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Quasi-Random Sampling for Condensation

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Part of the Lecture Notes in Computer Science book series (LNCS,volume 1843)

Abstract

The problem of tracking pedestrians from a moving car is a challenging one. The Condensation tracking algorithm is appealing for its generality and potential for real-time implementation. However, the conventional Condensation tracker is known to have difficulty with high-dimensional state spaces and unknown motion models. This paper presents an improved algorithm that addresses these problems by using a simplified motion model, and employing quasi-Monte Carlo techniques to efficiently sample the resulting tracking problem in the high-dimensional state space. For N sample points, these techniques achieve sampling errors of O(N -1), as opposed to O(N -1/2) for conventional Monte Carlo techniques. We illustrate the algorithm by tracking objects in both synthetic and real sequences, and show that it achieves reliable tracking and significant speed-ups over conventional Monte Carlo techniques.

Keywords

  • Process Noise
  • Importance Sampling
  • IEEE International Conf
  • Pedestrian Detection
  • Standard Deviation Error

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. Isard and A. Blake. Contour tracking by stochastic propagation of conditional density. Proc. European Conf. on Computer Vision, pages 343–356, 1996.

    Google Scholar 

  2. M. Isard and A. Blake. ICONDENSATION: Unifying low-level and high-level tracking in a stochastic framework. Proc. European Conf. on Computer Vision, vol. 1, pp. 893–908, 1998.

    Google Scholar 

  3. D. Gavrila and V. Philomin. Real-time object detection for “smart” vehicles. Proc. IEEE International Conf. on Computer Vision, vol. 1, pp. 87–93, 1999.

    CrossRef  Google Scholar 

  4. D. Gavrila and V. Philomin. Real-time object detection using distance transforms. Proc. Intelligent Vehicles Conf., 1998.

    Google Scholar 

  5. M. Oren, C. Papageorgiou, P. Sinha, E. Osuna, and T. Poggio. Pedestrian detection using wavelet templates. Proc. IEEE International Conf. on Computer Vision, pp. 193–199, 1997.

    Google Scholar 

  6. A. Blake, B. North and M. Isard. Learning multi-class dynamics. Advances in Neural Information Processing Systems11, in press.

    Google Scholar 

  7. J. Rittscher and A. Blake. Classification of human body motion. Proc. IEEE International Conf. on Computer Vision, pp. 634–639, 1999.

    Google Scholar 

  8. W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery. Numerical Recipes: The Art of Scientific Computing. 2nd Edition, Cambridge University Press, Cambridge, UK.

    Google Scholar 

  9. J. Carpenter, P. Clifford and P. Fearnhead. An improved particle filter for nonlinear problems. IEE Proc. Radar, Sonar and Navigation146, pp. 2–7, 1999.

    CrossRef  Google Scholar 

  10. H. Niederreiter. Random Number Generation and Quasi-Monte Carlo Methods. SIAM, Philadelphia, PA, 1992.

    CrossRef  MATH  Google Scholar 

  11. J. MacCormick and A. Blake. A probabilistic exclusion principle for tracking multiple objects. Proc. IEEE International Conf. on Computer Vision, vol. 1, pp. 572–578, 1999.

    CrossRef  MATH  Google Scholar 

  12. B. L. Fox. Algorithm 647: Implementation and relative efficiency of quasirandom sequence generators. ACM Transactions on Mathematical Software12, pp. 362–376, 1986.

    CrossRef  MATH  Google Scholar 

  13. P. Bratley and B. L. Fox. Algorithm 659: Implementing Sobol’s quasirandom sequence generator. ACM Transactions on Mathematical Software14, pp. 88–100, 1988.

    CrossRef  MATH  Google Scholar 

  14. P. Bratley, B. L. Fox, and H. Niederreiter. Implementation and tests of low-discrepancy sequences. ACM Transactions on Modeling and Computer Simulation2, pp. 195–213, 1992.

    CrossRef  MATH  Google Scholar 

  15. W. J. Morokoff and R. E. Caflisch. Quasi-random sequences and their discrepancies. SIAM J. Sci. Comput.15, pp. 1251–1279, 1994.

    MathSciNet  CrossRef  MATH  Google Scholar 

  16. P. Bratley, B. L. Fox, and H. Niederreiter. Algorithm 738: Programs to generate Niederreiter’s low-discrepancy sequences. ACM Transactions on Mathematical Software20, pp. 494–495, 1994.

    CrossRef  MATH  Google Scholar 

  17. B. Moskowitz and R. E. Caflisch. Smoothness and dimension reduction in quasi-Monte Carlo methods. Math. Comput. Modelling23, pp. 37–54, 1996.

    MathSciNet  CrossRef  MATH  Google Scholar 

  18. M. J. Black and A. D. Jepson. Recognizing temporal trajectories using the Condensation algorithm. Proc. IEEE International Conf. on Automatic Face and Gesture Recognition, 1998.

    Google Scholar 

  19. D. Reynard, A. Wildenberg, A. Blake and J. Merchant. Learning dynamics of complex motions from image sequences. Proc. European Conf. on Computer Vision, pp. 357–368, 1996.

    Google Scholar 

  20. B. North and A. Blake. Learning dynamical models using Expectation-Maximisation. Proc. IEEE International Conf. on Computer Vision, pp. 384–389, 1998.

    Google Scholar 

  21. L. Piegl and W. Tiller. The NURBS Book. Springer-Verlag, 1995.

    Google Scholar 

  22. T. F. Cootes, C. J. Taylor, A. Lanitis, D. H. Cooper, and J. Graham. Building and using flexible models incorporating grey-level information. Proc. IEEE International Conf. on Computer Vision, pp. 242–246, 1993.

    Google Scholar 

  23. A. Baumberg and D. C. Hogg. Learning flexible models from image sequences. Proc. European Conf. on Computer Vision, 1994.

    Google Scholar 

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© 2000 Springer-Verlag Berlin Heidelberg

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Philomin, V., Duraiswami, R., Davis, L. (2000). Quasi-Random Sampling for Condensation. In: Vernon, D. (eds) Computer Vision — ECCV 2000. ECCV 2000. Lecture Notes in Computer Science, vol 1843. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45053-X_9

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  • DOI: https://doi.org/10.1007/3-540-45053-X_9

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67686-7

  • Online ISBN: 978-3-540-45053-5

  • eBook Packages: Springer Book Archive

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