FAST CONVERGENCE OF REGULARISED REGION-BASED MIXTURE OF GAUSSIANS FOR DYNAMIC BACKGROUND MODELLING

 

Abstract

The momentum term has long been used in machine learning algorithms, especially back-propagation, to improve their speed of convergence. In this work, we derive an expression to prove the O(1/k2) convergence rate of the online gradient method, with momentum type updates, when the individual gradients are constrained by a growth condition. We then apply these type of updates to video background modelling by using it in the update equations of the Region-based Mixture of Gaussians algorithm. Extensive evaluations are performed on both simulated data, as well as challenging real world scenarios with dynamic backgrounds, to show that these regularised updates help the mixtures converge faster than the conventional approach and consequently improve the algorithms performance.

 

Results

Convergence of gradient methods without a momentum term (blue/dashed line) and with a momentum term (black/solid line) for 100, 1000 and 10,000 data samples from a Normal Distribution. First Row: Mean – 128, S.D. – 8; Second Row: Mean – 128, S.D. – 16; Third Row: Mean – 128, S.D. – 32; Fourth Row: Mean – 128, S.D. – 64.
Comparison of F-Measures for all the categories in CDNet 2014 Benchmark for the different types of MoG based background subtraction algorithms. MoG (S&G) - Stauffer and Grimson's MoG algorithm, MoG (ZZ) - Zoran Zivkovic's MoG algorithm , MoG (K&B) - KaewTraKulPong and Bowden's MoG algorithm, Regularised RMoG - This work.

 

Citation

Fast convergence of regularised Region-based Mixture of Gaussians for dynamic background modelling

Sriram Varadarajan, Hongbin Wang, Paul Miller, Huiyu Zhou

Computer Vision and Image Understanding, Volume 136, July 2015, Pages 45-58, ISSN 1077-3142

 

bibtex:

@article{Varadarajan201545,
title = "Fast convergence of regularised Region-based Mixture of Gaussians for dynamic background modelling",
journal = "Computer Vision and Image Understanding ",
volume = "136",
pages = "45 - 58",
year = "2015",
note = "Generative Models in Computer Vision and Medical Imaging ",
doi = "http://dx.doi.org/10.1016/j.cviu.2014.12.004",
url = "http://www.sciencedirect.com/science/article/pii/S1077314214002422",
author = "Sriram Varadarajan and Hongbin Wang and Paul Miller and Huiyu Zhou",
}