1. Improved Adaptive Gaussian Mixture Model for Background
Zoran Zivkovic
Pattern Recognition, ICPR Proceedings of the 17th International Conference on

2. Outline Introduction Gaussian Mixture Model
Select the number of components
Experiments
Conclusion

3. 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

4. Gaussian Mixture Model
are the estimate of the means
are the estimate of the variance
are mixing weight (non-negative and add up to one)

5. Gaussian Mixture Model
Update equation a
原本是pdf

6. Gaussian Mixture Model
If the current pixel didn’t match with any distributions s
Decide pixel is in background/foreground d sd

7. Select the number of components
Goal choose the proper number of component
Implement
Use prior and likelihood to select proper models for given data

8. Select the nmber of components
Maximum Likelihood (ML)
Likelihood function:
Assume we have t data samples a

9. Select the number of components
Maximum Likelihood (ML) a
Constraint: weights sum up to one
The prior update func.

10. Select the number of components
Dirichlet prior a
presents the prior evidence for the class m – the number of samples that belong to that class a priori
Use negative coefficients
means that accept class-m exist only if there is enough evidence from the data for the existence of this class

11. Select the number of components
Maximum Likelihood (ML) +Dirichlet prior a
Fixed
Expect a few components M and is small

12. Experiments
New GMM with slight improvement

13. Experiments
1 Dist.
Max 4 Dist.

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

15. Conclusion Present an improved GMM background subtraction scheme
The new algorithm can select the needed number of component

16. The method of Stauffer and Grimson
is the learning rate that is defined by usesr