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Boosted Particle Filter: Multitarget Detection and Tracking Fayin Li.
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Transcript of Boosted Particle Filter: Multitarget Detection and Tracking Fayin Li.
Boosted Particle Filter: Multitarget Detection and Tracking
Fayin Li
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
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
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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.
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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
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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
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Example
• A simple example governed by the equations
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),|()|( 22ytttt xyNxyp
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.
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
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rated" confidence" },{)( also xjh
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Adaboost Algorithm(Freund & Shapire) Weak
Classifier 1
WeightsIncreased
Weak classifier 3
Final classifier is linear combination of weak classifiers
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Weak Classifier 2
A variant of AdaBoost for aggressive feature selection G iven exam ple im ages (x1 ,y1) , … , (xn ,yn) w here y i = 0, 1 for negative and positive
exam ples respectively. In itialize w eights w 1 ,i = 1 /(2m ), 1 /(2 l) for train ing exam ple i, w here m and l are the
num ber of negatives and positives respectively. For t = 1 … T
1) N orm alize w eights so that w t is a d istribution 2) For each feature j train a classifier h j and evaluate its error j w ith respect to w t. 3) C hose the classifier h j w ith low est error. 4) U pdate w eights according to :
1,,1
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w here e i = 0 is x i is classified correctly, 1 o therw ise, and
1 t
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T he final strong classifier is:
otherwise
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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
vs false neg determined by
% False Pos
% D
etec
tion
0 50
50
100
ObjectIMAGESUB-WINDOW
Classifier 1
F
T
NON-Object
Classifier 3T
F
NON-Object
F
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NON-
Classifier 2T
F
NON-Object
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
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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
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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.
Tracking Results
• Video 1 and Video 2