Total Variation Regularized RPCA for Irregularly Moving Object Detection Under Dynamic Background Moving object detection is one of the most fundamental tasks in computer vision. Many classic and contemporary algorithms work well under the assumption that backgrounds are stationary and movements are continuous, but degrade sharply when they are used in a real detection system, mainly due to: 1) the dynamic background (e.g., swaying trees, water ripples and fountains in real scenarios, as well as raindrops and snowflakes in bad weather) and 2) the irregular object movement (like lingering objects). This paper presents a unified framework for addressing the difficulties mentioned above, especially the one caused by irregular object movement. This framework separates dynamic background from moving objects using the spatial continuity of foreground, and detects lingering objects using the temporal continuity of foreground. The proposed framework assumes that the dynamic background is sparser than the moving foreground that has smooth boundary and trajectory. We regard the observed video as being made up of the sum of a low-rank static background, a sparse and smooth foreground, and a sparser dynamic background. To deal with this decomposition, i.e., a constrained minimization problem, the augmented Lagrangian multiplier method is employed with the help of the alternating direction minimizing strategy. Extensive experiments on both simulated and real data demonstrate that our method significantly outperforms the state-of-the-art approaches, especially for the cases with dynamic backgrounds and discontinuous movements.