## 2 Registration Algorithms Based on Hierarchical Optimization
### Iterative Closest Point (ICP)-Based
However, due to the discreteness of laser measurement, there are not actually existing two matching measurement points. Therefore, problems like matching failure may occur during positioning, but the robustness is deteriorated, and it is more susceptible to the influence of the initial pose error. In this way, PL-ICP is less robust and more vulnerable to initial pose errors. [PERSON] et al. [39] introduced the General-ICP algorithm as a probabilistic framework. It integrates the point-to-point ICP and the point-to-line ICP into the uniform framework. Furthermore, the measurement weights of point-to-point and point-to-line distances will be adjusted to make effective use of the point cloud information, hence avoiding incorrectly matched points. This method ensures the ICP's speed and simplicity while boosting the matching accuracy. Unfortunately, it still does not address the issue of local optimum. [PERSON] et al. [40] put forward a scale-ICP algorithm based on seven-dimensional spatial iterations that has a certain degree of improvement in iteration speed and alignment accuracy and has better alignment robustness. [PERSON] et al. [41] presented a sparse ICP to enhance the robustness of the alignment algorithm against noise by modeling the alignment problem as an \(Lp\) minimization problem. This sparse ICP can control the effect of outliers on the alignment results by modifying parameter p. However, the algorithm converges slowly because of tackling the nonconvex optimization problem. To some extent, this strategy addresses the problem of ICP slipping into local optimum, but the basis of optimization remains local search. [PERSON] et al. [42] developed a global optimal solution (Go-ICP) algorithm to accomplish global registration by combining the branch and bound (BnB) framework. The method boosts registration speed by raising registration efficiency, preventing the ICP algorithm from slipping into the local optimum. Nevertheless, one shortcoming is poor velocity. [PERSON] et al. [43] introduced a GF-ICP algorithm based on point cloud features that seeks the correspondence between registered objects by point cloud geometric properties,such as curvature and surface normal. Features are also added to the error function for accurate registration. [PERSON] et al. [67] proposed the use of [PERSON]'s technique in ICP, which accelerates the convergence process by locating a fixed point in the shrinkage map that satisfies the required quality. This method takes fewer iterations than simple iterations to converge to the same error. [PERSON] and [PERSON] [44] suggested a deep closest point (DCP) based on machine learning. In this method, the dynamic graph convolution network, attention mechanism, and singular value decomposition matrix are utilized to mine the robustness point features, calculate the correlations of points in the deep features, and estimate the affine transformation, respectively, resulting in the accurate registration of unknown category point cloud data. The training samples are ideal three-dimensional objects. Hence, if the method is directly applied to real problems, the effect is not outstanding. [PERSON] and [PERSON] [45] introduced a PRNet based on the DCP in the following year that determined the correspondence between point clouds by incorporating Gumbel-Softmax and emulated the iterative process of ICP to increase accuracy. PRNet, on the other hand, presently requires inference-time fine-tuning on real-world scans to acquire usable data-dependent representations, which makes PRNet sluggish during inference. [PERSON] et al. [46] proposed a voxelized generalized iterative closest point (VGICP) that extends the voxelization of the GICP to avoid costly nearest neighbor searches while maintaining algorithm accuracy. [PERSON] et al. [68] developed a binocular stereo camera point cloud registration method based on IWOA (improved whale optimization algorithm) and improved ICP to address the problems of low accuracy and low efficiency of point cloud registration.