Positioning Algorithm of Homonymous Object Points in Multi-Vision System Based on Weighted Levenberg-Marquardt

Camera	f /mm	u₀ /pixel	v₀ /pixel	k₁ /10^-5	k₂ /10^-8	p₁ /10^-6	p₂ /10^-6
C₁	8.04782	1311.726	979.674	7.6504	9.1907	1.9608	7.3531
C₂	8.06759	1289.349	936.021	8.3771	9.4679	4.7539	2.6350
C₃	8.07361	1257.554	941.253	9.0845	5.2863	3.6931	4.5361
C₄	8.05470	1295.348	967.692	7.9584	8.0388	6.8472	3.7469

Table 2. Calibration results of external parameters

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Table 2. Calibration results of external parameters

Camera	External parameter matrix
C₁	$[\begin{array}{l} - 0.6424 & - 0.0262 & - 0.7659 & 3868.3 \\ 0.6957 & 0.3993 & - 0.5971 & 2798.9 \\ 0.3215 & - 0.9164 & - 0.2383 & 2704.8 \\ 0 & 0 & 0 & 1 \end{array}]$
C₂	$[\begin{array}{l} - 0.5712 & - 0.2832 & 0.7704 & - 3942.6 \\ - 0.8045 & 0.0071 & - 0.5939 & 2876.2 \\ 0.1627 & - 0.9590 & - 0.2319 & 2649.7 \\ 0 & 0 & 0 & 1 \end{array}]$
C₃	$[\begin{array}{l} 0.5606 & - 0.0219 & 0.8278 & - 3623.2 \\ - 0.7669 & - 0.3909 & 0.5090 & - 2835.7 \\ 0.3124 & - 0.9202 & - 0.2360 & 2633.1 \\ 0 & 0 & 0 & 1 \end{array}]$
C₄	$[\begin{array}{l} 0.5761 & 0.3102 & - 0.7563 & 3767.8 \\ 0.7970 & - 0.0079 & 0.6039 & - 2776.4 \\ 0.1814 & - 0.9506 & - 0.2518 & 2838.4 \\ 0 & 0 & 0 & 1 \end{array}]$

Table 3. Number of iterations when convergence condition is reached
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Table 3. Number of iterations when convergence condition is reached
Experimental sequence Algorithm of reference [14] Weighted LM algorithm
1 14 8
2 16 12
3 13 11
4 17 10
5 16 9
6 11 9
7 12 11
8 15 10
9 19 13
10 12 10
Average 14.5 10.3

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Aiguo Zhou, Jiangyang Yu, Jiakun Pu, Zhenyu Li, Ronghui Wei. Positioning Algorithm of Homonymous Object Points in Multi-Vision System Based on Weighted Levenberg-Marquardt[J]. Laser & Optoelectronics Progress, 2021, 58(24): 2415006

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