1. Michael Isard and Andrew Blake, IJCV 1998 Presented by Wen Li Department of Computer Science & Engineering Texas A&M University

2.  Problem Description  Previous Methods  CONDENSATION  Experiment  Conclusion

3.  What’s the task  Track outlines and features of foreground objects  Video frame-rate  Visual clutter

4.  Challenges  Elements in background clutter may mimic parts of foreground features  Efficiency

5.  Directed matching  Geometric model of object  + motion model  Kalman Filter

6.  Main Idea  Model the object  Prediction – predict where the object would be  Measurement – observe features that imply where the object is  Update – Combine measurement and prediction to update the object model

7.  Assumption  Gaussian prior  Markov assumption

9.  Essential Technique  Bayes filter  Limitation  Gaussian distribution  Does not work well in “clutter” background

10.  Stochastic framework + Random sampling  Difference with Kalman Filter  Kalman Filter – Gaussian densities  Condensation – General situation

12.  Symbols + goal  Assumptions  Modelling  Dynamic model  Observation model  Factored sampling  CONDENSATION algorithm

13.  Symbols  x t – the state of object at time t  X t – the history of x t, {x 1,…, x t }  z t – the set of image features at time t  Z t – the history of z t, {z 1,…, z t }  Goal  Calculate the model of x at time t, given the history of the measurements. -- P(x t | Z t )

14.  Assumptions  Markov assumption ▪ The new state is conditioned directly only on the immediately preceding state ▪ P(x t | X t-1 )=p(x t |x t-1 )  z t -- Independence (mutually and with respect to the dynamical process) ▪ P( Z t | X t )=∏ p(z i |x i ) ▪ P(z i |x i ) = p(z|x)

15.  Dynamic model   P(x t |x t-1 )  Observation model 

16.  Propagation – applying Bayes rules Cannot be evaluated in closed form

17.  Factored Sampling  Approximate the probability density p(x|z)  In single image  Step 1: generate a sample set {s (1),…, s (N) }  Step 2: calculate the weight π i corresponding to each s (i), using p(z | s (i) ) and normalization  Step 3: calculate the mean position of x, that

18.  Factored Sampling -- illustration

19.  The CONDENSATION algorithm – finally!  Initialize p(x 0 )  For any time t ▪ Predict: select a sample set {s’ t (1),…, s’ t (N) } from old sample set {s t- 1 (1),…, s t-1 (N) } according to π t-1 (n) predict a new sample-set {s t (1),…, s t (N) } from {s’ t (1),…, s’ t (N) }, using the dynamic model we mentioned previously ▪ Measure: calculate weights π i according to observed features, then calculate mean position of x t as in the single image

21.  On Multi-Model Distribution The shape-space for tracking is built from a hand-drawn template of head and shoulder

22. N=1000, frame rate=40 ms

23.  On Rapid Motions Through Clutter

25.  On Articulated Object

27.  On Camouflaged Object

28.  Good news:  Works on general distributions  Deals with Multi-model  Robust to background clutter  Computational efficient  Controllable of performance by sample size N  Not too difficult

29.  Problems might be  Initialization  “hand-drawn” shape-space