You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Although low-rank and sparse decomposition based methods have been successfully applied to the problem of moving object detection using structured sparsity-inducing norms, they are still vulnerable to significant illumination changes that arise in certain applications. We are interested in moving object detection in applications involving time-lapse image sequences for which current methods mistakenly group moving objects and illumination changes into foreground. Our method relies on the multilinear (tensor) data low-rank and sparse decomposition framework to address the weaknesses of existing methods. The key to our proposed method is to create first a set of prior maps that can characterize the changes in the image sequence due to illumination. We show that they can be detected by a k-support norm. To deal with concurrent, two types of changes, we employ two regularization terms, one for detecting moving objects and the other for accounting for illumination changes, in the tensor low-rank and sparse decomposition formulation. Through comprehensive experiments using challenging datasets, we show that our method demonstrates a remarkable ability to detect moving objects under discontinuous change in illumination, and outperforms the state-of-the-art solutions to this challenging problem.

Cited Abstract(s):
[1]: Foreground detection is the first step in video surveillance system to detect moving objects. Principal Components Analysis (PCA) shows a nice framework to separate moving objects from the background but without a mechanism of robust analysis, the moving objects may be absorbed into the background model. This drawback can be solved by recent researches on Robust Principal Component Analysis (RPCA). The background sequence is then modeled by a low rank subspace that can gradually change over time, while the moving foreground objects constitute the correlated sparse outliers. In this paper, we propose to use a RPCA method based on low-rank and block-sparse matrix decomposition to achieve foreground detection. This decomposition enforces the low-rankness of the background and the block-sparsity aspect of the foreground. Experimental results on different datasets show the pertinence of the proposed approach.

[2]: Background subtraction has been widely investigated in recent years. Most previous work has focused on stationary cameras. Recently, moving cameras have also been studied since videos from mobile devices have increased significantly. In this paper, we propose a unified and robust framework to effectively handle diverse types of videos, e.g., videos from stationary or moving cameras. Our model is inspired by two observations: 1) background motion caused by orthographic cameras lies in a low rank subspace, and 2) pixels belonging to one trajectory tend to group together. Based on these two observations, we introduce a new model using both low rank and group sparsity constraints. It is able to robustly decompose a motion trajectory matrix into foreground and background ones. After obtaining foreground and background trajectories, the information gathered on them is used to build a statistical model to further label frames at the pixel level. Extensive experiments demonstrate very competitive performance on both synthetic data and real videos.
The second group of methods used the additional prior knowledge on the spatial continuity of objects to constrain sparse matrix @math and improve the detection accuracy [1] [2] . Using spatial continuity (e.g., @math -norm in [1] ) to enforce the block-sparsity of the foreground, results become more stable than conventional RPCA in the presence of illumination changes. However, it remains a challenge to handle moving shadows or significant changes in illumination. Furthermore, the position of an object in a time-lapse image sequence is discontinuous from one image to another so that the continuity assumption is invalid as a way to separate moving objects and changes in illumination.