Nonnegative Robust PCA for Background and Foreground Image Decomposition

Abstract

Nowadays, video surveillance and motion detection system are widely used in various environments. With the relatively low-price cameras and highly automated monitoring system, video and image analysis on road, highway and skies becomes realistic. The key process in the analysis is to separate the useful information such as moving foreground objects from the original video sequence where Robust Principal Component Analysis (RPCA) plays an important role in extracting the foreground objects. RPCA have been widely used in data analysis and dimension reduction with applications in image recovery, information clustering and computer vision. But one drawback of RPCA lies in the fact that it does not guarantee the nonnegativity of pixels. It is important to have nonnegative foreground object since negative pixels that are not in the range between 0 and 255 are meaningless and the foreground objects are thus not visible. State-of-the-art methods do not consider the nonnegativity of the foreground object in their algorithms. This thesis focuses on the problem of extracting foreground moving object from background scenes and guarantee the nonnegativity of foreground object. This thesis proposes a method that combines RPCA and Nonnegative Matrix Factorization (NMF). It ensures the pixels that constitute the foreground object is nonnegative by using the basic model of RPCA and nonnegative components that NMF provides. The efficacy of the proposed algorithms is tested on publicly available dataset. Experiment shows in detail how the proposed algorithms achieve in recovering the foreground object with high true positive rate. Together with RPCA algorithm, the performance of recovery is compared and their advantages and disadvantages are discussed.