Hierarchical Bayesian Modeling for Estimating Shared Hidden States with  Application to Tracking

Kazuhiko Kawamoto

doi:10.20965/jaciii.2009.p0080

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JACIII Vol.13 No.2 pp. 80-85

doi: 10.20965/jaciii.2009.p0080

(2009)

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Hierarchical Bayesian Modeling for Estimating Shared Hidden States with Application to Tracking

Kazuhiko Kawamoto

Kyushu Institute of Technology, 1-1 Sensui-cho, Tobata-ku, Kitakyushu 804-8550, Japan

Received:

July 15, 2008

Accepted:

January 15, 2009

Published:

March 20, 2009

Keywords:

state estimation, hierarchical Bayesian model, tracking, particle filter

Abstract

We consider a problem of estimating shared hidden states of stochastic time–series models from individual observations. To solve the problem, we formulate the problem with hierarchical Bayesian Models and propose a particle filter, which yields a numerical solution to sequential Bayesian estimation, for the hierarchical models. The proposed method can be applied to the problem of tracking an extended object or a group of objects moving in formation. We decompose the state space into the shared and unshared substates, assuming that the individual unshared substate independently evolves with time. This assumption enables us to treat multiple targets individually. Experiments with numerical and real image sequences show the effectiveness of the proposed method.

Cite this article as:

K. Kawamoto, “Hierarchical Bayesian Modeling for Estimating Shared Hidden States with Application to Tracking,” J. Adv. Comput. Intell. Intell. Inform., Vol.13 No.2, pp. 80-85, 2009.

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References

[1] Y. Bar-Shalom, X. R. Li, and T. Kirubarajan, “Estimation with Applications to Tracking and Navigation: Algorithms and Software for Information Extraction,” Wiley, 2001.
[2] J. Vermaak, N. Ikoma, and S. Godsill, “Sequential Monte Carlo framework for extended object tracking,” IEE Proc. Radar, Sonar Navig., Vol.152(5), pp. 353-363, 2005.
[3] N. J. Gordon, D. J. Salmond, and D. Fisher, “Bayesian target tracking after group pattern distortion,” Proc. SPIE, Vol. 3163, pp. 238-248, 1997.
[4] K. Kanatani, “Statistical Optimization For Geometric Computation: Theory And Practice,” Dover Pubns, 2005.
[5] R. Hartley and A. Zisserman, “Multiple View Geometry in Computer Vision,” Cambridge University Press, 2004.
[6] M. A. Fischer, and R. C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” Comm. ACM, Vol.24(6), pp. 381-395, June 1981.
[7] P.J. Huber, “Robust Statistics,” John Wiley & Sons, 1981.
[8] R.J. Rousseeuw, “Least median of squares regression,” J. American Stat. Assoc., Vol.79, pp. 871-880, 1984.
[9] G. Kitagawa, “Monte Carlo filter and smoother for non-Gaussian nonlinear state space models,” J. Comput. Graph. Stat., Vol.5, No.1, pp. 1-25, 1996.
[10] N. J. Gordon, D. J. Salmond, and A. F. M. Smith, “Novel approach to nonlinear/non-Gaussian Bayesian state estimation,” IEE Proc. F, Vol.140 (2), pp. 107-113, 1993.
[11] M. Isard and A. Blake, “Condensation – Conditional density propagation for visual tracking,” Int. J. Computer Vision, Vol.29(1), pp. 5-28, 1998.
[12] A. Gelman, J. B. Carlin, H. S. Stern, D. B. Rubin, “Bayesian Data Analysis,” Chapman & Hall/CRC, 2003.
[13] J. Durbin and S. J. Koopman, “Time Series Analysis by State Space Methods,” Oxford University Press, 2001.
[14] B. Ristic, S. Arulampalam, and N. Gordon, “Beyond the Kalman Filter: Particle Filters for Tracking Applications,” Artech House Publishers, 2004.
[15] M. K. Pitt and N. Shephard, “Filtering Via Simulation: Auxiliary Particle Filters,” J. the American Statistical Association, Vol.94, pp. 590-599, 1999.
[16] A. Doucet, S. Godsill, and C. Andrieu, “On sequential Monte Carlo sampling methods for Bayesian filtering,” Statistics and Computing, Vol.10, pp. 197-208, 2000.
[17] C. Harris, and M. Stephens, “A combined corner and edge detector,” Proc. 4th Alvey Vision Conf., pp. 147-151, Aug, 1988.
[18] J. Shi, and C. Tomasi, “Good Features to Track,” Proc. Computer Vision Pattern Recognition, pp. 593-600, 1994.
[19] J. Y. Bouguet, “Pyramidal Implementation of the Lucas Kanade Feature Tracker,” Intel Corporation, Microprocessor Research Labs, 2000.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] Y. Bar-Shalom, X. R. Li, and T. Kirubarajan, “Estimation with Applications to Tracking and Navigation: Algorithms and Software for Information Extraction,” Wiley, 2001.

