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

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 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 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 be estimated and the observation, with subscript

- a) Partition the state space

- The scale change is related to its position alone targety 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.

- 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

- 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

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

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

- 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.

(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

- According to the Kalman filter model by a set of weighted particles:(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

Observationprediction

(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

- A simple operator is used to compute the gradient in by a set of weighted particles:x and y axis for pixelfinally, the gradient at point is computed as

- 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 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 by a set of weighted particles:for leaf variables

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

(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 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 by a set of weighted particles:

- Evaluate the performance between RBPF and PF.

Real data experiment by a set of weighted particles:

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 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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