1、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
2、 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 c
3、an be considered as the following Bayesian recursion:To deal with multiple targets, the posterior is modeled as M-component non-parametric mixture approachDenote,Mixture Approach and Particle Approximation,Then the prediction stepAnd the updated mixturewhere andThe new filtering is again a mixture o
4、f 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.,Particle Approximation,Particles filters are popular at tracking for non-linear and/or non-Gaussian
5、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 fro
6、m an proposal distributionwith weight Resample the particles based the weights to approximate the posterior,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 distri
7、bution is approximated byAnd the particle weight updated rule isAnd the mixture weights can be updated using particle weights,Example,A simple example governed by the equations,Mixture Computation and Variation,The number of modes is rarely known ahead and is unlikely to remain fixed. It may fluctua
8、te 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 mo
9、des, 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 classifiersNone much better than random Iterativ
10、ely combine classifiers Form a linear combinationTraining error converges to 0 quickly Test error is related to training margin,Adaboost Algorithm (Freund & Shapire),A variant of AdaBoost for aggressive feature selection,Cascading Classifiers for Object Detection,Given a nested set of classifier hyp
11、othesis classesComputational Risk Minimization. Each classifier has 100% detection rate and the cascading reduces the false positive rate,Boosted Particle Filter,Cascading Adaboost algorithm gets high detection rate but large number of false positives, which could be reduced by considering the motio
12、ns 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 samplingHere qada is a Gaussian distrib
13、ution 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,Observation Model,Hue-Saturation-Value (H
14、SV) 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 t
15、he object is represented by multiple regions, the likelihood function will be,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 t
16、hem. 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,
