Regularised region-based Mixture of Gaussians for dynamic background modelling

Abstract

This paper introduces a momentum-like regularisation term for the region-based Mixture of Gaussians framework. Momentum term has long been used in machine learning, especially in backpropagation algorithms to improve the speed of convergence and subsequently their performance. Here, we prove the convergence of the online gradient method with a momentum term and apply it to background modelling by using it in the update equations of the region-based Mixture of Gaussians algorithm. It is then shown with the help of experimental evaluation on both simulated data and well known video sequences that these regularised updates help improve the performance of the algorithm.

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

“…Here, we show the proof of convergence of the online gradient method with a momentum term [8]. The algorithm is usually of the form…”

“…The proof of convergence of this algorithm can be derived by using the Supermartingale Convergence Theorem [8]. For completeness, we include the derivation of this proof in Appendix.…”

“…Now, similar to [41], the expectation of the error term and the squared error term can then be obtained from (7), (8) and (10) as…”

“…Previously, a rate of convergence of Oð1=k 2 Þ has been proven for the batch version of heavy-ball [7]. Also, Varadarajan et al provided a proof of convergence for the online version of this algorithm in [8]. While this shows that the method converges, the rate of convergence was not given.…”