Abstract: In order to solve the problems such as low calculation efficiency, poor stability of initial value matching and difficult parameter setting of the automatic registration algorithm of point cloud under large amount of data, a fast rough registration algorithm based on the relative geometric invariance between matching pairs is proposed. Firstly, a certain number of key points are selected by the eigenvalue of the point cloud neighborhood, and then the nearest matching pair is obtained by the fast point feature histogram（FPFH） feature descriptor. Then, the exact matching pair is obtained through the symmetric candidate point finding strategy of the point cloud features and the two sets of correct matching pairs with the characteristic that the proportion of the corresponding edge 2-norm of the source point cloud and the target point cloud is unchanged. Finally, singular value decomposition（SVD） algorithm is used to solve the registration objective function. The experimental results show that the algorithm is reasonable and reliable, and the parameter setting is relatively simple. It has significant advantages of efficiency and precision, and can provide stable and accurate initial parameters for subsequent precision registration.

Key words: coarse registration of point cloud, fast point feature histogram（FPFH）, sample consensus initial alignment（SAC-IA）, relative geometric invariance

摘要： 针对目前点云在大数据量下的自动配准算法计算效率低下，粗配准初值匹配稳定性差，参数难以设置等问题，提出一种基于匹配对间相对几何不变性特点的快速粗配准算法。通过点云邻域特征值筛选一定量的关键点，利用快速点特征直方图（fast point feature histogram，FPFH）描述子初步获取最邻近匹配对；通过点云特征的对称候选寻点策略及两组正确匹配对在源点云与目标点云对应边的2-范数比例不变的特性获取精确的匹配对；利用奇异值分解算法（singular value decomposition，SVD）求解配准目标函数。实验表明，算法策略合理可靠，参数设置相对简易，具有显著的效率及稳定性优势，能够为后续精配准提供稳定精确的初始参数。

关键词: 点云粗配准, 快速点特征直方图（FPFH）, 采样一致性初始配准算法（SAC-IA）, 相对几何不变性