Moving Object Detection Method Based on Low-Rank and Sparse Decomposition in Dynamic Background
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摘要: 针对背景运动引起动目标检测精度显著下降的问题，该文提出一种基于低秩及稀疏分解的动目标检测方法。所提方法首先引入伽马范数(
$\gamma {\rm{ - norm}}$ )近乎无偏地逼近秩函数以解决核范数过度惩罚较大奇异值从而导致所得最小化问题无法获得最优解进而降低检测性能的问题，而后利用${L_{{1 / 2}}}$ 范数抽取稀疏前景目标以增强对噪声的稳健性，同时基于虚警像素所具有稀疏且空间不连续特性提出空间连续性约束以抑制动态背景像素，进而构建目标检测模型。最后利用基于交替方向最小化(ADM)策略扩展的增广拉格朗日乘子(ALM)法对所得优化问题求解。实验结果表明，与现有主流算法对比，所提方法可显著改善动态背景情况下动目标检测精度。Abstract: Focusing on the issue that the detection accuracy of moving object is significantly reduced by background motion, a low-rank and sparse decomposition based moving object detection method is developed. Firstly, in order to solve the problem that the nuclear norm over-penalizing large singular values lead to the optimal solution of the obtained minimization problem can not be obtained and then the detection performance is decreased, the gamma norm ($\gamma {\rm{ - norm}}$ ) is introduced to acquire almost unbiased approximation of rank function. In what follows, the${L_{{1 / 2}}}$ norm is used to extract the sparse foreground object to enhance the robustness to noise, and the spatial continuity constraint is proposed to suppress dynamic background pixels such that the moving object detection model can be constructed on the basis of the sparse and spatially discontinuous nature of the false alarm pixels. After that, the Augmented Lagrange Multiplier (ALM) method, which is the extension of the Alternating Direction Minimizing (ADM) strategy, can be employed to deal with the acquired constrained minimization problem. Compared with some state-of-the-art algorithms, the experimental results show that the proposed method can significantly improve the accuracy of moving object detection in the case of dynamic background.-
Key words:
- Foreground detection /
- Dynamic background /
- Low-rank /
- Sparsity /
- L1/2 regularization
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表 1 低秩与稀疏分解动目标检测方法
算法：使用ADM策略扩展的ALM法求解问题式(7) 输入：观测矩阵${{Z}}$，参数$\gamma $, ${\lambda _1}$, ${\lambda _2}$, ${\mu _1}$, ${\mu _2}$和$\varphi $。 输出：${{H}}$, ${{K}}$和${{G}}$。 (1)：固定其他变量，计算式(12)以更新变量${{H}}$； (2)：固定其他变量，由式(17)更新变量${{K}}$； (3)：固定其他变量，计算式(22)以更新变量${{G}}$； (4)：由式(23)和式(24)更新拉格朗日乘子${{{Y}}_1}$和${{{Y}}_2}$； (5)：重复步骤(1)—(4)，直至满足收敛条件。 
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表 2 不同场景下6种算法评价指标平均值
评价指标 PCP MoG PRMF DEC BRPCA 本文算法 Precision 0.4715 0.4896 0.5556 0.6938 0.7908 0.8967 Recall 0.7888 0.7978 0.8193 0.9199 0.8953 0.9181 F-measure 0.5440 0.5885 0.6387 0.7643 0.8333 0.9022
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表 3 不同动目标检测算法平均运行时间对比(s)
算法 PCP MoG PRMF DEC BRPCA 本文算法 运行时间 541.55 177.70 105.31 288.36 6161.29 498.42
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