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A New Set of Quartic Trivariate Polynomial Equations for Stratified Camera Self-calibration under Zero-Skew and Constant Parameters Assumptions

  • Adlane Habed
  • Kassem Al Ismaeil
  • David Fofi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7577)

Abstract

This paper deals with the problem of self-calibrating a moving camera with constant parameters. We propose a new set of quartic trivariate polynomial equations in the unknown coordinates of the plane at infinity derived under the no-skew assumption. Our new equations allow to further enforce the constancy of the principal point across all images while retrieving the plane at infinity. Six such polynomials, four of which are independent, are obtained for each triplet of images. The proposed equations can be solved along with the so-called modulus constraints and allow to improve the performance of existing methods.

Keywords

Camera Self-calibration Multiple View Geometry 

References

  1. 1.
    Sturm, P.: Critical Motion Sequences for Monocular Self-calibration and Uncalibrated Euclidean Reconstruction. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1100–1105 (1997)Google Scholar
  2. 2.
    Luong, Q.: Self-calibration of a Moving Camera from Point Correspondences and Fundamental Matrices. International Journal of Computer Vision 22, 261–289 (1997)CrossRefGoogle Scholar
  3. 3.
    Nistér, D.: Untwisting a Projective Reconstruction. International Journal of Computer Vision 60, 165–183 (2004)CrossRefGoogle Scholar
  4. 4.
    Triggs, B.: Autocalibration and the Absolute Quadric. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 609–614 (1997)Google Scholar
  5. 5.
    Heyden, A., Åström, K.: Euclidean Reconstruction from Constant Intrinsic Parameters. In: International Conference on Pattern Recognition, vol. 1, pp. 339–343. IEEE (1996)Google Scholar
  6. 6.
    Valdés, A., Ronda, J.I., Gallego, G.: The Absolute Line Quadric and Camera Autocalibration. International Journal of Computer Vision 66, 283–303 (2006)CrossRefGoogle Scholar
  7. 7.
    Ponce, J., Mc Henry, K., Papadopoulo, T., Teillaud, M., Triggs, B.: On the Absolute Quadratic Complex and its Application to Autocalibration. In: IEEE Conference on Computer Vision and Pattern Recognition, vol. 1, pp. 780–787 (2005)Google Scholar
  8. 8.
    Hartley, R., Hayman, E., Agapito, L., Reid, I.: Camera Calibration and the Search for Infinity. In: IEEE International Conference on Computer Vision, pp. 510–517 (1999)Google Scholar
  9. 9.
    Hartley, R.I., Zisserman, A.: Multiple View Geometry in Computer Vision, 2nd edn. Cambridge University Press (2004)Google Scholar
  10. 10.
    Gherardi, R., Fusiello, A.: Practical Autocalibration. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part I. LNCS, vol. 6311, pp. 790–801. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  11. 11.
    Pollefeys, M., van Gool, L.: Stratified Self-calibration with the Modulus Constraint. IEEE Transactions on Pattern Analysis and Machine Intelligence 21, 707–724 (1999)CrossRefGoogle Scholar
  12. 12.
    Chandraker, M., Agarwal, S., Kriegman, D., Belongie, S.: Globally Optimal Algorithms for Stratified Autocalibration. International Journal of Computer Vision 90, 236–254 (2010)CrossRefGoogle Scholar
  13. 13.
    Pollefeys, M., Koch, R., van Gool, L.: Self-calibration and Metric Reconstruction in spite of Varying and Unknown Internal Camera Parameters. International Journal of Computer Vision 32, 7–25 (1999)CrossRefGoogle Scholar
  14. 14.
    Gurdjos, P., Bartoli, A., Sturm, P.F.: Is Dual Linear Self-calibration Artificially Ambiguous? In: IEEE International Conference on Computer Vision, pp. 88–95 (2009)Google Scholar
  15. 15.
    Chandraker, M., Agarwal, S., Kahl, F., Kriegman, D., Nister, D.: Autocalibration via Rank-Constrained Estimation of the Absolute Quadric. In: IEEE Conference on Computer Vision and Pattern Recognition, pp. 1–8 (2007)Google Scholar
  16. 16.
    Schaffalitzky, F.: Direct Solution of Modulus Constraints. In: Indian Conference on Computer Vision, Graphics and Image Processing, pp. 314–321 (2000)Google Scholar
  17. 17.
    Heyden, A., Astrom, K.: Flexible Calibration: Minimal Cases for Auto-calibration. In: IEEE International Conference on Computer Vision, vol. 1, pp. 350–355 (1999)Google Scholar
  18. 18.
    Rothwell, C.A., Faugeras, O.D., Csurka, G.: Different Paths towards Projective Reconstruction. In: Europe-China Workshop on Geometrical Modelling and Invariants for Computer Vision. Xidan University Press (1995)Google Scholar
  19. 19.
    Verschelde, J.: Polynomial Homotopy Continuation with PhcPack. ACM Communications in Computer Algebra 44, 217–220 (2011)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Adlane Habed
    • 1
  • Kassem Al Ismaeil
    • 2
  • David Fofi
    • 1
  1. 1.Le2i UMR CNRS 6306University of BourgogneAuxerre/Le CreusotFrance
  2. 2.Interdisciplinary Centre for Security, Reliability and TrustUniversity of LuxembourgLuxembourg

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