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收稿日期：2024-09-06，
修回日期：2025-01-06，
录用日期：2025-03-03，
网络出版日期：2025-03-04，
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三维点云是空间中的一组数据点，主要包括刚性点云和非刚性点云，是表达物体或场景几何信息的重要数据形式，广泛应用于计算机视觉、机器人导航、自动驾驶、增强现实等领域。但是由于传感器移动、噪声遮挡等原因导致数据产生偏移、不完整和不准确等问题，给后续处理带来挑战，因此，如何实现精确、高效、鲁棒的三维点云配准显得尤为重要。点云配准是对从同一场景的不同位置采集的两个或多个三维点云进行配准的过程，需要找到源点云和目标点云之间的对应关系，然后求解他们之间的变换矩阵。经过配准后可以使点云数据能够在同一个坐标系下进行对齐，方便进行处理。本文将点云配准方法进行梳理并按照求解对应关系和求解变换矩阵进行分类，更直观地对点云配准方法进行介绍与对比。本文分别介绍了刚性点云配准方法和非刚性点云配准方法，总结了目前基于优化的学习方法与基于深度学习方法的概况，介绍了一些代表性的点云配准方法，为进一步的研究提供帮助。此外，本综述总结了基准数据集。最后，提出了今后在这一专题上可能产生的问题以及进行研究的建议。
A 3D point cloud is a set of data points in space， which is an important form of data to express the geometric information of an object or a scene， and is widely used in computer graphics， computer vision， robot navigation， automatic driving， augmented reality and other fields. In practical applications， incomplete and inaccurate data due to sensor movement， noise occlusion， etc.， bring challenges to the subsequent processing， so it is particularly important to realize accurate， efficient and robust 3D point cloud registration. The point cloud registration process is the process of aligning two or more 3D point clouds collected from different locations in the same scene， which generally requires two steps： finding the correspondence and solving the transformation. Specifically， finding the correspondence means finding the correspondence between the source and target point clouds and the connection between them. Solving the transformation is to compute the correspondence between the source and target point clouds into a transformation matrix. After the alignment， the point cloud data can be aligned under the same coordinate system for easy processing. In this paper， we organize and summarize the 3D point cloud registration methods up to now， classify them according to the two modules of solving the correspondence and solving the transformation matrix， and sort out the relationship between each 3D point cloud registration method， so as to make a more intuitive comparison of the point cloud registration methods. This paper introduces rigid and non-rigid point cloud registration methods， summarizes the overview of the current optimization-based learning methods and deep learning-based methods， and introduces some representative point cloud registration methods to provide assistance for further research. A rigid point cloud is a point cloud in which the relative distances and positions between points in the point cloud data remain unchanged when moving or rotating. This means that the entire point cloud is transformed as a rigid body without deformation or distortion. Rigid point clouds are commonly used to represent the 3D form of solid objects or structures， such as buildings， machine parts， etc. The task of rigid point cloud alignment is to align two or more rigid point clouds so that they have consistent spatial positions in the same coordinate system. In this paper， the rigid alignment methods are introduced in two major blocks： solving correspondences and solving rigid transformations， and the methods for solving rigid correspondences are categorized into three parts： iterative solving， feature extraction and matching correspondences. The methods of iterative solving mainly include iterative nearest point and its variants， normal distribution and its variants and other traditional methods. These methods can realize high-precision alignment and do not require training， but they are too demanding and require complete data and a good initial pose. The method of extracting features is to extract the salient features of the source and target point clouds and then the features are compared to get the correspondence. This paper describes in detail the 3D point cloud registration method using extracted point features， line features， surface features， rotation invariant features and texture features. Matching correspondence methods are used to find the correct correspondence between the features of the source point cloud to compute the transformation matrix， mainly nearest neighbor search methods and soft matching methods. In this paper， rigid transform solving methods such as random sampling method， singular value decomposition method and deep learning methods are described in detail. This paper also introduces the non-rigid alignment method. Non-rigid point cloud means that the relative distance and position between points in the point cloud data can be changed， i.e.， non-rigid deformation such as deformation， stretching， and twisting may occur in the point cloud during the transformation process. Non-rigid point clouds are usually used to describe three-dimensional forms with dynamic deformation characteristics such as human bodies， animals， fabrics or flexible structures. The task of non-rigid point cloud alignment is to align two or more non-rigid point clouds so that they have consistent spatial positions and shapes in the same coordinate system by estimating deformation fields or transformations. The non-rigid alignment method introduced in this paper is divided into two main blocks： solving the correspondence and solving the non-rigid transformation. The part of solving non-rigid correspondences mainly introduces some deformation field representations， such as point-by-point positional representation， point-by-point radial representation， deformation map representation and a priori based representation. The non-rigid deformation field is the field that describes how each point in the point cloud is displaced and deformed during the transformation process in the non-rigid point cloud alignment. It can be used to represent complex deformation relationships such as stretching， compression， and rotation of local shapes in a point cloud. The non-rigid deformation field is usually represented in the form of continuous mathematical function or discrete vector field， which is a key tool to realize accurate alignment and deformation reconstruction of point cloud. In introducing the part of solving non-rigid transformations， this paper focuses on optimization-based solving methods and deep learning-based solving methods. The deep learning-based solving methods are mainly introduced， such as mainstream CNN（convolutional neural networks） methods， GCNN（graph convolutional neural network） methods and Transfomers methods. In addition， benchmark datasets and evaluation metrics are summarized in this survey. The commonly used datasets for point cloud alignment are described in detail， including ModelNet dataset， 7-Scenes dataset， 3DMatch dataset， KITTI dataset， ETHdata dataset， and 4DMatch dataset. The commonly used evaluation metrics， including root-mean-square error， alignment recall， and mean relative error， are described in detail. Finally， the possible future problems facing this topic and suggestions for conducting research are presented.
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