998)

    Google Scholar 

  3. Bougnoux, S.: From Projective to Euclidean Space under any Practical Situation, a Criticism of Self-Calibration. In: Proc. of the ICCV, Bombay, India, vol. 1, pp. 790–796 (1998)

    Google Scholar 

  4. Triggs, B.: Autocalibration from Planar Scenes. In: Proc. of the ECCV, Freiburg, Germany, vol. 2, pp. 89–105 (1998)

    Google Scholar 

  5. Malis, E., Cipolla, R.: Multi-view Constraints between Collineations: Application to Self-Calibration from Unknown Planar Structures. In: Proc. of the ECCV, Dublin, Ireland, vol. 2, pp. 610–624 (2000)

    Google Scholar 

  6. Gurdjos, P., Sturm, P.: Methods and Geometry for Plane-Based Self-Calibration. In: Proc. of the CVPR, Madison, Wisconsin, USA, vol. 1, pp. 491–496 (2003)

    Google Scholar 

  7. Jiang, G., Tsui, H., Quan, L.: Circular Motion Geometry Using Minimal Data. IEEE Trans. on PAMI 26, 721–731 (2004)

    Google Scholar 

  8. Knight, J., Zisserman, A., Reid, I.: Linear Auto-Calibration for Ground Plane Motion. In: Proc. of the CVPR, Madison, Wisconsin, USA, pp. 503–510 (2003)

    Google Scholar 

  9. Neumaier, A.: Introduction to Numerical Analysis. Cambridge University Press, Cambridge (2001)

    Book  MATH  Google Scholar 

  10. Hansen, E.R., Walster, G.W.: Global Optimization Using Interval Analysis, 2nd edn. Marcel Dekker, New York (2003)

    Google Scholar 

  11. Fusiello, A., Benedetti, A., Farenzena, M., Busti, A.: Globally Convergent Autocalibration Using Interval Analysis. IEEE Trans. on PAMI 26, 1633–1638 (2004)

    Google Scholar 

  12. Golub, G., Loan, C.V.: Matrix computations, 3rd edn. John Hopkins University Press, Baltimore (1996)

    MATH  Google Scholar 

  13. Moore, R.E.: Interval Analysis. Prentice-Hall, Englewood Cliffs (1966)

    MATH  Google Scholar 

  14. Kearfott, R.B.: Rigorous Global Search: Continous Problems. Kluwer Academic Publishers, Dordrecht (1996)

    Google Scholar 

  15. Kanatani, K., Ohta, N.: Accuracy Bounds and Optimal Computation of Homography for Image Mosaicing Applications. In: Proc. of the ICCV, Kerkyra, Greece, vol. 1, pp. 73–78 (1999)

    Google Scholar 

  16. Sturm, P., Maybank, S.J.: On plane-based camera calibration: A general algorithm, singularities, applications. In: Proc. of the CVPR, Fort Collins, Colorado, USA, vol. 1, pp. 432–437 (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bocquillon, B., Gurdjos, P., Crouzil, A. (2006). Towards a Guaranteed Solution to Plane-Based Self-calibration. In: Narayanan, P.J., Nayar, S.K., Shum, HY. (eds) Computer Vision – ACCV 2006. ACCV 2006. Lecture Notes in Computer Science, vol 3851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11612032_2

Download citation

  • DOI: https://doi.org/10.1007/11612032_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-31219-2

  • Online ISBN: 978-3-540-32433-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics