以待标定鱼眼相机近似垂直棋盘格获取的单张影像为对象,综合利用多种几何约束分阶段求解鱼眼相机参数初值并进行全局优化:利用鱼眼图像轮廓对称性计算得到准确的相机主点位置(u₀,v₀),并通过轮廓外接矩形扫描搜索巧妙回避了黑色背景下的轮廓点检测困难;精确拟合棋盘格两组互相垂直平行直线在鱼眼图像上投影椭圆,计算椭圆交点并将其反投影到单位球面获得平行直线灭点,根据灭点方向正交约束得到相机等效焦距初值(f_x,f_y)及旋转矩阵角度初值;利用径向对准约束及棋盘格角点信息先线性求解平移矢量(t_x,t_y)初值,进而建立一元二次方程求解平移矢量t_z初值,最后通过最小化棋盘格角点重投影误差对除主点外的全部相机参数进行全局优化,并利用优化参数对鱼眼图像实施立方盒展开纠正。对海康威视两种型号(视野范围不同)定焦鱼眼相机的标定及其影像纠正试验结果表明,本文方法重投影均方根误差(RMSE)小于1/3 pixel,标定参数对鱼眼图像不同区域的平面透视纠正效果总体上较稳健,中心区域纠正效果略优于边缘处,纠正影像上棋盘格角点直线拟合RMSE均小于0.7 pixel,效果明显优于网上标定工具箱结果,具有较好的应用价值。

By taking the single checkerboard image of fisheye cameras to characterize as targets and comprehensively using multiple geometric constraints, the initial values of fisheye camera parameters are solved in different steps and the global optimization is simultaneously implemented. The exact principal point location (u0, v0) of the camera is obtained by means of fisheye image contours and their symmetry, in which the difficulty in detecting contour points under a black background is skillfully avoided through scanning the bounding box of fisheye image contours. Two group of projection ellipses on the fisheye checkerboard images are accurately fitted whose intersection points are back-projected to the unit sphere to obtain vanishing points of the parallel lines, and the initial value (fx, fy) of the equivalent focal length of camera and the initial angle of rotation matrix are deduced from the orthogonal constraints of two vanishing points. With the radial alignment constraint and the checkerboard corner point information, the initial values of the translation vectors (tx, ty) are first solved linearly, then that of tz is obtained after the establishment of a quadratic equation with one unknown, and finally, through minimizing the re-projection error of the checkerboard corner point, all the camera parameters except for the principal point are globally optimized and these optimized parameters are used for the correction of fisheye images. Two focus-fixed Hikvision fisheye cameras with different fields of view are selected for the calibration and image correction tests. The results show that the re-projection root mean square error (RMSE) of each camera for the proposed method is less than 1/3 pixel, and the calibration parameters can keep a good stability in the planar perspective correction effect at different areas of the fisheye image with the correction effect in the central region slightly better than that at the edge. The RMSE in the checkerboard corner point line fitting of the corrected fisheye images is less than 0.7 pixel which is obviously superior to that from the online calibration toolbox, and thus it has a relatively good application value.