Moving Object Detection Based on Nonconvex Rank Approximation and Three-Dimensional Total Variation

Yongli Wang; Xiaoyun Ding; Juliang Tao

doi:10.3788/LOP212988

Laser & Optoelectronics Progress, Volume. 60, Issue 4, 0410010(2023)

Moving Object Detection Based on Nonconvex Rank Approximation and Three-Dimensional Total Variation

Yongli Wang, Xiaoyun Ding^*, and Juliang Tao

College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China

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Abstract Get PDF(in Chinese)

Figures & Tables(7)

Fig. 1. Comparison of approximate results of different approximate functions on rank of matrix

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Fig. 2. Foreground detection effect diagrams of different algorithms under dynamic background

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Fig. 3. Foreground detection effect diagrams of different algorithms under continuous frames

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Table 0. [in Chinese]

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Table 0. [in Chinese]

Algorithm 2 The algorithm of moving object detection model（7）
Input：Original video sequence $A$ ，parameter $λ_{1}$ ， $λ_{2}$ ， $μ > 0$ ， $τ > 1$ ，Maximum number of iterations $k_{m a x}$ ；
Initialization： $L = F = G = 0$ ， $X = 0$ ， $k = 0$ ；
1：Update $L^{k + 1}$ via equation（11）；
2：Update $F^{k + 1}$ via algorithm 1；
3：Update $G^{k + 1}$ via equation（24）；
4：Update $X^{k + 1}$ via equation（25）；
5：Update $μ^{k + 1}$ via equation（26）；
6：Check the convergence condition：If $k > k_{m a x}^{}$ or $\frac{{‖A - L^{k + 1} - F^{k + 1} - G^{k + 1}‖}_{F}^{2}}{{‖A‖}_{F}^{2}} \leq ε$ ，stop iteration；
7：Otherwise，let $k = k + 1$ ，return step 1.
Output：Optimal solution $L = L^{k + 1}$ ， $F = F^{k + 1}$ ， $G = G^{k + 1}$ .

Table 0. [in Chinese]

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Table 0. [in Chinese]

Algorithm 1 Update algorithm of $F^{k + 1}$
Input： $A$ ， $L^{k + 1}$ ， $G^{k}$ ， $X^{k}$ ， $μ^{k}$ ， $λ_{1}$ ， $t_{m a x}$ ；
Initialization： $Y^{0} = K^{0} = 0$ ， $γ^{0} > 0$ ， $ρ > 1$ ， $t = 0$ ；
1：Update $F^{t + 1}$ via equation（18）；
2：Update $K^{t + 1}$ via equation（20）；
3：Update $Y^{t + 1}$ via equation（21）；
4：Update $γ^{t + 1}$ via equation（22）；
5：Check the convergence condition：If $t > t_{m a x}$ or $\frac{{‖K^{t + 1} - D f‖}_{F}^{2}}{{‖K^{t + 1}‖}_{F}^{2}} \leq ε$ ，stop iteration； 6：Otherwise，let $t = t + 1$ ，return step 1 and continue the iteration
Output：Optimal solution $F^{k + 1} = F^{t + 1}$ ， $K = K^{t + 1}$ .

Table 1. Comparison of evaluation indicators for foreground detection of different algorithms

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Table 1. Comparison of evaluation indicators for foreground detection of different algorithms

Dateset	Index	RPCA	SUN	AccAltproj	WNNM	NC	LRSD	NCSC	Proposed algorithm
boats	R	0.593	0.629	0.782	0.598	0.821	0.928	0.629	0.934
	P	0.539	0.465	0.459	0.782	0.976	0.376	0.974	0.976
	F	0.565	0.535	0.578	0.678	0.892	0.535	0.764	0.954
curtain	R	0.353	0.412	0.425	0.327	0.784	0.875	0.8997	0.903
	P	0.395	0.448	0.423	0.224	0.785	0.403	0.486	0.786
	F	0.373	0.380	0.424	0.266	0.784	0.557	0.632	0.785
fountain	R	0.714	0.675	0.746	0.533	0.419	0.673	0.673	0.781
	P	0.724	0.422	0.464	0.528	0.850	0.799	0.799	0.803
	F	0.719	0.519	0.572	0.531	0.561	0.731	0.731	0.792
skating	R	0.803	0.371	0.454	0.293	0.179	0.338	0.902	0.972
	P	0.364	0.633	0.547	0.702	0.702	0.553	0.816	0.835
	F	0.501	0.468	0.496	0.413	0.286	0.420	0.974	0.756
Water-surface	R	0.188	0.515	0.535	0.934	0.800	0.933	0.923	0.928
	P	0.401	0.426	0.577	0.584	0.863	0.815	0.816	0.905
	F	0.256	0.466	0.556	0.729	0.850	0.870	0.866	0.892
Waving -trees	R	0.375	0.739	0.738	0.404	0.517	0.374	0.905	0.998
	P	0.609	0.764	0.763	0.468	0.525	0.456	0.966	0.909
	F	0.464	0.751	0.750	0.434	0.521	0.411	0.935	0.951

Table 2. Comparison of evaluation indicators for foreground detection of different algorithms under continuous frames

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Table 2. Comparison of evaluation indicators for foreground detection of different algorithms under continuous frames

Dateset	Index	RPCA	SUN	AccAltproj	WNNM	NC	LRSD	Proposed algorithm
Frame 1613	R	0.781	0.516	0.443	0.530	0.529	0.923	0.912
	P	0.374	0.611	0.580	0.517	0.517	0.664	0.982
	F	0.505	0.560	0.502	0.523	0.531	0.722	0.945
Frame 1614	R	0.765	0.408	0.496	0.500	0.461	0.904	0.887
	P	0.340	0.692	0.539	0.657	0.653	0.666	0.954
	F	0.471	0.513	0.517	0.541	0.541	0.767	0.925
Frame 1615	R	0.808	0.521	0.530	0.430	0.430	0.889	0.911
	P	0.320	0.496	0.517	0.466	0.465	0.666	0.966
	F	0.460	0.509	0.523	0.448	0.447	0.761	0.942

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Yongli Wang, Xiaoyun Ding, Juliang Tao. Moving Object Detection Based on Nonconvex Rank Approximation and Three-Dimensional Total Variation[J]. Laser & Optoelectronics Progress, 2023, 60(4): 0410010

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Paper Information

Category: Image Processing

Received: Nov. 17, 2021

Accepted: Jan. 5, 2022

Published Online: Feb. 13, 2023

The Author Email: Ding Xiaoyun (dxy@sdust.edu.cn)

DOI:10.3788/LOP212988

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology