Inequality-Constrained RPCA for Shadow Removal and Foreground Detection

State-of-the-art background subtraction and foreground detection methods still face a variety of challenges, including illumination changes, camouflage, dynamic backgrounds, shadows, intermittent object motion. Detection of foreground elements via the robust principal component analysis (RPCA) method and its extensions based on low-rank and sparse structures have been conducted to achieve good performance in many scenes of the datasets, such as Changedetection.net (CDnet); however, the conventional RPCA method does not handle shadows well. To address this issue, we propose an approach that considers observed video data as the sum of three parts, namely a row-rank background, sparse moving objects and moving shadows. Next, we cast inequality constraints on the basic RPCA model and use an alternating direction method of multipliers framework combined with Rockafeller multipliers to derive a closed-form solution of the shadow matrix sub-problem. Our experiments have demonstrated that our method works effectively on challenging datasets that contain shadows.