基于几何代数的SVS-NLMS点云配准算法  

SVS-NLMS point cloud registration algorithm based on geometric algebra

作　　者：崔文弢 焦卫东[1] 庞艳丽 Cui Wentao;Jiao Weidong;Pang Yanli(Key Laboratory of Intelligent Signal and Image Processing,Civil Aviation University of China,Tianjin 300300,China)

机构地区：[1]中国民航大学天津市智能信号与图像处理重点实验室,天津300300

出　　处：《红外与激光工程》2021年第12期564-573,共10页Infrared and Laser Engineering

基　　金：国家重点研发计划(2020YFB1600101)。

摘　　要：针对欧氏空间点云配准方法匹配精度低、计算成本大、收敛速度慢等问题,利用几何代数对于高维空间的表达能力,提出一种基于几何代数的点云配准算法。首先,将点云数据转化为几何代数形式,基于几何代数的rotor转子,给出了几何代数空间点云配准的代价函数。其次,结合归一化最小均方算法,将求解rotor转子模拟为信号滤波问题,在几何代数空间基于最速下降法构建rotor转子迭代公式,使每次迭代计算仅使用一对匹配点对而不是全部点对。迭代计算得到的转子可用于任意维度的旋转估计问题,从而将三维点云逐步旋转配准。最后,为进一步解决收敛速度与稳态误差之间的冲突,利用Sigmoid函数给出了一种变步长的rotor转子迭代公式,在加快收敛速度的同时降低稳态误差。采用模型数据集与公共数据集验证所提算法的配准性能,与经典迭代最近点算法相比,模型数据集的配准精度由10^(-2)提升至10^(-8)数量级,公共数据集的配准精度提升35%,所提算法收敛速度更快,配准精度更高,且具有较低的稳态误差。To address the problems of low matching accuracy, high computational cost and slow convergence speed of point cloud registration methods in Euclidean space, a point cloud registration algorithm based on geometric algebra was proposed by using geometric algebra ’s expressive power for high dimensional space.Firstly, the point cloud data was transformed into geometric algebraic form, and based on the rotor of geometric algebra, the cost function of point cloud registration in geometric algebra space was given. Secondly, combined with the normalized least mean square algorithm, the solution of the rotor was simulated as a signal filtering problem, and the rotor iteration formula was constructed based on the steepest descent method in the geometric algebraic space, so that only one points pair instead of all point pairs was used for each calculation. The rotor obtained by iterative calculation could be used for any dimensional rotation estimation problem, so that the threedimensional point cloud was gradually rotated and registered. Finally, in order to further optimize the conflict between the convergence speed and the steady-state error, a variable-step rotor iteration formula was given by using the Sigmoid function, which can speed up the convergence speed while reducing the steady-state error. The registration performance of the proposed algorithm was verified by using the model data set and the public data set. Compared with the classical iterative closest point algorithm, the registration accuracy of the model data set is increased from 10^(-2)to 10^(-8)orders of magnitude, and the registration accuracy of the public data set is increased by 35%. The proposed algorithm has faster convergence speed, higher registration accuracy and lower steadystate error.

关 键 词：几何代数 点云配准 rotor转子 归一化最小均方 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]