High-precision occlusion-resistant quad-vision camera 3D reconstruction system

立体相机组	旋转矩阵 $R$	平移向量 $T$	重投影误差/pixel
Cam_1,2	$[\begin{matrix} 0.0000 & - 0.8602 & - 0.5099 \\ 0.8396 & 0.2769 & - 0.4673 \\ 0.5432 & - 0.4281 & 0.7223 \end{matrix}]$	$[\begin{matrix} 6659.2510 \\ 6103.2552 \\ 31774.5547 \end{matrix}]$	0.340 5
Cam_2,3	$[\begin{matrix} 0.0014 & - 0.8503 & - 0.5263 \\ 0.8471 & 0.2807 & - 0.4513 \\ 0.5314 & - 0.4452 & 0.7207 \end{matrix}]$	$[\begin{matrix} 21692.7618 \\ 18610.7355 \\ - 27990.8437 \end{matrix}]$	1.212 9
Cam_3,4	$[\begin{matrix} - 0.0171 & - 0.8632 & - 0.5046 \\ 0.8828 & 0.2238 & - 0.4129 \\ 0.4694 & - 0.4525 & 0.7582 \end{matrix}]$	$[\begin{matrix} 875.7858 \\ 696.7939 \\ 19489.3290 \end{matrix}]$	1.195 3
Cam_4,1	$[\begin{matrix} 0.0163 & - 0.8921 & - 0.4516 \\ 0.8442 & 0.2543 & - 0.4719 \\ 0.5357 & - 0.3735 & 0.7573 \end{matrix}]$	$[\begin{matrix} 9383.3689 \\ 9802.6803 \\ - 2675.6765 \end{matrix}]$	0.343 7

Table 2. Position and pose of each camera in unified coordinate system

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Table 2. Position and pose of each camera in unified coordinate system

相机	旋转矩阵 $R$	平移向量 $T$
Cam₁	$[\begin{matrix} 1.0000 & 0.0000 & 0.0000 \\ 0.0000 & 1.0000 & 0.0000 \\ 0.0000 & 0.0000 & 1.0000 \end{matrix}]$	$[\begin{matrix} 0.0000 \\ 0.0000 \\ 0.0000 \end{matrix}]$
Cam₂	$[\begin{matrix} 0.0000 & - 0.8602 & - 0.5099 \\ 0.8396 & 0.2769 & - 0.4673 \\ 0.5432 & - 0.4281 & 0.7223 \end{matrix}]$	$[\begin{matrix} 6659.2510 \\ 6103.2552 \\ 31774.5547 \end{matrix}]$
Cam₃	$[\begin{matrix} - 0.9998 & - 0.0113 & 0.0165 \\ - 0.0095 & - 0.4577 & - 0.8891 \\ 0.0177 & - 0.8889 & 0.4576 \end{matrix}]$	$[\begin{matrix} - 210.4613 \\ 11625.1142 \\ - 4296.3654 \end{matrix}]$
Cam₄	$[\begin{matrix} 0.0163 & 0.8439 & 0.5362 \\ - 0.8920 & 0.2546 & - 0.3734 \\ - 0.4516 & - 0.4722 & 0.7570 \end{matrix}]$	$[\begin{matrix} - 7001.0921 \\ 4875.5202 \\ 10893.1415 \end{matrix}]$

Table 3. Comparison of direct and derived results of position and pose for No.4 camera

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Table 3. Comparison of direct and derived results of position and pose for No.4 camera

	直接结果 $X^{*}$	推导结果 $X$	相对误差矩阵 $Δ E$
$R$	$[\begin{matrix} 0 .0163 & 0 .8442 & 0 .5358 \\ - 0. 8921 & 0 .2543 & - 0. 3735 \\ - 0. 4515 & - 0. 4718 & 0 .7572 \end{matrix}]$	$[\begin{matrix} 0.0163 & 0.8439 & 0.5362 \\ - 0.8920 & 0.2546 & - 0.3734 \\ - 0.4516 & - 0.4722 & 0.7570 \end{matrix}]$	$[\begin{matrix} 0 .0010 & 0 .0004 & 0 .0008 \\ 0.0000 & 0 .0013 & 0 .0004 \\ 0 .0002 & 0 .0008 & 0 .0003 \end{matrix}]$
$T$	$[\begin{matrix} - 6995 .3004 \\ 4878 .8552 \\ 10887 .7741 \end{matrix}]$	$[\begin{matrix} - 7001.0921 \\ 4875.5202 \\ 10893.1415 \end{matrix}]$	$[\begin{matrix} 0 .0008 \\ 0 .0007 \\ 0 .0005 \end{matrix}]$

Table 4. Checkerboard grid point spacing measurement results mm
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Table 4. Checkerboard grid point spacing measurement results mm
间距统计数量/个最大值最小值最大误差均值标准差
纵向间距 4 224 0.517 0.489 0.017 0.500 0.005
横向间距 4 225 0.515 0.483 0.017 0.500 0.005
所有间距 8 449 0.517 0.483 0.017 0.500 0.005

Table 5. Relative errors
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Table 5. Relative errors
已知间距/mm 对角距离/mm 相对误差/%
45.610 45.638 0.061
45.594 0.035

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Peng CHEN, Huiting LIU, Lei ZHANG, Keyi WANG, Bolin CAI. High-precision occlusion-resistant quad-vision camera 3D reconstruction system[J]. Journal of Applied Optics, 2024, 45(2): 307

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