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MCMC-Based Particle Filtering for Tracking a Variable Number of Interacting Targets
November 2005 (vol. 27 no. 11)
pp. 1805-1918
We describe a particle filter that effectively deals with interacting targets—targets that are influenced by the proximity and/or behavior of other targets. The particle filter includes a Markov random field (MRF) motion prior that helps maintain the identity of targets throughout an interaction, significantly reducing tracker failures. We show that this MRF prior can be easily implemented by including an additional interaction factor in the importance weights of the particle filter. However, the computational requirements of the resulting multitarget filter render it unusable for large numbers of targets. Consequently, we replace the traditional importance sampling step in the particle filter with a novel Markov chain Monte Carlo (MCMC) sampling step to obtain a more efficient MCMC-based multitarget filter. We also show how to extend this MCMC-based filter to address a variable number of interacting targets. Finally, we present both qualitative and quantitative experimental results, demonstrating that the resulting particle filters deal efficiently and effectively with complicated target interactions.

[1] T. Balch, Z. Khan, and M. Veloso, “Automatically Tracking and Analyzing the Behavior of Live Insect Colonies,” Proc. Conf. Autonomous Agents, 2001.
[2] D. Reid, “An Algorithm for Tracking Multiple Targets,” IEEE Trans. Automatic Control, vol. 24, no. 6, pp. 84-90, Dec. 1979.
[3] Y. Bar-Shalom, T. Fortmann, and M. Scheffe, “Joint Probabilistic Data Association for Multiple Targets in Clutter,” Proc. Conf. Information Sciences and Systems, 1980.
[4] T. Fortmann, Y. Bar-Shalom, and M. Scheffe, “Sonar Tracking of Multiple Targets Using Joint Probabilistic Data Association,” IEEE J. Oceanic Eng., vol. 8, July 1983
[5] R. Deriche and O. Faugeras, “Tracking Line Segments,” Image and Vision Computing, vol. 8, pp. 261-270, 1990.
[6] I. Cox and J. Leonard, “Modeling a Dynamic Environment Using a Bayesian Multiple Hypothesis Approach,” Artificial Intelligence, vol. 66, no. 2, pp. 311-344, Apr. 1994.
[7] C. Rasmussen and G. Hager, “Probabilistic Data Association Methods for Tracking Complex Visual Objects,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 23, no. 6, pp. 560-576, June 2001.
[8] D. Schulz, W. Burgard, D. Fox, and A.B. Cremers, “Tracking Multiple Moving Targets with a Mobile Robot Using Particle Filters and Statistical Data Association,” IEEE Int'l Conf. Robotics and Automation, 2001.
[9] N. Gordon, D. Salmond, and A. Smith, “Novel Approach to Nonlinear/Non-Gaussian Bayesian State Estimation,” IEE Proc. F, vol. 140, no. 2, pp. 107-113, 1993.
[10] M. Isard and A. Blake, “Contour Tracking by Stochastic Propagation of Conditional Density,” Proc. European Conf. Computer Vision, pp. 343-356, 1996.
[11] J. Carpenter, P. Clifford, and P. Fernhead, “An Improved Particle Filter for Non-Linear Problems,” technical report, Dept. Statistics, Univ. of Oxford, 1997.
[12] F. Dellaert, D. Fox, W. Burgard, and S. Thrun, “Monte Carlo Localization for Mobile Robots,” IEEE Int'l Conf. Robotics and Automation, 1999.
[13] Z. Khan, T. Balch, and F. Dellaert, “Efficient Particle Filter-Based Tracking of Multiple Interacting Targets Using an MRF-Based Motion Model,” Proc. IEEE/RSJ Int'l Conf. Intelligent Robots and Systems, 2003.
[14] P. Green, “Trans-Dimensional Markov Chain Monte Carlo,” Highly Structured Stochastic Systems, Oxford Univ. Press, 2003.
[15] P. Green, “Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination,” Biometrika, vol. 82, pp. 711-732, 1995, .
[16] L.D. Stone, C.A. Barlow, and T.L. Corwin, Bayesian Multiple Target Tracking. Boston: Artech House, 1999.
[17] R. Popoli and S.S. Blackman, Design and Analysis of Modern Tracking Systems. Artech House Radar Library, Aug. 1999.
[18] M. Isard and J. MacCormick, “BraMBLe: A Bayesian Multiple-Blob Tracker,” Proc. Int'l Conf. Computer Vision, pp. 34-41, 2001.
[19] S. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, “A Tutorial on Particle Filters for On-Line Non-Linear/Non-Gaussian Bayesian Tracking,” IEEE Trans. Signal Processing, vol. 50, no. 2, pp. 174-188, Feb. 2002.
