圆心不对称投影修正的相机标定

Camera calibration based on correction of asymmetric circle center projection

采用圆心作控制点的相机标定方法需要修正由不对称投影引起的投影误差,以提高标定精度。本文根据成像模型推导了基于直接线性变换法的投影误差计算公式。提出了先估计投影变换矩阵,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。该方法无需矩阵分解,避免了不同坐标系的转换。模拟实验结果证明了投影误差计算公式的正确性。实际实验表明,在相机分辨率为780pixel×582pixel,空间圆半径为20mm时,修正误差后的标定误差为0.19pixel,优于未修正时的误差0.20pixel,结果表明该方法可行有效。

In order to improve the calibration accuracy,the camera calibration method using a circular center as the control point needs to correct bias errors caused by the asymmetric projection. This paper deduces the mathematical formulations of correction terms based on the Direct Linear Transform （DLT） to calculate projection errors. The perspective transform matrix is firstly estimated by using DLT method, and then the projection of the circle is obtained directly by the elements of perspective transform matrix. The circle centers in the image plane are corrected with the elements of perspective transform matrix. The proposed method eliminates the matrix decomposition and avoids the transformation between the two coordinates. Synthetic test results prove that the mathematical formulations are correct and show that the calibration error after correcting asymmetric projection is 0. 19 pixel in the resolutions of 780 pixel×582 pixel and the circle radius of 20 mm, which is better than 0.20 pixel before the correct. The proposed algorithm is feasible and valid.