Improved Adaptive Gaussian Mixture Model for Background

Zoran Zivkovic

Pattern Recognition, 2004. ICPR 2004. Proceedings of the 17th International Conference on

Outline

Introduction Gaussian Mixture Model Select the number of components Experiments Conclusion

Introduction Background subtraction is the common

process for surveillance system

Gaussian mixture model (GMM) was proposed for background subtraction Like Gaussian Dist-s model

These GMM-s use a fixed number of components

Gaussian Mixture Model

are the estimate of the means are the estimate of the variance are mixing weight (non-negative an

d add up to one)

Gaussian Mixture Model

Update equation a

a

a

Gaussian Mixture Model

If the current pixel didn’t match with any distributions s

Decide pixel is in background/foreground d

sd

Select the number of components

Goal choose the proper number of component

Implement Use prior and likelihood to select

proper models for given data

Select the nmber of components Maximum Likelihood (ML)

Likelihood function:

Assume we have t data samples

a

Select the number of components

Maximum Likelihood (ML) a

a

Constraint: weights sum up to one

The prior update func.

Select the number of components

Dirichlet prior a presents the prior evidence for the cla

ss m – the number of samples that belong to that class a priori

Use negative coefficients means that accept class-m exist only if there i

s enough evidence from the data for the existence of this class

Cm

Select the number of components

Maximum Likelihood (ML) +Dirichlet prior a

a

Fixed Expect a few components M and is small

a

Experiments

New GMM with slight improvement

Experiments

Max 4 Dist.

1 Dist.

Experiments

In highly dynamic ‘tree’, the processing time is almost the same

Conclusion

Present an improved GMM background subtraction scheme

The new algorithm can select the needed number of component

The method of Stauffer and Grimson

is the learning rate that is defined by usesr