  Moving object detection and its associated background-foreground separation
have been widely used in a lot of applications, including computer vision,
transportation and surveillance. Due to the presence of the static background,
a video can be naturally decomposed into a low-rank background and a sparse
foreground. Many regularization techniques, such as matrix nuclear norm, have
been imposed on the background. In the meanwhile, sparsity or smoothness based
regularizations, such as total variation and $\ell_1$, can be imposed on the
foreground. Moreover, graph Laplacians are further imposed to capture the
complicated geometry of background images. Recently, weighted regularization
techniques including the weighted nuclear norm regularization have been
proposed in the image processing community to promote adaptive sparsity while
achieving efficient performance. In this paper, we propose a robust dual-graph
regularized moving object detection model based on the weighted nuclear norm
regularization, which is solved by the alternating direction method of
multipliers (ADMM). Numerical experiments on body movement data sets have
demonstrated the effectiveness of this method in separating moving objects from
background, and the great potential in robotic applications.
