動態(tài)背景下基于低秩及稀疏分解的動目標(biāo)檢測方法
doi: 10.11999/JEIT190452 cstr: 32379.14.JEIT190452
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大連大學(xué)信息工程學(xué)院 大連 116622
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浙江理工大學(xué)信息學(xué)院 杭州 310018
基金項目: 國家自然科學(xué)基金(61301258, 61271379)，中國博士后科學(xué)基金(2016M590218)，重點實驗室基金(61424010106)，河南省高等學(xué)校重點科研項目支持計劃(14A520079)，河南省科技攻關(guān)計劃(162102210168)
Moving Object Detection Method Based on Low-Rank and Sparse Decomposition in Dynamic Background
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College of Information Engineering, Dalian University, Dalian 116622, China
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School of Information Science and technology, Zhejiang Sci-Tech University, Hangzhou 310018, China
Funds: The National Natural Science Foundation of China (61301258, 61271379), China Postdoctoral Science Foundation (2016M590218), The Key Laboratory Foundation (61424010106), The Henan Province Support Plans for Key Scientific Research Projects of Colleges and Universities (14A520079), The Henan Province Plans for Science and Technology Development (162102210168)
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摘要: 針對背景運動引起動目標(biāo)檢測精度顯著下降的問題，該文提出一種基于低秩及稀疏分解的動目標(biāo)檢測方法。所提方法首先引入伽馬范數(shù)(
$\gamma {\rm{ - norm}}$ )近乎無偏地逼近秩函數(shù)以解決核范數(shù)過度懲罰較大奇異值從而導(dǎo)致所得最小化問題無法獲得最優(yōu)解進(jìn)而降低檢測性能的問題，而后利用${L_{{1 / 2}}}$ 范數(shù)抽取稀疏前景目標(biāo)以增強(qiáng)對噪聲的穩(wěn)健性，同時基于虛警像素所具有稀疏且空間不連續(xù)特性提出空間連續(xù)性約束以抑制動態(tài)背景像素，進(jìn)而構(gòu)建目標(biāo)檢測模型。最后利用基于交替方向最小化(ADM)策略擴(kuò)展的增廣拉格朗日乘子(ALM)法對所得優(yōu)化問題求解。實驗結(jié)果表明，與現(xiàn)有主流算法對比，所提方法可顯著改善動態(tài)背景情況下動目標(biāo)檢測精度。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 低秩與稀疏分解動目標(biāo)檢測方法
算法：使用ADM策略擴(kuò)展的ALM法求解問題式(7) 輸入：觀測矩陣${{Z}}$，參數(shù)$\gamma $, ${\lambda _1}$, ${\lambda _2}$, ${\mu _1}$, ${\mu _2}$和$\varphi $。 輸出：${{H}}$, ${{K}}$和${{G}}$。 (1)：固定其他變量，計算式(12)以更新變量${{H}}$； (2)：固定其他變量，由式(17)更新變量${{K}}$； (3)：固定其他變量，計算式(22)以更新變量${{G}}$； (4)：由式(23)和式(24)更新拉格朗日乘子${{{Y}}_1}$和${{{Y}}_2}$； (5)：重復(fù)步驟(1)—(4)，直至滿足收斂條件。 
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表 2 不同場景下6種算法評價指標(biāo)平均值
評價指標(biāo) 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 不同動目標(biāo)檢測算法平均運行時間對比(s)
算法 PCP MoG PRMF DEC BRPCA 本文算法 運行時間 541.55 177.70 105.31 288.36 6161.29 498.42
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