中文摘要：

针对相机外部参数标定中参照物不在相机视野范围内的情况,提出了一种基于环形镜面的相机外部参数自动标定方法.使用半径已知的环形镜面作为反射中介,相机通过镜面反射获得参照物的图像;椭圆检测获得镜面内外圆在相平面中的方程,使用外圆方程计算出镜面在相机坐标系中的位置,然后使用内圆进行位置参数优化;在已知相机内部参数的情况下,通过解决Pn P（perspective-n-point）问题获得相机的虚像和参照物之间的旋转平移矩阵;根据平面镜成像原理,最终计算出相机与参照物之间的实际外部参数;最后通过仿真和实际实验,证明该方法简单易用,可自动完成相机外部参数的标定,并且具有较高的标定精度.

英文摘要：

Aiming at the extrinsic camera calibration with respect to a reference object without a direct view, an annular mirror based automatic calibration method is proposed. The camera captures the images of the reference object through the reflection of a known-radius annular mirror. The equations of the inner and outer circles of the mirror in the image plane can be obtained with ellipse detection method. The equation of the outer circle is used to get the position of the mirror surface in the coordinate frame of the camera, while the inner circle is used to optimize the position parameter. The rotation and translation matrices between the virtual image of the camera and the reference object can be obtained after solving the PnP （perspective-n-point） problem as the intrinsic parameter of the camera is already known. Finally, the real extrinsic parameters between the camera and the reference object are obtained according to the mirror imaging principle. Simulation and real experiment results show that the method is simple and automatic with high accuracy.