Boosted Particle Filter: Multitarget Detection and Tracking

1. Boosted Particle Filter: Multitarget Detection and Tracking Fayin Li

2. Motivation and Outline • For a varying number of non-rigid objects, the observation models and target distribution be highly non-linear and non-Gaussian. • The presence of a large, varying number of objects creates complex interactions with overlap and ambiguities. • How object detection can guide the evolution of particle filters? • Mixture particle filter • Boosted objection detection • Boosted particle filter • Observation model in this paper

3. Multitarget Tracking Using Mixture Approach • Given observation and transition models, tracking can be considered as the following Bayesian recursion: • To deal with multiple targets, the posterior is modeled as M-component non-parametric mixture approach • Denote

4. Mixture Approach and Particle Approximation • Then the prediction step • And the updated mixture • where • and • The new filtering is again a mixture of individual component filtering. And the filtering recursion can be performed for each component individually. The normalized weights is only the part of the procedure where the components interact.

5. Particle Approximation • Particles filters are popular at tracking for non-linear and/or non-Gaussian Models. • However they are poor at consistently maintaining the multi-modality of the target distributions that may arise due to ambiguity or the presence of multiple objects. • In standard particle filter, the distribution can be represented by N particles . During recursion, first sample particles from an proposal distribution with weight • Resample the particles based the weights to approximate the posterior

6. Particle Approximation • Because each component can be considered individually in mixture approach, the particles and weights can be updated for each component individually. • The posterior distribution is approximated by • And the particle weight updated rule is • And the mixture weights can be updated using particle weights

7. Example • A simple example governed by the equations

8. Mixture Computation and Variation • The number of modes is rarely known ahead and is unlikely to remain fixed. • It may fluctuate as ambiguities arise and are resolved, or objects appear and disappear. • It is necessary to recompute the mixture representation • Based on the particles and weights, we can use k-means to cluster the sample set and update the number of modes, particles weights, and mixture weights. • In stead of M modes, we can use M different likelihood distributions. When one or more new objects appear, they are detected and initialized with an observation model. Different observation model (data association) allow us track objects.

9. AdaBoost • Given a set of weak classifiers • None much better than random • Iteratively combine classifiers • Form a linear combination • Training error converges to 0 quickly • Test error is related to training margin

10. Weak Classifier 1 Weights Increased Weak Classifier 2 Weak classifier 3 Final classifier is linear combination of weak classifiers Adaboost Algorithm(Freund & Shapire)

11. A variant of AdaBoost for aggressive feature selection

12. % False Pos 0 50 vs false neg determined by 50 100 % Detection T T T T IMAGE SUB-WINDOW Classifier 2 Classifier 3 Object Classifier 1 F F F F NON-Object NON-Object NON- NON-Object Cascading Classifiers for Object Detection • Given a nested set of classifier hypothesis classes • Computational Risk Minimization. Each classifier has 100% detection rate and the cascading reduces the false positive rate

13. Boosted Particle Filter • Cascading Adaboost algorithm gets high detection rate but large number of false positives, which could be reduced by considering the motions of the objects (players). • As with many particle filters, the algorithm simply proceeds by sampling from the transition prior without using the data information. • Boosted Particle Filter uses the following mixture distribution as the proposal distribution for sampling • Here qada is a Gaussian distribution and  can be set dynamically with affecting the convergence of the particle filter. If there is overlap between a component of mixture particle filters and the nearest cluster detected by Adaboost, use the mixture proposal distribution, otherwise set  = 0

14. Observation Model • Hue-Saturation-Value (HSV) histogram is used to represent the region containing the object. It has N = NhNs + Nv bins. • Then a kernel density estimation of the color distribution at time t is given: • Bhattacharyya coefficient is applied to measure the distance between two color histograms • And the likelihood function is • If the object is represented by multiple regions, the likelihood function will be

15. Experiments and Conclusion • Boosted particle filter works well no matter how many objects and adapts successfully to the changes (players come in and out). • Adaboost detects the new players and BPF assigns the particles to them. • Mixture components are well maintained even Adaboost fails. • Object detection and dynamics are combined by forming the proposal distribution for the particle filter: the detections in current frame and the dynamic prediction from the previous time step. • It incorporates the recent observations, which improves the robustness of the dynamics • The detection algorithm gives a powerful tool to obtain and maintain the mixture representation.

16. Tracking Results • Video 1 and Video 2