Balanced Recovery of 3D Structure and Camera Motion from Uncalibrated Image Sequences

  • Bogdan Georgescu
  • Peter Meer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2351)


Metric reconstruction of a scene viewed by an uncalibrated camera undergoing an unknown motion is a fundamental task in computer vision. To obtain accurate results all the methods rely on bundle adjustment, a nonlinear optimization technique which minimizes the reprojection error over the structural and camera parameters. Bundle adjustment is optimal for normally distributed measurement noise, however, its performance depends on the starting point. The initial solution is usually obtained by solving a linearized constraint through a total least squares procedure, which yields a biased estimate. We present a more balanced approach where in main computational modules of an uncalibrated reconstruction system, the initial solution is obtained from a statistically justified estimator which assures its unbiasedness. Since the quality of the new initial solution is already comparable with that of the result of bundle adjustment, the burden on the latter is drastically reduced while its reliability is significantly increased. The performance of our system was assessed for both synthetic data and standard image sequences.


Camera Motion Camera Parameter Projection Matrice Bundle Adjustment Total Little Square 
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  1. 1.
    P. Beardsley, P. Torr, and A. Zisserman. 3D model aquisition from extended image sequences. In B. Buxton and R. Cipolla, editors, Computer Vision-ECCV 1996, volume II, pages 683–695, Cambridge, UK, April 1996. Springer.Google Scholar
  2. 2.
    N. Canterakis. A minimal set of constraints for the trifocal tensor. In D. Vernon, editor, Computer Vision-ECCV 2000, volume I, pages 84–99, Dublin, Ireland, 2000. Springer.Google Scholar
  3. 3.
    O. Faugeras and T. Papadopoulo. A nonlinear method for estimating the projective geometry of 3 views. In 6th International Conference on Computer Vision, pages 477–484, Bombay, India, January 1998.Google Scholar
  4. 4.
    A.W. Fitzgibbon and A. Zisserman. Automatic camera recovery for closed or open image sequences. In H. Burkhardt and B. Neumann, editors, Computer Vision-ECCV 1998, volume I, pages 311–326, Freiburg, Germany, June 1998. Springer.Google Scholar
  5. 5.
    R.I. Hartley. Euclidean reconstruction from uncalibrated views. InJ.L. Mundy, A. Zisserman, and D. Forsyth, editors, Applications of Invariance in Computer Vision, pages 237–256, 1994.Google Scholar
  6. 6.
    R. I. Hartley. In defence of the 8-point algorithm. In 5th International Conference on Computer Vision, pages 1064–1070, Cambridge, MA, June 1995.Google Scholar
  7. 7.
    R. I. Hartley and P. Sturm. Triangulation. Computer Vision and Image Understanding, 68:146–157, 1997.CrossRefGoogle Scholar
  8. 8.
    R. I. Hartley and A. Zisserman. Multiple View Geometry in Computer Vision. Cambridge University Press, 2000.Google Scholar
  9. 9.
    A. Heyden and K. Astrom. Euclidean reconstruction from image sequences with varying and unknown focal length and principal point. In 1997 IEEE Conference on Computer Vision and Pattern Recognition, pages 438–443, San Juan, Puerto Rico, June 1997.Google Scholar
  10. 10.
    K. Kanatani. Statistical Optimization for Geometric Computation: Theory and Practice. Elsevier, 1996.Google Scholar
  11. 11.
    B. Matei. Heteroscedastic Errors-In-Variables Models in Computer Vision. PhD thesis, Department of Electrical and Computer Engineering, Rutgers University, 2001. Available at
  12. 12.
    B. Matei, B. Georgescu, and P. Meer. A versatile method for trifocal tensor estimation. In 8th International Conference on Computer Vision, volume II, pages 578–585, Vancouver, Canada, July 2001.Google Scholar
  13. 13.
    P.F. McLauchlan and D.W. Murray. A unifying framework for structure and motion recovery from image sequences. In 5th International Conference on Computer Vision, pages 314–320, Cambridge, Massachusetts, June 1995.Google Scholar
  14. 14.
    M. Pollefeys. Self-calibration and Metric 3D Reconstruction from Uncalibrated Image Sequences. PhD thesis, K. U. Leuven, 1999.Google Scholar
  15. 15.
    M. Pollefeys. Self calibration and metric reconstruction in spite of varying and unknown intrinsic camera parameters. International J. of Computer Vision, 32:7–25, 1999.CrossRefGoogle Scholar
  16. 16.
    C. Schmid, R. Mohr, and C. Bauckhage. Evaluation of interest point detectors. Computer Vision and Image Understanding, 78:151–172, 2000.Google Scholar
  17. 17.
    A. Shashua. Algebraic functions for recognition. IEEE Trans. Pattern Anal. Machine Intell., 17:779–780, 1995.CrossRefGoogle Scholar
  18. 18.
    P. H. S. Torr and A. Zisserman. Robust parameterization and computation of the trifocal tensor. Image and Vision Computing, 15:591–605, August 1997.Google Scholar
  19. 19.
    P.H.S. Torr and A. Zisserman. Robust computation and parametrization of multiple view relations. In 6th International Conference on Computer Vision, pages 727–732, Bombay, India, January 1998.Google Scholar
  20. 20.
    B. Triggs. Autocalibration and the absolute quadric. In 1997 IEEE Conference on Computer Vision and Pattern Recognition, pages 609–614, San Juan, Puerto Rico, June 1997.Google Scholar
  21. 21.
    B. Triggs, P. F McLauchlan, R. I. Hartley, and A. W. Fitzgibbon. Bundle adjustment — A modern synthesis. In B. Triggs, A. Zisserman, and R. Szelisky, editors, Vision Algorithms: Theory and Practice, pages 298–372. Springer, 2000.Google Scholar
  22. 22.
    S. Van Huffel and J. Vanderwalle. Analysis and properties of GTLS in problem AX ≈ B. SIAM Journal on Matrix Analysis and Applications, 10:294–315, 1989.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Bogdan Georgescu
    • 1
  • Peter Meer
    • 1
    • 2
  1. 1.Computer Science DepartmentUSA
  2. 2.Electrical and Computer Engineering DepartmentRutgers UniversityPiscatawayUSA

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