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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 10 — Oct. 1, 1999
  • pp: 2419–2424

Algebraic derivation of the Kruppa equations and a new algorithm for self-calibration of cameras

Gang Xu and Noriko Sugimoto  »View Author Affiliations


JOSA A, Vol. 16, Issue 10, pp. 2419-2424 (1999)
http://dx.doi.org/10.1364/JOSAA.16.002419


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Abstract

An algebraic derivation of the Kruppa equations is presented. This derivation is much simpler and thus easier to understand than the conventional derivation based on projective geometry. Using the newly derived Kruppa equations, we further propose a new algorithm for determining a camera’s intrinsic parameters. Experimental results and discussions are given for both synthetic and real images.

© 1999 Optical Society of America

OCIS Codes
(080.2730) Geometric optics : Matrix methods in paraxial optics
(080.3630) Geometric optics : Lenses
(100.3190) Image processing : Inverse problems
(150.6910) Machine vision : Three-dimensional sensing

History
Original Manuscript: April 5, 1999
Revised Manuscript: June 21, 1999
Manuscript Accepted: June 21, 1999
Published: October 1, 1999

Citation
Gang Xu and Noriko Sugimoto, "Algebraic derivation of the Kruppa equations and a new algorithm for self-calibration of cameras," J. Opt. Soc. Am. A 16, 2419-2424 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-10-2419


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References

  1. R. Y. Tsai, “Synopsis of recent progress on camera calibration for 3D machine vision,” in The Robotics Review, O. Khatib, J. J. Craig, T. Lozano-Pirez, eds. (MIT Press, Cambridge, Mass., 1989), pp. 147–159.
  2. O. D. Faugeras, Three-Dimensional Computer Vision: A Geometric Viewpoint (MIT Press, Cambridge, Mass., 1993).
  3. Z. Zhang, “A flexible new technique for camera calibration,” (Microsoft Research, Redmond, Wash.1998).
  4. S. J. Maybank, O. D. Faugeras, “A theory of self-calibration of a moving camera,” Int. J. Comput. Vision 8, 123–152 (1992). [CrossRef]
  5. C. Zeller, O. Faugeras, “Camera self-calibration from video sequences: the Kruppa equations revisited,” (Institut National de Recherche en Informatique et d’Automatique, Sophia-Antipolis, France, 1996).
  6. Q.-T. Luong, O. Faugeras, “Self-calibration of a moving camera from point correspondences and fundamental matrices,” Int. J. Comput. Vision 22, 261–289 (1997). [CrossRef]
  7. R. Hartley, “Kruppa’s equations derived from the fundamental matrix,” IEEE Trans. Pattern. Anal. Mach. Intell. 19, 133–135 (1997). [CrossRef]
  8. S. Bougnoux, “From projective to Euclidean space under any practical situation, a critism of self-calibration,” in Proceedings of the Sixth International Conference on Computer Vision (Narosa, New Delhi, India, 1998), pp. 790–796.
  9. M. Pollefeys, R. Koch, L. van Gool, “Self-calibration and metric reconstruction in spite of varying and unknown internal camera parameters,” in Proceedings of the Sixth International Conference on Computer Vision, (Narosa, New Delhi, India, 1998), pp. 90–95.
  10. B. Trigg, “Autocalibration and the absolute quadric,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, New York, 1997), pp. 609–614.
  11. A. Heyden, X. Astrom, “Euclidean reconstruction from image sequences with varying and unknown focal length and principal point,” in Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (IEEE, New York, 1997), pp. 438–443.
  12. G. Xu, Z. Zhang, Epipolar Geometry in Stereo, Motion and Object Recognition: A Unified Approach (Kluwer Academic, Dordrecht, The Netherlands, 1996).
  13. Z. Zhang, “Determining the epipolar geometry and its uncertainty: a review,” Int. J. Comput. Vision 27, 161–195 (1998). [CrossRef]
  14. H. C. Longuet-Higgins, “A computer algorithm for reconstructing a scene from two projections,” Nature 293, 133–135 (1981). [CrossRef]
  15. Z. Zhang, R. Deriche, O. Faugeras, Q.-T. Luong, “A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry,” Artif. Intel. 78, 87–119 (1995). [CrossRef]
  16. R. Hartley, “In defense of the eight-point algorithm,” IEEE Trans. Pattern. Anal. Mach. Intell. 19, 580–593 (1997). [CrossRef]
  17. W. H. Press, B. P. Flannery, S. A. Teukolsky, W. T. Vetterling, Numerical Recipes in C (Cambridge U. Press, Cambridge, UK, 1988).
  18. R. Hartley, “Estimation of relative camera positions for uncalibrated cameras,” in Proceedings of the Second European Conference on Computer Vision (Springer-Verlag, Berlin, 1992), pp. 579–588.
  19. Z. Zhang, “Motion and structure from two perspective views: from essential parameters to Euclidean motion through the fundamental matrix,” J. Opt. Soc. Am. A 14, 2938–2950 (1997). [CrossRef]
  20. K. Kanatani, Geometric Computation for Machine Vision (Oxford Sci. Publ., Oxford, UK, 1993).
  21. K. Kanatani, “Optimal estimation of fundamental matrices and its reliability,” http://www.ail.cs.gunmau.ac.jp/labo/paper/fundamatrix.ps.gz (Department of Computer Science, Gunma University, Kiryu, Japan, 1998; in Japanese).

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