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Robust techniques for the estimation of structure from motion in the uncalibrated case

Part of the Lecture Notes in Computer Science book series (LNCS,volume 1406)

Abstract

Robust techniques are developed for determining structure from motion in the uncalibrated case. The structure recovery is based on previous work [7] in which it was shown that a camera undergoing unknown motion and having an unknown, and possibly varying, focal length can be self-calibrated via closed-form expressions in the entries of two matrices derivable from an instantaneous optical flow field. Critical to the recovery process is the obtaining of accurate numerical estimates, up to a scalar factor, of these matrices in the presence of noisy optical flow data. We present techniques for the determination of these matrices via least-squares methods, and also a way of enforcing a dependency constraint that is imposed on these matrices. A method for eliminating outlying flow vectors is also given. Results of experiments with real-image sequences are presented that suggest that the approach holds promise.

Keywords

  • Computer Vision
  • Optical Flow
  • Camera Frame
  • Robust Technique
  • Structure Recovery

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. M. Armstrong, A. Zisserman, and R. Hartley, Self-calibration from image triplets, In Buxton and Cipolla [8], pp. 3–16.

    Google Scholar 

  2. K. åström and A. Heyden, Continuous time matching constraints for image streams, International Journal of Computer Vision, to appear.

    Google Scholar 

  3. -, Multilinear forms in the infinitesimal-time case, Proceedings, CVPR '96, IEEE Computer Society Conference on Computer Vision and Pattern Recognition (San Francisco, CA, June 18–20, 1996), IEEE Computer Society Press, Los Alamitos, CA, 1996, pp. 833–838.

    Google Scholar 

  4. J. L. Barron and R. Eagleson, Recursive estimation of time-varying motion and structure parameters, Pattern Recognition 29 (1996), no. 5, 797–818.

    CrossRef  Google Scholar 

  5. P. A. Beardsley, A. Zisserman, and D. W. Murray, Sequential updating of projective and affine structure from motion, International Journal of Computer Vision 23 (1997), no. 3, 235–259.

    CrossRef  Google Scholar 

  6. F. Bookstein, Fitting conic sections to scattered data, Computer Vision, Graphics, and Image Processing 9 (1979), no. 1, 56–71.

    Google Scholar 

  7. M. J. Brooks, W. Chojnacki, and L. Baumela, Determining the egomotion of an uncalibrated camera from instantaneous optical flow, Journal of the Optical Society of America A 14 (1997), no. 10, 2670–2677.

    Google Scholar 

  8. B. Buxton and R. Cipolla (eds.), Computer Vision—ECCV '96, Lecture Notes in Computer Science, vol. 1064, Fourth European Conference on Computer Vision, Cambridge, UK, April 14–18,1996, Springer, Berlin, 1996.

    Google Scholar 

  9. O. D. Faugeras, Q. T. Luong, and S. J. Maybank, Camera self-calibration: Theory and experiments, Computer Vision—ECCV '92 (Second European Conference on Computer Vision, Santa Margherita Ligure, Italy, May 19–22, 1992) (G. Sandini, ed.), Springer, Berlin, 1992, pp. 321–334.

    Google Scholar 

  10. N. C. Gupta and L. N. Kanal, 3-D motion estimation from motion field, Artificial Intelligence 78 (1995), no. 1–2, 45–86.

    CrossRef  Google Scholar 

  11. D. J. Heeger and A. D. Jepson, Subspace methods for recovering rigid motion I: algorithm and implementation, International Journal of Computer Vision 7 (1992), no. 2, 95–117.

    CrossRef  Google Scholar 

  12. K. Kanatani, 3-D interpretation of optical flow by renormalization, International Journal of Computer Vision 11 (1993), no. 3, 267–282.

    CrossRef  Google Scholar 

  13. -, Statistical Optimization for Geometric Computation: Theory and Practice, Elsevier, Amsterdam, 1996.

