Auto-regressive dynamical models

1. Auto-regressive dynamical models • Continuous form of Markov process • Linear Gaussian model • Hidden states and stochastic observations (emissions) • Statistical filters: Kalman, Particle • EM learning • Mixed states

2. Auto-regressive dynamical model • Configuration • AR model • Parametric shape/texture model, • eg curve model: ARP order driven by independent noise possibly nonlinear

3. Deformable curve model curve model: Planar affine + learned warps Active shape models (Cootes&Taylor, 93) Residual PCA (“Active Contours”, Blake & Isard, 98) Active appearance models (Cootes, Edwards &Taylor, 98)

4. Linear AR model (“Active Contours”, Blake and Isard, Springer 1998) • Configuration • Linear Gaussian AR model • Prior shape • “Steady state” prior (1st order)

5. Gaussian processes for shape & motion intra-class single object (Reynard, Wildenberg, Blake & Marchant, ECCV 96)

6. Kalman filter (Gelb 74) • Stochastic observer • Kalman filter (Forward filter) • Kalman smoothing filter (Forward-Backward) independent noise also etc.

7. Classical Kalman filter

8. Visual clutter

9. Visual clutter  observational nonlinearity

10. Particle Filter: Non-Gaussian Kalman filter www.research.microsoft.com/~ablake/talks/MonteCarlo.ppt

11. Particle Filter (PF) continue

12. “JetStream”: cut-and-paste by particle filtering • particles “sprayed” along the contour

13. Propagating Particles • particles “sprayed” along the contour • contour smoothness prior

14. Branching

15. Direct observations: “Classic” Yule-Walker • Learn parameters • by maximizing: • which for linear AR process  minimizing • Finally solve: • where “sufficient statistics” are: MLE Learning of a linear AR Model

16. Handwriting “Scribble” -- simulation of learned ARP model -- disassembly

17. Simulation of learned Gait -- simulation of learned ARP model

18. Walking Simulation (ARP)

19. Walking Simulation (ARP + HMM) (Toyama & Blake 2001)

20. Dynamic texture (S. Soatto, G. Doretto, Y. N. Wu, ICCV 01; A. Fitzgibbon, ICCV01)

21. Speech-tuned filter (Blake, Isard & Reynard, 1985)

22. EM learning • Stochastic observations z: unknown -- hidden unavailable – classic EM: • M-step i.e. • E-step FB smoothing

23. PF: forward only

24. PF: forward-backward continue

25. Juggling (North et al., 2000)

26. Learned Dynamics of Juggling State lifetimes and transition rates also learned

27. Juggling

28. Perception and Classification Ballistic (left) Catch, carry, throw (left)

29. Underlying classifications

30. Learning Algorithms EM-P

31. 1D  Markov models • 1D  Markov models • 2D Markov models

32. EM-PF Learning • Forward-backward particle smoother (Kitagawa 96, Isard and Blake, 98) for non-Gaussian problems: • Generates particles with weights • Autocorrelations: • Transition Frequencies: