Bayesian state estimation and application to tracking

1. Bayesian state estimation and application to tracking Jamal Saboune jsaboune@site.uottawa.ca VIVA Lab - SITE - University of Ottawa Jamal Saboune - CRV10 Tutorial Day

2. Dynamic state estimation A dynamic process described using a number of random variables (state variables) The evolution of the variables follows a model Indication on all or some of the variables (observation) Evaluate at time t in a recursive manner (using t-1) the process represented by its state vector Xt , given the history of observations Yt Jamal Saboune - CRV10 Tutorial Day 2

3. Dynamic state estimation Xt= ft (Xt-1 ,Πt ) X0 The Markov process is defined by its transition model and the initial state vector: The observation is defined by the observation model : Yt= ht (Xt ,vt ) Jamal Saboune - CRV10 Tutorial Day

4. Dynamic state estimation- Bayesian approach Estimate the a posteriori probability density function P(Xt / Yt ) using the transition model, the observation model and the probability density function P(Xt-1 / Yt-1 ) Jamal Saboune - CRV10 Tutorial Day

5. Kalman filter Probability density propagation = Theoretical solution not an analytical one Particular case : The observation and process noises distributions are Gaussian + The transition and observation functions are linear  The probability density functions are Gaussian mono-modal Jamal Saboune - CRV10 Tutorial Day

6. Kalman filter A number of equations using the transition/observation functions and covariance matrices  Optimal estimation of the state vector Minimizes the mean square error between the estimated state vector X’t andthe ‘real’ state vector Xt E[(X’t - Xt )2] given the history of observations Yt Extended Kalman Filter (EKF) is the non linear version of the KF = The transition and observation function can be non-linear Jamal Saboune - CRV10 Tutorial Day 6

7. Kalman filter example Jamal Saboune - CRV10 Tutorial Day

8. Condensation algorithm (Isard, Blake 98) Multimodal and non Gaussian probability densities Model the uncertainty Each possible configuration of the state vector is represented by a ‘particle' The likelihood of a certain configuration is called ‘weight’ The posterior (a posteriori) density is represented using N ‘weighted’ particles Jamal Saboune - CRV10 Tutorial Day

9. Particles at t-1 CONDENSATION – time t Selection Prediction Likelihood function Measure Jamal Saboune - CRV10 Tutorial Day Chosen particle

10. Condensation algorithm (Isard, Blake 98) Tracking of a hand movement using an edge detector Jamal Saboune - CRV10 Tutorial Day

11. Condensation algorithm for tracking Hands and head movement tracking using color models and optical flow (Tung et al. 2008) Jamal Saboune - CRV10 Tutorial Day

12. Condensation algorithm for tracking Head tracking with contour models (Zhihong et al. 2002) Jamal Saboune - CRV10 Tutorial Day

13. Interval Particle Filtering for 3D motion capture (Saboune et al. 05,07,08) • 3D humanoid model adapted to the height of the person • 32 degrees of freedom to simulate the human movement Find the best fitting 3D model configuration Jamal Saboune - CRV10 Tutorial Day 13

14. Interval Particle Filtering for 3D motion capture (Saboune et al. 05,07,08) • Modify the Condensation algorithm and adapt it to the human motion tracking  Good estimation using a reduced number of particles Jamal Saboune - CRV10 Tutorial Day 14

15. Particle Filtering for multi-targets tracking • Joint state vector for all targets and joint likelihood function (Isard, MacCormick 2001, Zhao, Nevatia 2004) • Multiple particle filters (one/target) and combined global likelihood function (Koller-Maier 2001) • The Explorative particle filtering for 3D people tracking (Saboune, Laganiere 09) Jamal Saboune - CRV10 Tutorial Day 15

16. Q & A Jamal Saboune - CRV10 Tutorial Day 16