基于圆心不对称投影修正的相机标定方法

提出了采用圆心做控制点标定相机，根据成像模型推导了计算误差所需的数学公式，并在标定过程中修正了圆心图像坐标由不对称投影引起的投影误差，以提高标定精度。首先利用直接线性模型估计投影变换矩阵，直接用其元素计算空间圆在图像平面上的投影，对圆心的图像坐标进行修正后，再次计算投影变换矩阵。该方法无需对该矩阵做分解，避免了不同坐标系的转换。模拟试验考察了投影误差与各种空间圆方位参数的关系，实际试验表明:在相机分辨率为780×582，空间圆半径为20mm时，修正误差后的标定误差为0.19437像素，优于未修正的结果，同时也表明该方法可行有效。

A Camera Calibration Based on Correction of the Asymmetric Circle Center Projection

This paper presents a camera calibration method using circular control points whose centers need to correct bias error caused by asymmetric projection. The mathematical formulations of the correction terms are discussed. The perspective transformation matrix is first estimated using DLT (Direct Linear Transformation) method without decomposition. And then the projection of the circle is obtained directly using the elements of perspective transformation matrix. The centers of circle in the image plane are then corrected with the elements of perspective transformation matrix that will be recomputed after correction. The proposed method avoids the transformation between different coordinates. The relationships between bias error and the parameters of the circle are reported through synthetic. The real tests show that the calibration error is 0.19437 pels when the resolution of camera is 780×582 pels and the radius of circle is 20mm. The accuracy is improved after correcting asymmetric projection, and the presented algorithm is feasible and valid.