[20] D. Tweed and A. Calway, “Tracking Many Objects Using Subordinate Condensation,” Proc. British Machine Vision Conf., 2002.
[21] J. Vermaak, A. Doucet, and P. Perez, “Maintaining Multi-Modality through Mixture Tracking,” Proc. Int'l Conf. Computer Vision, 2003.
[22] K. Okuma, A. Taleghani, N. de Freitas, J. Little, and D. Lowe, “A Boosted Particle Filter: Multitarget Detection and Tracking,” Proc. European Conf. Computer Vision, 2004.
[23] J. MacCormick and A. Blake, “A Probabilistic Exclusion Principle for Tracking Multiple Objects,” Proc. Int'l Conf. Computer Vision, pp. 572-578, 1999.
[24] J. Vermaak, S.J. Godsill, and A. Doucet, “Radial Basis Function Regression Using Trans-Dimensional Sequential Monte Carlo,” Proc. 12th IEEE Workshop Statistical Signal Processing, pp. 525-528, 2003.
[25] H. Sidenbladh and S. Wirkander, “Tracking Random Sets of Vehicles in Terrain,” Proc. Second IEEE Workshop Multi-Object Tracking, 2003.
[26] H. Sidenbladh and S. Wirkander, “Particle Filtering for Random Sets,” 2004, unpublished.
[27] T. Zhao and R. Nevatia, “Tracking Multiple Humans in Crowded Environment,” proc. IEEE Conf. Computer Vision and Pattern Recognition, 2004.
[28] C. Sminchisescu and B. Triggs, “Kinematic Jump Processes for Monocular 3D Human Tracking,” Proc. IEEE Conf. Computer Vision and Pattern Recognition, pp. 69-76, 2003.
[29] W. Gilks and C. Berzuini, “Following a Moving Target— Bayesian Inference for Dynamic Bayesian Models,” J. Royal Statistical Soc., Series B, vol. 63, no. 1, pp. 127-146, 2001.
[30] S.N. MacEachern and P. Muller, “Estimating Mixture of Dirichlet Process Models,” J. Computational and Graphical Statistics, vol. 7, pp. 223-238, 1998.
[31] C. Berzuini, N.G. Best, W. Gilks, and C. Larizza, “Dynamic Conditional Independence Models and Markov Chain Monte Carlo Methods,” J. Am. Statistical Assoc., vol. 92, pp. 1403-1412, 1996.
[32] C. Andrieu, M. Davy, and A. Doucet, “Sequential MCMC for Bayesian Model Selection,” Proc. IEEE Signal Processing Workshop Higher Order Statistics, 1999.
[33] C. Berzuini and W. Gilks, “RESAMPLE-MOVE Filtering with Cross-Model Jumps,” Sequential Monte Carlo Methods in Practice, A. Doucet, N. de Freitas, and N. Gordon, eds. New York: Springer-Verlag, 2001.
[34] S. Li, Markov Random Field Modeling in Computer Vision. Springer, 1995.
[35] R. Neal, “Probabilistic Inference Using Markov Chain Monte Carlo Methods,” Technical Report CRG-TR-93-1, Dept. of Computer Science, Univ. of Toronto, 1993.
[36] Markov Chain Monte Carlo in Practice, W. Gilks, S. Richardson, and D. Spiegelhalter, eds. Chapman and Hall, 1996.
[37] W. Hastings, “Monte Carlo Sampling Methods Using Markov Chains and Their Applications,” Biometrika, vol. 57, pp. 97-109, 1970.
[38] Z. Tu and S. Zhu, “Image Segmentation by Data-Driven Markov Chain Monte Carlo,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 24, no. 5, pp. 657-673, 2002.
[39] Z. Khan and F. Dellaert, “Robust Generative Subspace Modeling: The Subspace t Distribution,” Technical Report GIT-GVU-04-11, GVU Center, College of Computing, Georgia Tech, 2004.
[40] K.L. Lange, R.J.A. Little, and J.M. G. Taylor, “Robust Statistical Modeling Using the $t$ Distribution,” J. Am. Statistical Assoc., vol. 84, no. 408, pp. 881-896, 1989.
[41] J. Bruce, T. Balch, and M. Veloso, “Fast and Inexpensive Color Image Segmentation for Interactive Robots,” Proc. IEEE/RSJ Int'l Conf. Intelligent Robots and Systems, 2000.

Index Terms:
Index Terms- Particle filters, multitarget tracking, Markov random fields, Markov chain Monte Carlo.
Zia Khan, Tucker Balch, Frank Dellaert, "MCMC-Based Particle Filtering for Tracking a Variable Number of Interacting Targets," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 27, no. 11, pp. 1805-1918, Nov. 2005, doi:10.1109/TPAMI.2005.223
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