Adaptive RaoBlackwellized Particle Filter and Its Evaluation for Tracking in Surveillance

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Adaptive Rao-Blackwellized Particle Filter and
Its Evaluation for Tracking in Surveillance

• Xinyu Xu and Baoxin Li, Senior Member, IEEE

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Abstract

• 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).

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Introduction

• 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
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• 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

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RBPF for tracking in surveillance

• a) Partition the state space

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• In this paper ,using 8-D ellipse model to
  describe the target

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• The scale change is related to its position alone
  y axis, so the scale change can be estimated
  conditional on the location components. The 8-D
  state space can separate into 2 groups

Root variables containing the motion information.
Leaf variables containing the scale parameters.
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• b) Overview of the method
• 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
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• Since both color histogram and gradient cues do
  not follow a linear-Gaussian relationship with
  state variable, the observation model is given in
  a general form
• The observations form a linear relationship
  with state L

Image observation
Random noise
Nonlinear function
Gaussian random noise
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Relationship between variables
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The RBPF algorithm
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• Just like regular PF, RBPF represents the
  posterior density by a set of weighted particles
• Each particle is represented by a triplet
  .
• The proposed RBPF algorithm will sample the
  motion using PF, while apply Kalman filter to
  estimate the scale parameters and conditional on
  the motion state.

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(1)Propagate samples

• 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

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• According to the Kalman filter model(4)and(6),
  we project forward the state and error covariance
  using
• After this step, we have

Prediction for the mean of the leaf variables
Covariance for leaves
Observation prediction
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(2)Evaluate weight for each particle

• a) Compute the color histogram for each sample
  ellipse G characterized by ellipse center
  and scale
• Pixels that are closer to the region center are
  given higher weights specified by

Kronecker delta function
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• b) Compute the gradient for each sample ellipse G
  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

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• A simple operator is used to compute the gradient
  in x and y axis for pixelfinally, the
  gradient at point is computed as

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• c) Compute the weight
• one is based 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.

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• Another is based on gradient
• Notice that all the sample is divided by the
  maximum gradient to normalize into range0,1,
  the final weight for each sample is given by

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(3)Select samples

• 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,

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(4)Kalman update for leaf variables

• Kalman update is accomplished by
• After this step, we have

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(5)Compute the mean state at time t

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

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(6)Compute the new noise variance

• 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

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Evaluation of the RBPF algorithm

• Evaluate the performance between RBPF and PF.

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Real data experiment
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Discussion

• Failure caseswhen camera is not mounted higher
  than the target object
• Computation costthe same level of estimation
  accuracy, RBPF needs far fewer particles than PF
  dose hence, it is more efficient than PF.

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Conclusion

• 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.