基于凸松弛全局优化算法的视觉测量位姿估计

Pose estimation based on convex-relaxation global optimization algorithm in videogrammetry

针对参考点存在较大噪声时基于光束法平差的视觉测量位姿估计无法确保目标函数在全局极小处收敛,本文提出利用凸松弛(LMI)全局优化算法进行视觉测量全局最优位姿估计。利用归一化图像点和摄像机光心组成的正交投影矩阵,构造以旋转矩阵四元数为参数的物空间误差目标非凸多项式函数。对非凸多项式进行LMI,可以逼近其全局极小值,进而求解出全局最优旋转矩阵和平移矢量。数值仿真表明,通过与正交迭代全局优化算法比较,本文算法可以求得全局最优解,结果稍优于光束法平差。利用实物实验,验证了算法的可行性。

The bundle adjustment based pose estimation in videogrammetry can′t be guaranteed to be convergent at global minimum,when there exists severe noise on the reference points.This paper proposes a pose estimation based on convex-relaxation global optimization algorithm.Utilizing the orthogonal projection matrix composed of the normalized image coordinates and the camera center,the object space error function is constructed.The object space error function is a non-convex polynomial parameterized by quaternions in the rotation matrix space.The non-convex polynomial can be convex-relaxation to approach the global minimum,and the rotation matrix and translation can be computed in the global optimum.The numerical simulation demonstrates that the algorithm can reach the global minimum compared with the orthogonal iteration algorithm,and the results somewhat outperform those of the bundle adjustment.Also,real data experiments are performed to verity the algorithm.