A Dynamic Bayesian Network Approach to Tracking Using Learned Switching Dynamic Models

  • Vladimir Pavlović
  • James M. Rehg
  • Tat-Jen Cham
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1790)


Switching linear dynamic systems (SLDS) attempt to describe a complex nonlinear dynamic system with a succession of linear models indexed by a switching variable. Unfortunately, despite SLDS’s simplicity exact state and parameter estimation are still intractable. Recently, a broad class of learning and inference algorithms for time-series models have been successfully cast in the framework of dynamic Bayesian networks (DBNs). This paper describes a novel DBN-based SLDS model. A key feature of our approach are two approximate inference techniques for overcoming the intractability of exact inference in SLDS. As an example, we apply our model to the human figure motion analysis. We present experimental results for learning figure dynamics from video data and show promising results for tracking, interpolation, synthesis, and classification using learned models.


Hide Markov Model Bayesian Network Switching State Dynamic Bayesian Network Switching Model 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    B. D. O. Anderson and J. B. Moore. Optimal filtering. Prentice-Hall, Inc., Englewood Clifis, NJ, 1979.zbMATHGoogle Scholar
  2. [2]
    Y. Bar-Shalom and X.-R. Li. Estimation and tracking: principles, techniques, and software. YBS, Storrs, CT, 1998.Google Scholar
  3. [3]
    A. Blake, B. North, and M. Isard. Learning multi-class dynamics. In NIPS’ 98, 1998.Google Scholar
  4. [4]
    M. Brand. Pattern discovery via entropy minimization. Technical Report TR98-21, Mitsubishi Electric Research Lab, 1998. Available at
  5. [5]
    C. Bregler and S. M. Omohundro. Nonlinear manifold learning for visual speech recognition. In Proceedings of International Conference on Computer Vision, pages 494–499, Cambridge, MA, June 1995.Google Scholar
  6. [6]
    T.-J. Cham and J. M. Rehg. A multiple hypothesis approach to figure tracking. In Computer Vision and Pattern Recognition, pages 239–245, 1999.Google Scholar
  7. [7]
    T. Dean and K. Kanazawa. A model for reasoning about persistance and causation. Computational Intelligence, 5(3), 1989.Google Scholar
  8. [8]
    Z. Ghahramani. Learning dynamic Bayesian networks. In C. L. Giles and M. Gori, editors, Adaptive processing of temporal information, Lecture notes in artificial intelligence. Springer-Verlag, 1997.Google Scholar
  9. [9]
    Z. Ghahramani and G. E. Hinton. Switching state-space models. submitted for publication, 1998.Google Scholar
  10. [10]
    J. K. Hodgins, W. L. Wooten, D. C. Brogan, and J. F. O’Brien. Animating human athletics. In Computer Graphics (Proc. SIGGRAPH’ 95), pages 71–78, 1995.Google Scholar
  11. [11]
    V. T. Inman, H. J. Ralston, and F. Todd. Human Walking. Williams and Wilkins, 1981.Google Scholar
  12. [12]
    M. Isard and A. Blake. A mixed-state CONDENSATION tracker with automatic model-switching. In Proceedings of International Conference on Computer Vision, pages 107–112, Bombay, India, 1998.Google Scholar
  13. [13]
    F. V. Jensen. An introduction to Bayesian Networks. Springer-Verlag, 1995.Google Scholar
  14. [14]
    M. I. Jordan, Z. Ghahramani, T. S. Jaakkola, and L. K. Saul. An introduction to variational methods for graphical models. In M. I. Jordan, editor, Learning in graphical models. Kluwer Academic Publishers, 1998.Google Scholar
  15. [15]
    I. A. Kakadiaris and D. Metaxas. Model-based estimation of 3D human motion with occlusion based on active multi-viewpoint selection. In Computer Vision and Pattern Recognition, pages 81–87, San Fransisco, CA, June 18–20 1996.Google Scholar
  16. [16]
    R. E. Kalman and R. S. Bucy. New results in linear filtering and prediction. Journal of Basic Engineering (ASME), D(83):95–108, 1961.MathSciNetGoogle Scholar
  17. [17]
    C.-J. Kim. Dynamic linear models with markov-switching. Journal of Econometrics, 60:1–22, 1994.zbMATHCrossRefMathSciNetGoogle Scholar
  18. [18]
    V. Krishnamurthy and J. Evans. Finite-dimensional filters for passive tracking of markov jump linear systems. Automatica, 34(6):765–770, 1998.zbMATHCrossRefMathSciNetGoogle Scholar
  19. [19]
    D. D. Morris and J. M. Rehg. Singularity analysis for articulated object tracking. In Computer Vision and Pattern Recognition, pages 289–296, Santa Barbara, CA, June 23–25 1998.Google Scholar
  20. [20]
    R. M. Neal. Connectionist learning of belief networks. Artificial Intelligence, pages 71–113, 1992.Google Scholar
  21. [21]
    R. M. Neal and G. E. Hinton. A new view of the EM algorithm that justifies incremental and other variants. In M. Jordan, editor, Learning in graphical models, pages 355–368. Kluwer Academic Publishers, 1998.Google Scholar
  22. [22]
    V. Pavlovic, B. Frey, and T. S. Huang. Time-series classification using mixed-state dynamic Bayesian networks. In Computer Vision and Pattern Recognition, pages 609–615, June 1999.Google Scholar
  23. [23]
    J. Pearl. Probabilistic reasoning in intelligent systems. Morgan Kaufmann, San Mateo, CA, 1998.Google Scholar
  24. [24]
    L. R. Rabiner and B. Juang. Fundamentals of Speech Recognition. Prentice Hall, Englewood Clifis, New Jersey, USA, 1993.Google Scholar
  25. [25]
    H. E. Rauch. Solutions to the linear smoothing problem. IEEE Trans. Automatic Control, AC-8(4):371–372, October 1963.CrossRefGoogle Scholar
  26. [26]
    R. H. Shumway and D. S. Stoffer. Dynamic linear models with switching. Journal of the American Statistical Association, 86(415):763–769, September 1991.CrossRefMathSciNetGoogle Scholar
  27. [27]
    C. R. Wren and A. P. Pentland. Dynamic models of human motion. In Proceeding of the Third International Conference on Automatic Face and Gesture Recognition, pages 22–27, Nara, Japan, 1998.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Vladimir Pavlović
    • 1
  • James M. Rehg
    • 1
  • Tat-Jen Cham
    • 1
  1. 1.Cambridge Research LabCompaq Computer Corp.Cambridge

Personalised recommendations