Generative Graphical Models for Maneuvering Object Tracking and Dynamics Analysis

1. Generative Graphical Models for Maneuvering Object Tracking and Dynamics Analysis Xin Fan and Guoliang Fan Visual Computing and Image Processing Lab School of Electrical and Computer Engineering Oklahoma State University 4th Joint IEEE International Workshop on Object Tracking and Classification Beyond the Visible Spectrum(OTCBVS'07) Minneapolis, MN, USA, June 22, 2007

2. Problem Statement • Motion models • Deal with object movements • Why important? • complex motion patterns, e.g., maneuvering • no good appearance model, e.g., low SNR • provide good prediction for robust and efficient tracking • Challenges • Hardly predict maneuvering actions • Model constraints • A motion model that incorporates constraints

3. Our observations • Maneuvering actions are due to forces and torques. • forces and torques cause kinematic changes • Newton equations for rigid body motion • Rigid body motion VS point motion • Newton equations • Forces are dependent on kinematics • Limited output power of engines. • Uncertainties exist, e.g., air resistance, road friction, mechanical instability, etc.

4. Problem Formulation • Switching statistical models for maneuvering variables (forces and torques) • Maneuvering actions are due to forces and torques. • Newton equations to define kinematics evolution densities • Newton equations of rigid body motion • Rayleigh distribution to model velocity-force constraints • Physical constraints reveal how forces are dependent on kinematics. • Organize these dependencies with a probabilistic graphical model

5. Related work • White Gaussian noise acceleration (WGNA) • Point target assumption • Miller’s condition mean estimation • Rigid Newton dynamics • Jump-diffusion process, not sequentially • Switching Linear dynamic system (SLDS) or Jump Markov linear system (JMLS) • Discrete switching variables for maneuvering actions • No explicit physical dynamics • Inference algorithms • IMM works for Gaussian densities • BP works for tree structures • Sampling based approximation

6. Generative Model - Structure Forces Velocity Position Frames Orientation Torques • Generative model • How forces and torques generate kinematics changes • how kinematics generate observations

7. Generative model-Cause variables • Switching continuous probabilistic models • Specify three switching normal distributions for forces. • Ternary uniform mixture for torques (angular velocity)

8. Generative model – Temporal constraints • Newton equations • Investigate the dynamics of 3D rigid motion • Define the kinematic dependence by Newton equations of rigid body motion.

9. Generative model – Temporal constraints • Newton equations for 3D rigid motion • p-linear momentum and f- force • h - angular momentum and τ- torque • Simplified for ground vehicles

10. Generative model – Temporal constraints Velocity Position Orientation • kinematics dependency via Newton equations

11. Generative model- VF constraints • Rayleigh distribution for velocity-force constraints • Driving force conditional on velocities • Resistance force conditional on velocities

12. Generative model - Likelihood • Simple template matching to define likelihood

13. Generative model - Inference • SMC based inference algorithm • Predict with temporal densities • Evaluate weights with likelihood • MCMC to generate samples of forces

14. Experiments – Simulated data • Compared with a particle filter (PF) for JMLS • Tracking with coupled linear and angular motion • No coupling JMPF Ours

15. Experiments – Simulated data • Compared with a particle filter (PF) for JMLS • Tracking with coupled linear and angular motion • Has coupling JMPF Ours

16. Experiments – Simulated data • Compared with a particle filter (PF) for JMLS • Tracking with velocity-force constraints

17. Experiments – Real world video • Compared with constant velocity constant turn (CVCT) model Ours CVCT

18. Conclusions and future work • Conclusions • Graphical model for maneuvering targets, which encode the Newtonian dynamics in a probabilistic framework. • Explicitly and directly build the cause-effect relationship • Feedback constraint from velocity to the forces • Future work • Handle multiple views. • Multiple targets with data association