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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
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