A new incremental principal component analysis with a forgetting factor for background estimation

Background subtraction is one of commonly used techniques for many applications such as human detection in images. For background estimation, principal component analysis (PCA) is an available method. Since the background sometimes changes according to illumination change or due to a newly appeared stationary article, the eigenspace should be updated momentarily. A naive algorithm for eigenspace updating is to update the covariance matrix. Then, the eigenspace is updated by solving the eigenvalue problem for the covariance matrix. But this procedure is very time consuming because covariance matrix is a very large size matrix. In this paper we propose a novel method to update the eigenspace approximately with exceedingly low computational cost. Main idea to decrees computational cost is to approximate the covariance matrix by low dimensional matrix. Thus, computational cost to solve eigenvalue problem becomes exceedingly decrease. A merit of the proposed method is discussed.