Adaptive rao blackwellized particle filter and it s evaluation for tracking in surveillance
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Adaptive Rao-Blackwellized Particle Filter and It’s Evaluation for Tracking in Surveillance. Xinyu Xu and Baoxin Li, Senior Member, IEEE. Abstract.

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Adaptive rao blackwellized particle filter and it s evaluation for tracking in surveillance

Adaptive Rao-Blackwellized Particle Filter and It’s Evaluation for Tracking in Surveillance

Xinyu Xu and Baoxin Li, Senior Member, IEEE


Abstract
Abstract Evaluation for Tracking in Surveillance

  • In this paper, by proposing an adaptive Rao-Blackwellized Particle Filter (RBPF) for tracking in surveillance, we show how to exploit the analytical relationship among state variables to improve the efficiency and accuracy of a regular particle filter (PF).


Introduction
Introduction Evaluation for Tracking in Surveillance

  • Visual tracking is an important step in many practical applications.

  • Generally, suppose we have an estimator depending upon 2 variables R and L, the RB theorem reveals its variance satisfies:

Non-negative


  • For the visual tracking problem, let denote the state to be estimated and the observation, with subscript t the time index.

  • The key idea of RBPF is to partition the original state-space into two parts and .

  • The justification for this decomposition follows from the factorization of the posterior probability


Rbpf for tracking in surveillance
RBPF for tracking in surveillance be estimated and the observation, with subscript

  • a) Partition the state space



Root variables containing the motion information.

Leaf variables containing the scale parameters.


  • b) Overview of the method target

  • In this work, root variables are propagated by a first order system motion model defined by

  • Conditional on the root variables, the leaf variables forms a linear-Gaussian substructure specified by

transition matrix

random noise

Gaussian random noise

A function encoding the conditional relation of L


Image observation

Random noise

Nonlinear function

Gaussian random noise


Relationship between variables
Relationship between variables linear-Gaussian relationship with state variable, the observation model is given in a general form:


The rbpf algorithm
The RBPF algorithm linear-Gaussian relationship with state variable, the observation model is given in a general form:



1 propagate samples
(1)Propagate samples by a set of weighted particles:

  • a) Sample the object motion according to

    After this step, we have

    minus sign is denotes the corresponding variable is a priori estimate

  • b) Kalman prediction for leaf states according to


Prediction for the mean of the leaf variables

Covariance for leaves

Observationprediction


2 evaluate weight for each particle
(2)Evaluate weight for each particle by a set of weighted particles:

  • a) Compute the color histogram for each sample ellipseΓ characterized by ellipse center and scale

  • Pixels that are closer to the region center are given higher weights specified by

Kronecker delta function


  • b) Compute the gradient by a set of weighted particles:for each sample ellipseΓ characterized by ellipse center and scalethe gradient of a sample ellipse is computed as an average over gradients of all the pixels on the boundarywhere the gradient at pixel is set to the maximum gradient by a local search along the normal line of the ellipse at location



  • c) Compute the weight by a set of weighted particles:

  • one isbased on color histogram similarity between the hypothetical region and the target modelp stands for the color histogram of a sample hypothesis in the newly observed image, and q represents the color histogram of target model.


  • Another is based on gradient by a set of weighted particles:

  • Notice that all the sample is divided by the maximum gradient to normalize into range[0,1], the final weight for each sample is given by


3 select samples
(3)Select samples by a set of weighted particles:

  • Resampling with replacementthe latest measurements will be used to modify the prediction PDF of not only the root variables but also the leaf variables.

  • After this step,


4 kalman update for leaf variables
(4)Kalman update by a set of weighted particles:for leaf variables

  • Kalman update is accomplished by

  • After this step, we have


5 compute the mean state at time t
(5)Compute the mean state by a set of weighted particles:at time t

  • Since resampling has been done, the mean state can be simply computed as the average of the state particles


6 compute the new noise variance
(6)Compute the new noise variance by a set of weighted particles:

  • We found that when velocity is small and constant, we only need a small noise variance to reach the smallest MSE, if velocity changes dramatically, we need a much larger noise variance to reach the lowest MSE.

  • The noise variance is computed by


Evaluation of the rbpf algorithm
Evaluation of the RBPF algorithm by a set of weighted particles:

  • Evaluate the performance between RBPF and PF.


Real data experiment
Real data experiment by a set of weighted particles:


Discussion
Discussion by a set of weighted particles:

  • Failure cases:when camera is not mounted higher than the target object…

  • Computation cost:the same level of estimation accuracy, RBPF needs far fewer particles than PF dose; hence, it is more efficient than PF.


Conclusion
Conclusion by a set of weighted particles:

  • Comparative studies using both simulated and real data have demonstrated the improved performance of the proposed RBPF over regular PF.

  • Future working: to find a proper dependency model from a large number of state variables.


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