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摘要:
针对现有标定方法在相机无公共视场情况下的局限性，本文提出使用双平面标定板对双相机进行同时标定的方法。通过推导两个相机与两个标定板间的坐标变换，将待标定相机与参考相机的相对位姿关系的求解转换为较为成熟的手眼标定方程求解。通过实验验证：该方法可实现双相机的同时标定，且方法的绝对误差不超过0.089 mm，较为可靠；在双视角三维测量系统中，与相位-深度的累积误差不超过0.116 mm，可为进一步的数据融合提供可靠的初值。此外，由于本方法灵活方便，可适用于多视角三维测量系统的同时标定。
Abstract:In view of the limitations of the existing methods when the camera has no common field of view, this paper proposes a method of using two plane calibration plates to calibrate two cameras at the same time. By deriving the coordinate transformation between the two cameras and two calibration plates, the solution of the relative pose relationship between any camera and the reference camera is transformed into a more mature hand-eye calibration equation. The experimental results show that this method can achieve simultaneous calibration of two cameras, and the absolute error is less than 0.089 mm. In the dual vision 3D measurement system, the cumulative error with phase height is less than 0.116 mm, which can provide a reliable initial value for the next step of data fusion.
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Key words:
- dual vision measurement /
- global calibration /
- system calibration /
- fringe projection
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Overview: The fringe projection measurement method is widely used in various fields due to its simple structure, high precision, and resolution, full field measurement, etc. The research on the single-view system of the fringe projection measurement method has been relatively mature. The dual-view fringe projection measurement system is an extension of the single-view fringe projection measurement system, a larger range of three-dimensional geometric information can be obtained by expanding the camera's field of view. In the dual-view fringe projection measurement system, the three-dimensional measurement results of the subsystem are always restored in the camera coordinate system, while the two camera coordinate systems are independent of each other in the dual-view fringe projection measurement system. Therefore, it is necessary to solve the transformation relationship between the two camera coordinate systems, the process of solving the transformation relationship between the two camera coordinate systems is called global calibration. Global calibration is the most important task in the calibration of dual and multi view systems. However, the existing global calibration methods require expensive auxiliary equipment when the two cameras have no common field of view, which adds a certain cost to the calibration, and when the viewing angle of the system is more than two, the method of relying on the auxiliary equipment is limited. Aiming at the limitations of the existing global calibration methods, this paper proposes a method to achieve dual-view global calibration by using two plane calibration boards: Firstly, through a series of derivation, the problem of solving the transformation matrix between the two camera coordinate systems is transformed into the problem of solving the hand-eye calibration equation which is more mature in the field of robot; Secondly, adjust the two calibration boards to the appropriate position according to the placement of the camera, and fix the two calibration boards; Thirdly, place the two calibration boards at several positions in the field of view of the two cameras at the same time to obtain several equations; Finally, the conversion matrix between the two cameras is obtained by using the quaternion method, least square method, and nonlinear optimization. The method identified in this paper does not require additional auxiliary equipment, and it is proved by quantitative experiments: this method can realize the calibration of dual cameras simultaneously and the absolute error of the method does not exceed 0.089 mm, which is relatively reliable; in the dual-view 3D measurement system, the cumulative error of global calibration and phase-depth does not exceed 0.116 mm, which can provide a reliable initial value for further data fusion. In addition, the global calibration method determined in this paper is suitable for multi-view 3D measurement systems. When the number of cameras is more than two, the calibration board corresponding to the number of cameras can be added to achieve simultaneous calibration of multiple cameras.
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图 8 视角1恢复的台阶三维形貌
Figure 8. Three dimensional topography of steps restored by perspective 1
图 9 相机2视角恢复的台阶三维形貌
Figure 9. Three dimensional topography of steps restored by perspective 2
表 1 全局标定精度验证结果
Table 1. Verification results of global calibration accuracy
摆放位置 最大误差/mm 最小误差/mm 平均误差/mm 1 0.089 0.036 0.075 2 0.077 0.039 0.069 3 0.084 0.045 0.071 
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表 2 双视角测量结果(单位：mm)
Table 2. Measurement results of double view angle (unit: mm)
台阶实际间距 17.603 18.422 13.258 18.212 视角1测量间距 17.637 18.386 13.291 18.255 视角1测量误差 0.034 0.036 0.033 0.043 视角2测量间距 17.643 18.387 13.225 18.253 视角2测量误差 0.040 0.035 0.033 0.041 双视角测量结果 18.408 17.611 13.994 17.618 双视角测量误差 0.102 0.097 0.090 0.116
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