    MATH  Google Scholar 

  14. Q.-T. Luong and O. D. Faugeras, The fundamental matrix: theory, algorithms, and stability analysis, International Journal of Computer Vision 17 (1996), no. 1, 43–75.

    CrossRef  Google Scholar 

  15. -, Self-calibration of a moving camera from point correspondences and fundamental matrices, International Journal of Computer Vision 22 (1997), no. 3, 261–289.

    CrossRef  Google Scholar 

  16. S. J. Maybank, The angular velocity associated with the optical flowfield arising from motion through a rigid environment, Proceedings of the Royal Society of London Ser. A 401 (1985), 317–326.

    MathSciNet  CrossRef  Google Scholar 

  17. S. J. Maybank and O. D. Faugeras, A theory of self-calibration of a moving camera, International Journal of Computer Vision 8 (1992), no. 2, 123–151.

    CrossRef  Google Scholar 

  18. N. Ohta and K. Kanatani, Optimal structure-from-motion algorithm for optical flow, IEICE Transactions on Information and Systems E78-D (1995), no. 12, 1559–1566.

    Google Scholar 

  19. M. Pollefeys, M. Van Gool, and M. Proesmans, Euclidean 3D reconstruction from image sequences with variable focal length, In Buxton and Cipolla [8], pp. 31–42.

    Google Scholar 

  20. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C, Cambridge University Press, Cambridge, 1995.

    Google Scholar 

  21. P. J. Rousseeuw and A. M. Leroy, Robust Regression and Outlier Regression, John Wiley & Sons, New York, 1987.

    MATH  Google Scholar 

  22. P. D. Sampson, Fitting conics sections to ‘very scattered’ data: An iterative refinement of the Bookstein algorithm, Computer Graphics and Image Processing 18 (1982), no. 1, 97–108.

    CrossRef  Google Scholar 

  23. S. Soatto and P. Perona, Recursive 3D visual motion estimation using subspace constraints, International Journal of Computer Vision 22 (1997), no. 3, 235–259.

    CrossRef  Google Scholar 

  24. P. H. S. Torr and D. W. Murray, The development and comparison of robust methods for estimating the fundamental matrix, International Journal of Computer Vision 24 (1997), no. 3, 271–300.

    CrossRef  Google Scholar 

  25. T. Viéville and O. D. Faugeras, Motion analysis with a camera with unknown, and possibly varying intrinsic parameters, Proceedings of the Fifth International Conference on Computer Vision (Cambridge, MA, June 1995), IEEE Computer Society Press, Los Alamitos, CA, 1995, pp. 750–756.

    Google Scholar 

  26. T. Viéville, O. D. Faugeras, and Q.-T. Luong, Motion of points and lines in the uncalibrated case, International Journal of Computer Vision 17 (1996), no. 1, 7–41.

    CrossRef  Google Scholar 

  27. T. Viéville, C. Zeller, and L. Robert, Using collineations to compute motion and structure in an uncalibrated image sequence, International Journal of Computer Vision 20 (1996), no. 3, 213–242.

    Google Scholar 

  28. J. Weng, T. S. Huang, and N. Ahuja, Motion and structure from two perspective views: algorithms, error analysis, and error estimation, IEEE Transactions on Pattern Analysis and Machine Intelligence 11 (1989), no. 5, 451–476.

    CrossRef  Google Scholar 

  29. Z. Zhang, Parameter estimation techniques: a tutorial with application to conic fitting, Image and Vision Computing 15 (1997), no. 1, 57–76.

    Google Scholar 

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© 1998 Springer-Verlag Berlin Heidelberg

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Brooks, M.J., Chojnacki, W., van den Hengel, A., Baumela, L. (1998). Robust techniques for the estimation of structure from motion in the uncalibrated case. In: Burkhardt, H., Neumann, B. (eds) Computer Vision — ECCV'98. ECCV 1998. Lecture Notes in Computer Science, vol 1406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055673

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  • DOI: https://doi.org/10.1007/BFb0055673

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