稳健李代数旋转平均用于GPS辅助无人机影像三维重建

GPS-supported 3D reconstruction of UAV images based on robust Lie-algebraic rotation averaging

针对最小二乘的旋转平均方法对粗差敏感,求解影像旋转参数不够精确的问题,提出了一种稳健的旋转平均方法。先利用李群和李代数之间的映射关系,将旋转矩阵的乘积运算简化为李代数中的减法运算,推导出旋转平均迭代解算的线性化方程;然后利用L1范数优化和迭代加权最小二乘相结合的方法求解全局一致旋转最优解;最后采用迭代策略剔除粗差,得到精确的旋转矩阵。实验结果表明,与传统最小二乘方法相比,提出方法的旋转参数求解精度更高,稳健性更好,用于三维重建可以得到更密集均匀的点云,重建完整性更好。旋转平均的精度优于0.15度,计算时间不超过0.31s,光束法平差后,重投影误差在1.3个像素以内。基本满足快速稳健三维重建的要求。

As the sensitivity of the rotation averaging method for the Least Squares to the gross error would lead to inaccurate solution of image rotation parameters,a robust rotation averaging method was proposed.Taking advantages of the mapping relations between the Lie group and Lie algebra,the linear equation of rotation averaging iteration resolving was deduced by simplifying the product operation of rotation matrix to subtraction operation in Lie algebra;then the globally uniform rotation optimum solution was solved by combining L1 norm optimization with the iteratively reweighted least squares;and the iterative strategy was used to eliminate the gross error for obtaining accurate rotation matrix.The method was applicable to low-precison GPS supported three-dimensional reconstruction of Unmanned Aerial Vehicle（UAV）images.The result of the experiment shows that compared with traditional least square method,the proposed method exhihits an higher solution accuracy of rotation parameters and better robustness,which can be applied to three-dimensional reconstruction for obtainingmore intensive and homogeneous point cloud with better integrity.The accuracy of rotation averaging overmatches 0.15°with the computing time no more than 0.31s,and after bundle adjustment,the reprojection error is within 1.3 pixels,which meet the requirement of fast and robust three-dimensional reconstruction.