Abstract: Low rank and sparse decomposition based methods use [l1]-norm penalty to model moving object as sparse outliers. With these methods, the observed video matrix can be decomposed into a sparse matrix and a low-rank matrix, which model the foreground and background respectively. However, in many practical scenarios, the background is usually affected by dynamic background（e.g.water surface, waving trees）, thus the fixed [l1]-norm cannot offer a satisfactory performance. The distributions of the moving parts are not only pixel-wised sparse but also spatial continuous. In this paper, by introducing the spatial fused sparse constraint into low-rank model, the foreground is constrained by both spatial continuity constraint and sparse constraint. Furthermore, an adaptive parameter selection method is adopted in the proposed method. Experiments on public datasets demonstrate that the proposed method outperforms the state-of-the-arts methods and works effectively on complex videos.

Key words: Robust Principle Component Analysis（RPCA）, low-rank modeling, spatial constraint, foreground detection

摘要： 传统的低秩稀疏分解方法使用[l1]范数把场景中的运动目标建模为稀疏离群值，分离出低秩的背景成分与稀疏的运动目标成分。然而，在许多实际场景中往往会有动态背景的情形（例如水面波纹、树木摇动），[l1]范数并不能区分出这些干扰与真实目标，从而大大影响检测效果。实际上，运动目标区域中的像素不仅仅具有稀疏性，还具有空间分布上的连续性。通过引入空间融合稀疏约束，在空间连续性和稀疏性两方面对运动目标进行建模，使模型更符合目标像素的分布规律。同时，设计了一种自适应的参数更新方法，使算法的鲁棒性进一步提升。在公共数据集上的大量实验表明，相比于传统方法，该算法在准确率和鲁棒性方法有很大提高。

关键词: 鲁棒主成分分析（RPCA）, 低秩建模, 空间约束, 前景检测