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A new multistage approach to motion and structure estimation by gradually enforcing geometric constraints

  • Zhengyou Zhang
Poster Session III
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1352)

Abstract

The standard 2-stage algorithm first estimates the 9 essential parameters defined up to a scale factor and then refines the motion estimation based on some statistically optimal criteria. We propose in this paper a novel approach by introducing an intermediate stage which consists in estimating a 3 x 3 matrix defined up to a scale factor by imposing the rank-2 constraint (the matrix has seven independent parameters). The idea is to gradually project parameters estimated in a high dimensional space onto a slightly lower-dimensional space, namely from 8 dimensions to 7 and finally to 5. Experiments with synthetic and real data show a considerable improvement over the 2-stage algorithm. Our conjecture from this work is that the imposition of the constraints arising from projective geometry should be used as an intermediate step in order to obtain reliable 3D Euclidean motion and structure estimation from multiple calibrated images.

Keywords

Motion and stereo 3D reconstruction Structure from motion Multipleview geometry Gradual constraint enforcing 

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References

  1. 1.
    H. Nagel, “Image sequences-ten (octal) years-from phenomenology towards a theoretical foundation,” in Proceedings 8th ICPR, Paris, France, pp. 1174–1185, IEEE, Oct. 1986.Google Scholar
  2. 2.
    J. Aggarwal and N. Nandhakumar, “On the computation of motion from sequences of images — a review,” Proc. IEEE, vol. 76, pp. 917–935, Aug. 1988.Google Scholar
  3. 3.
    T. Huang and A. Netravali, “Motion and structure from feature correspondences: A review,” Proc. IEEE, vol. 82, pp. 252–268, Feb. 1994.Google Scholar
  4. 4.
    C. Braccini, G. Gambardella, A. Grattarola, and S. Zappatore, “Motion estimation of rigid bodies: Effects of the rigidity constraints,” in Proc. EUSIPCO, Signal Processing III: Theories and Applications, pp. 645–648, Sept. 1986.Google Scholar
  5. 5.
    J. Oliensis and V. Govindu, “Experimental evaluation of projective reconstruction in structure from motion,” tech. rep., NEC Research Institute, Princeton, NJ 08540, USA, Oct. 1995.Google Scholar
  6. 6.
    Q.-T. Luong and O. D. Faugeras, “The fundamental matrix: Theory, algorithms and stability analysis,” The International Journal of Computer Vision, vol. 17, pp. 43–76, Jan. 1996.Google Scholar
  7. 7.
    O. Faugeras, “Stratification of 3-D vision: projective, affine, and metric representations,” Journal of the Optical Society of America A, vol. 12, pp. 465–484, Mar. 1995.Google Scholar
  8. 8.
    H. Longuet-Higgins, “A computer algorithm for reconstructing a scene from two projections,” Nature, vol. 293, pp. 133–135, 1981.Google Scholar
  9. 9.
    O. Faugeras, Three-Dimensional Computer Vision: a Geometric Viewpoint. MIT Press, 1993.Google Scholar
  10. 10.
    J. More, “The levenberg-marquardt algorithm, implementation and theory,” in Numerical Analysis (G. A. Watson, ed.), Lecture Notes in Mathematics 630, Springer-Verlag, 1977.Google Scholar
  11. 11.
    Z. Zhang, “Determining the epipolar geometry and its uncertainty: A review,” The International Journal of Computer Vision, 1997. In Press. Updated version of INRIA Research Report No.2927, 1996.Google Scholar
  12. 12.
    R. Hartley, “In defence of the 8-point algorithm,” in Proceedings of the 5th International Conference on Computer Vision, (Boston, MA), pp. 1064–1070, June 1995.Google Scholar
  13. 13.
    Z. Zhang, “Motion and structure from two perspective views: From essential parameters to euclidean motion via fundamental matrix,” Journal of the Optical Society of America A, vol. 14, no. 11, 1997. In Press.Google Scholar
  14. 14.
    K. Kanatani, “Automatic singularity test for motion analysis by an information criterion,” in Proceedings of the 4th European Conference on Computer Vision (B. Buxton, ed.), (Cambridge, UK), pp. 697–708, Apr. 1996.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Zhengyou Zhang
    • 1
    • 2
  1. 1.INRIASophia-Antipolis CedexFrance
  2. 2.ATR HIPKyotoJapan

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