[2] [2] J. Vermaak, N. Ikoma, and S. Godsill, “Sequential Monte Carlo framework for extended object tracking,” IEE Proc. Radar, Sonar Navig., Vol.152(5), pp. 353-363, 2005.

[3] [3] N. J. Gordon, D. J. Salmond, and D. Fisher, “Bayesian target tracking after group pattern distortion,” Proc. SPIE, Vol. 3163, pp. 238-248, 1997.

[4] [4] K. Kanatani, “Statistical Optimization For Geometric Computation: Theory And Practice,” Dover Pubns, 2005.

[5] [5] R. Hartley and A. Zisserman, “Multiple View Geometry in Computer Vision,” Cambridge University Press, 2004.

[6] [6] M. A. Fischer, and R. C. Bolles, “Random sample consensus: a paradigm for model fitting with applications to image analysis and automated cartography,” Comm. ACM, Vol.24(6), pp. 381-395, June 1981.

[7] [7] P.J. Huber, “Robust Statistics,” John Wiley & Sons, 1981.

[8] [8] R.J. Rousseeuw, “Least median of squares regression,” J. American Stat. Assoc., Vol.79, pp. 871-880, 1984.

[9] [9] G. Kitagawa, “Monte Carlo filter and smoother for non-Gaussian nonlinear state space models,” J. Comput. Graph. Stat., Vol.5, No.1, pp. 1-25, 1996.

[10] [10] N. J. Gordon, D. J. Salmond, and A. F. M. Smith, “Novel approach to nonlinear/non-Gaussian Bayesian state estimation,” IEE Proc. F, Vol.140 (2), pp. 107-113, 1993.

[11] [11] M. Isard and A. Blake, “Condensation – Conditional density propagation for visual tracking,” Int. J. Computer Vision, Vol.29(1), pp. 5-28, 1998.

[12] [12] A. Gelman, J. B. Carlin, H. S. Stern, D. B. Rubin, “Bayesian Data Analysis,” Chapman & Hall/CRC, 2003.

[13] [13] J. Durbin and S. J. Koopman, “Time Series Analysis by State Space Methods,” Oxford University Press, 2001.

[14] [14] B. Ristic, S. Arulampalam, and N. Gordon, “Beyond the Kalman Filter: Particle Filters for Tracking Applications,” Artech House Publishers, 2004.

[15] [15] M. K. Pitt and N. Shephard, “Filtering Via Simulation: Auxiliary Particle Filters,” J. the American Statistical Association, Vol.94, pp. 590-599, 1999.

[16] [16] A. Doucet, S. Godsill, and C. Andrieu, “On sequential Monte Carlo sampling methods for Bayesian filtering,” Statistics and Computing, Vol.10, pp. 197-208, 2000.

[17] [17] C. Harris, and M. Stephens, “A combined corner and edge detector,” Proc. 4th Alvey Vision Conf., pp. 147-151, Aug, 1988.

[18] [18] J. Shi, and C. Tomasi, “Good Features to Track,” Proc. Computer Vision Pattern Recognition, pp. 593-600, 1994.

[19] [19] J. Y. Bouguet, “Pyramidal Implementation of the Lucas Kanade Feature Tracker,” Intel Corporation, Microprocessor Research Labs, 2000.