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摘要:
针对传统方法未考虑透视偏差的存在，提取椭圆圆心作为真实物理圆心投影点造成相机标定误差的问题，提出了一种基于平面变换的高精度相机标定方法。提取标定板内外边框上的角点，对标定板进行平面变换，将标记点由椭圆投影成近似的标准圆；利用图像矩提取标准圆圆心的坐标，投影回原标定板平面，得到标记点实际圆心的像素坐标；根据圆形标记点实际圆心的坐标，利用张正友标定法完成相机标定。实验结果表明：与传统方法相比，所提方法将相机标定的误差降低了66.169%，有效提高了相机标定的精度。
Abstract:Traditional methods do not consider the existence of perspective deviation, and usually extract the center of the ellipse as the projection point of a real physical center, resulting in camera calibration errors. A calibration method for high precision cameras was proposed based on plane transformation. The corner points on the inner and outer borders of the calibration plate were extracted to carry out the plane transformation of the calibration plate, and the marked points were projected from ellipses into approximate standard circles. The coordinates of the center of the standard circle were extracted by image moments, and were projected back to the plane of the original calibration plate to obtain the pixel coordinates of the actual center of the marked points. According to the coordinates of the actual center of the circular markers, the Zhang Zhengyou calibration method was used to complete the camera calibration. Experimental results show that compared thus the traditional method, the proposed method reduced the camera calibration error by 66.169%, thus effectively improving the camera calibration accuracy.
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图 7 点阵标定板的像素坐标系轴线分布
Figure 7. Axis distribution of pixel coordinate system of lattice calibration plate
图 8 点阵标定板的世界坐标系轴线分布
Figure 8. Axis distribution of world coordinate system of lattice calibration plate
表 1 点阵标定板规格
Table 1. Specification of lattice calibration plate
参数 数值 标定板尺寸/mm 200×200 圆点数量/个 7×7 圆点直径/mm 12.5 圆心距/mm 25 外边框长度/mm 200 内边框长度/mm 187.5 
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表 2 相机标定结果对比
Table 2. Comparison of camera calibration results
参数 传统方法 本文方法 焦距 fx/像素 904.829 920.942 fy/像素 905.350 918.769 主点坐标 u0/像素 604.321 616.318 v0/像素 344.552 333.515 镜头畸变系数 k1 0.016 2 0.003 4 k2 0.010 2 0.002 0 k3 -0.103 4 -0.028 9 p1 0.001 3 -0.000 8 p2 -0.003 2 0.001 2
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表 3 相机标定的重投影误差对比
Table 3. Comparison of re-projection errors in camera calibration
图像序号 重投影误差/像素 传统方法 本文方法 1 0.077 992 668 0.027 848 8 2 0.160 459 9 0.050 742 9 3 0.099 213 23 0.024 396 3 4 0.139 651 5 0.050 264 5 5 0.066 711 65 0.023 466 5 6 0.125 555 3 0.045 840 3 7 0.097 389 74 0.037 083 4 8 0.128 29 0.057 831 3 9 0.099 505 6 0.034 262 6 10 0.151 173 0.043 132 7 11 0.049 206 0.018 771 4 12 0.070 045 991 0.024 623 1 13 0.089 888 6 0.023 999 7 14 0.112 454 0.036 633 7 15 0.060 713 33 0.022 829 6 16 0.079 800 88 0.022 511 8
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表 4 相机标定的平均重投影误差对比
Table 4. Comparison of average re-projection errors in camera calibration
标定方法 平均重投影误差/像素 传统方法 0.100 5 本文方法 0.034 0
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