People tracking using hybrid Monte Carlo filtering

Particle filters are used for hidden state estimation with nonlinear dynamical systems. The inference of 3-D human motion is a natural application, given the nonlinear dynamics of the body and the nonlinear relation between states and image observations. However, the application of particle filters has been limited to cases where the number of state variables is relatively small, because the number of samples needed with high dimensional problems can be prohibitive. We describe a filter that uses hybrid Monte Carlo (HMC) to obtain samples in high dimensional spaces. It uses multiple Markov chains that use posterior gradients to rapidly explore the state space, yielding fair samples from the posterior. We find that the HMC filter is several thousand times faster than a conventional particle filter on a 28 D people tracking problem.

[1]  S. Duane,et al.  Hybrid Monte Carlo , 1987 .

[2]  Kiam Choo.  Learning hyperparameters for neural network models using Hamiltonian dynamics , 2000 .

[3]  David J. Fleet,et al.  Stochastic Tracking of 3 D Human Figures Using 2 D Image Motion , 2000 .

[4]  David A. Forsyth,et al.  Finding people by sampling , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[5]  James M. Rehg,et al.  A multiple hypothesis approach to figure tracking , 1999, Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149).

[6]  Michael A. West,et al.  Combined Parameter and State Estimation in Simulation-Based Filtering , 2001, Sequential Monte Carlo Methods in Practice.

[7]  Jun S. Liu,et al.  Sequential Monte Carlo methods for dynamic systems , 1997 .

[8]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[9]  Wolfram Burgard,et al.  Monte Carlo Localization: Efficient Position Estimation for Mobile Robots , 1999, AAAI/IAAI.

[10]  Bradley P. Carlin,et al.  Markov Chain Monte Carlo conver-gence diagnostics: a comparative review , 1996 .

[11]  Neil J. Gordon,et al.  Editors: Sequential Monte Carlo Methods in Practice , 2001 .

[12]  P. Fearnhead,et al.  Improved particle filter for nonlinear problems , 1999 .

[13]  Andrew Blake,et al.  Articulated body motion capture by annealed particle filtering , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[14]  Timothy J. Robinson,et al.  Sequential Monte Carlo Methods in Practice , 2003 .

[15]  Geoffrey E. Hinton,et al.  Bayesian Learning for Neural Networks , 1995 .

[16]  Michael J. Black,et al.  A Probabilistic Framework for Matching Temporal Trajectories: CONDENSATION-Based Recognition of Gestures and Expressions , 1998, ECCV.

[17]  Michael Isard,et al.  ICONDENSATION: Unifying Low-Level and High-Level Tracking in a Stochastic Framework , 1998, ECCV.

[18]  David J. Fleet,et al.  Stochastic Tracking of 3D Human Figures Using 2D Image Motion , 2000, ECCV.

[19]  David J. Fleet,et al.  Probabilistic detection and tracking of motion discontinuities , 1999, Proceedings of the Seventh IEEE International Conference on Computer Vision.

[20]  Michael Isard,et al.  Partitioned Sampling, Articulated Objects, and Interface-Quality Hand Tracking , 2000, ECCV.

[21]  W. Freeman,et al.  Bayesian Estimation of 3-D Human Motion , 1998 .

[22]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[23]  S. Rosenthal,et al.  A review of asymptotic convergence for general state space Markov chains , 2002 .