针对可旋转相机的参数标定问题, 提出了一种基于二维旋转平台的相机成像模型。首先,通过一对坐标系的变换与逆变换, 将相机的旋转平移变换关系转换为二维旋转平台纯旋转关系;然后,借助旋转平台读数以及相机到旋转平台的固定变换关系, 实现相机内参的精确标定以及任意位置间相机外参的相互转换;最后,利用标定出的相机与旋转平台间变换矩阵实现不同位置相机参数的转换。相比于传统固定相机的标定方法, 本文提出的方法标定获得的相机内参具有更好的收敛性, 而且能够标定出相机到旋转平台的变换矩阵, 从而实现相机坐标系变换参数的精确计算。实验结果表明, 在标定模板图像数量相同时, 与常用的张氏标定法相比, 本文提出的方法标定获得的相机内参具有更快的收敛速度。棋盘格角点重投影坐标与实际拍摄图像中棋盘格角点坐标相对比, 平均误差约为0.12 pixel, 表明该方法具有较高精度。

A camera imaging model based on two-dimensional rotating platform was proposed in order to solve the problem of parameter calibration for rotatable camera. Firstly, through the transformation and inverse transformation of coordinate systems, the rotation translation transformation of the camera was converted to the pure rotation motion of the two-dimensional rotating platform; Then, taking advantages of the readings of the rotating platform and the fixed transformation between camera and rotating platform, accurate calibration for internal parameters of the camera and mutual transformation for the extrinsic parameters at optional position of the camera were realized; Finally, taking advantages of calibrated transformation matrix between the camera and the rotating platform, the transformation of camera parameters at different positions were realized. Comparing with the traditional calibration method for the fixed camera, internal parameters of the camera obtained from the calibration method proposed have better convergence, and the transformation matrix from the camera to the rotating platform could be calibrated in order to realize accurate calculation for transformation parameters on the coordinate system of the camera. The experimental result shows that when the quantity of calibrated template images are identical, comparing with the common Zhang's calibration, internal parameters of the camera obtained from the calibration method proposed have faster convergence rate. Comparing with x-comers coordinate in actual shooting images, the average error of the x-comers re-projection coordinate is about 0.12 pixel, which shows the method has higher accuracy.