2. Stanford CS223B Computer Vision, Winter 2005 Lecture 12: Filters / Motion Tracking Sebastian Thrun, Stanford Rick Szeliski, Microsoft Hendrik Dahlkamp and Dan Morris, Stanford

3. Sebastian Thrun Stanford University CS223B Computer Vision Moving Objects

4. Sebastian Thrun Stanford University CS223B Computer Vision Kalman Filter Tracking

5. Sebastian Thrun Stanford University CS223B Computer Vision Particle Filter Tracking

6. Sebastian Thrun Stanford University CS223B Computer Vision Mixture of KF / PF (Unscented PF)

7. Sebastian Thrun Stanford University CS223B Computer Vision Tracking: First Idea! updateinitial position x y x y prediction x y measurement x y

8. Sebastian Thrun Stanford University CS223B Computer Vision Kalman Filters

9. Sebastian Thrun Stanford University CS223B Computer Vision Kalman Filters prior Measurement evidence posterior

10. Sebastian Thrun Stanford University CS223B Computer Vision A Quiz prior Measurement evidence posterior?

11. Sebastian Thrun Stanford University CS223B Computer Vision Kalman Filter n Linear Measurement model n Linear Change

12. Sebastian Thrun Stanford University CS223B Computer Vision Partially Observable Markov Chains statestate x 4 state x 3 state x 2 state x 1 z2z2 z3z3 z4z4 measurement z 1 state x 4 state x 3 state x 2 state x 1 Bayes filters: HMMs DBNs POMDPs Kalman filters Condensation

13. Sebastian Thrun Stanford University CS223B Computer Vision Bayes Filters x = state z = observation u = control t = time [Kalman 60, Rabiner 85] Markov Bayes Markov

14. Sebastian Thrun Stanford University CS223B Computer Vision Kalman Filter: Measurement Update n Linear Measurement model

15. Sebastian Thrun Stanford University CS223B Computer Vision Kalman Filter: Prediction n Linear Change

16. Sebastian Thrun Stanford University CS223B Computer Vision Putting It All Together n Measurements n Change n Prediction n Measurement Update updateinitial position x y x y prediction x y measurement x y

17. Sebastian Thrun Stanford University CS223B Computer Vision Can We Do Better?

18. Sebastian Thrun Stanford University CS223B Computer Vision Kalman, Better! initial positionpredictionmeasurement next prediciton update

19. Sebastian Thrun Stanford University CS223B Computer Vision We Can Estimate Velocity! past measurements prediction

20. Sebastian Thrun Stanford University CS223B Computer Vision Kalman Filter For 2D Tracking n Linear Measurement model (now with 4 state variables) n Linear Change

21. Sebastian Thrun Stanford University CS223B Computer Vision Putting It Together Again n Measurements n Change n Prediction n Measurement Update

22. Sebastian Thrun Stanford University CS223B Computer Vision Why Linear??

23. Sebastian Thrun Stanford University CS223B Computer Vision Nonlinear Functions…

24. Sebastian Thrun Stanford University CS223B Computer Vision Linearization: Extended Kalman Filter

25. Sebastian Thrun Stanford University CS223B Computer Vision Unscented Kalman Filter

26. Sebastian Thrun Stanford University CS223B Computer Vision Particle Filters n An alternative technique for tracking n Easier to implement n Nonlinear n Better for data association n In CV, known as “Condensation Algorithm”

27. Sebastian Thrun Stanford University CS223B Computer Vision Particle Filter

28. Sebastian Thrun Stanford University CS223B Computer Vision Particle Filters: Basic Idea (equality for ) set of n particles X t See e.g., [Doucet 98, deFreitas 98]

29. Sebastian Thrun Stanford University CS223B Computer Vision Basic Particle Filter Algorithm Initialization: X 0  n particles x 0 [i] ~ p(x 0 ) particleFilters( X t  1 ){ for i=1 to n x t [i] ~ p(x t | x t  1 [i] ) (prediction) w t [i] = p(z t | x t [i] ) (importance weights) endfor for i=1 to n include x t [i] in X t with probability  w t [i] (resampling) }

30. Sebastian Thrun Stanford University CS223B Computer Vision Particle Filters: Illustration With: Wolfram Burgard, Dieter Fox, Frank Dellaert

31. Sebastian Thrun Stanford University CS223B Computer Vision Examples Siu Chi Chan McGill University

32. Sebastian Thrun Stanford University CS223B Computer Vision Another Example Mike Isard and Andrew Blake

33. Sebastian Thrun Stanford University CS223B Computer Vision Tracking Fast moving Objects K. Toyama, A.Blake

34. Sebastian Thrun Stanford University CS223B Computer Vision Tracking with Omni directional Vision n Ben Krose’s Research

35. Sebastian Thrun Stanford University CS223B Computer Vision More Particle Filter Tracking David Stavens, Andrew Lookingbill, David Lieb, CS223b Winter 2004

36. Sebastian Thrun Stanford University CS223B Computer Vision Ninlinearity in the Particle Filter