基于Frobenius范数奇异值分解的快速ICP算法

迭代最近点法(ICP)及其变体是三维点云刚性配准的典型方法，但此类通过迭代计算逐点距离矩阵实现点云配准的方式，严重制约了点云的配准效率。本文提出一种快速ICP算法，利用Frobenius范数表示待配准的两幅点云之间的误差函数，获得误差值最小点位置，并对此位置进行奇异值分解，从而得到旋转矩阵和平移向量，极大压缩了迭代次数和配准时间。在Standford数据集和3DMatch数据集上进行试验，与传统ICP算法及其变体、3种基于学习的点云配准算法进行对比，本文方法配准效率最优；在达到相近的配准精确度时，提出的快速ICP方法的迭代次数仅为传统ICP算法的0.2倍，在Standford数据集上配准所需时间为传统ICP算法的1/4，在3D Match数据集上配准所需时间为传统ICP算法的1/8倍。本文提出的快速ICP算法在数据量大的点云场景下，具有更高的效率。

A fast ICP method based on Frobenius norm singular value decomposition

Although Iterative Closest Point(ICP) algorithm and its variant are the basic method for 3D point cloud rigid body registration, the point cloud iteration-based registration method get low convergence efficiency, severely constraining registration efficiency. In this paper, the Frobenius norm property is employed to represent error function between source point cloud and target point cloud, and due to the property of the Frobenius norm, the closest distance between 2 point clouds can be converted into a single calculation form to get transformation matrix. This method greatly reduce iteration times and registration time. The experiment in this paper is compared with three classical ICP algorithms and three learning-based algorithms on the Standford dataset and 3DMatch dataset respectively, and the registration time of fast ICP is less than that of other algorithms. When the registration accuracy is similar, the fast ICP method only has 20% of the iteration times of the traditional ICP algorithm, and 1/4 times the registration time on the Standford dataset, 1/8 times on the 3DMatch dataset of the traditional ICP algorithm. The fast ICP algorithm is more efficient when the amount of points is large.