稳健李代数旋转平均用于GPS辅助无人机影像三维重建

李劲澎; 姜挺; 龚志辉; 江刚武

doi:10.3788/OPE.20172506.1607

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稳健李代数旋转平均用于GPS辅助无人机影像三维重建

信息科学 | 更新时间：2020-07-07

- 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
- 光学精密工程 2017年25卷第6期页码：1607-1618
- 作者机构：
  
  信息工程大学, 河南郑州 450001
- 作者简介：
  
  李劲澎(1987-), 男, 河南正阳人, 博士研究生, 2010年于信息工程大学获得学士学位, 2013年于信息工程大学获得硕士学位, 现为信息工程大学博士研究生, 主要从事数字图像处理、计算机视觉等方面的研究。E-mail:hc116007@163.com LI Jin-peng, E-mail:hc116007@163.com
- 基金信息：
  
  国家自然科学基金资助项目(41471387);国家自然科学基金资助项目(41301526)
- DOI：10.3788/OPE.20172506.1607
  中图分类号： TP242.6
- 收稿日期：2016-12-19，
  
  录用日期：2017-2-9，
  
  纸质出版日期：2017-06-25
- 稿件说明：
移动端阅览
李劲澎, 姜挺, 龚志辉, 等. 稳健李代数旋转平均用于GPS辅助无人机影像三维重建[J]. 光学精密工程, 2017,25(6):1607-1618.

Jin-peng LI, Ting JIANG, Zhi-hui GONG, et al. GPS-supported 3D reconstruction of UAV images based on robust Lie-algebraic rotation averaging[J]. Optics and precision engineering, 2017, 25(6): 1607-1618.
李劲澎, 姜挺, 龚志辉, 等. 稳健李代数旋转平均用于GPS辅助无人机影像三维重建[J]. 光学精密工程, 2017,25(6):1607-1618. DOI： 10.3788/OPE.20172506.1607.

Jin-peng LI, Ting JIANG, Zhi-hui GONG, et al. GPS-supported 3D reconstruction of UAV images based on robust Lie-algebraic rotation averaging[J]. Optics and precision engineering, 2017, 25(6): 1607-1618. DOI： 10.3788/OPE.20172506.1607.

摘要

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。

Abstract

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 obtaining more intensive and homogeneous point cloud with better integrity. The accuracy of rotation averaging overmatches 0.15° with the computing time no more than 0.31 s

and after bundle adjustment

the re-projection error is within 1.3 pixels

which meet the requirement of fast and robust three-dimensional reconstruction.

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