平面镜反射辅助视场下相机位姿估计问题的Cramer-Rao下界  

On the Cramer-Rao Lower Bound of Camera Pose Estimation using Planar Mirror Reflection for Expanding the Camera's FOV

作　　者：王刚[1,2] 郭鹏宇[1,2] 尚洋[1,2] 李鑫[1,2] 张小虎[1,2] 

机构地区：[1]国防科学技术大学航天科学与工程学院,长沙410073 [2]国防科学技术大学图像测量与视觉导航湖南省重点实验室,长沙410073

出　　处：《实验力学》2016年第1期39-46,共8页Journal of Experimental Mechanics

基　　金：国家自然科学基金(11332012);国家重大科学仪器设备开发专项(2013YQ140517)资助

摘　　要：针对不通视条件下的相机位姿估计问题,可通过移动平面镜实现相机对目标镜像的多次观测,进而求解相机与目标之间的相对位姿关系。本文研究了该配置下位姿估计误差的CramerRao下界问题,推导了平面镜反射中心透视投影模型中物点、光心、镜像虚拟像点三者之间的共线方程及位姿估计误差理论下界的计算公式,并进行了数字仿真验证。结果表明:增大平面镜摆动角度、减小平面镜到相机的距离或增加平面镜有效移动次数,都可降低位姿估计误差的CRLB。上述结果可为某些不通视条件下摄像测量的现场布设提供可靠的性能指标。Camera pose estimation is an important and challenging problem when the target is out of a camera＇s field of view（FOV）.Relative position and posture relation between camera and target can be solved by moving planar mirror to realize multiple observations of the camera to target image.The Cramer-Rao lower bound of pose estimation error under this condition is studied in this paper.Collinear equation relating the object point in planar mirror-based perspective projection model,the optical center and the virtual image point and a formula for calculating the lower bound in pose estimation error were derived,and digital simulation validation was carried out.Results show that Cramer-Rao lower bound（CRLB）of pose estimation error can be reduced by increasing the swing angle of planar mirror,by reducing the distance from planar mirror to camera,or increasing the effective moving times of planar mirror.Above results may provide a reliable performance index for the instrument layout for camera shooting,when the target is sometimes non-visibility.

关 键 词：平面镜 不通视 位姿估计 CRAMER-RAO下界 

分 类 号：O348[理学—固体力学]