## 3 Point Cloud Registration Method
### NDT-Based Variants  
NDT was originally presented by [PERSON] for 2D scan matching [25]. [PERSON] et al. [66] extended 2D NDT to 3D. [PERSON] et al. [67] conducted a comprehensive comparison of the 3D scan-matching algorithms of ICP and NDT. The experimental results demonstrate that NDT performs faster than ICP and converges from a wider range of initial pose estimations. However, the NDT convergent pose is unpredictable, and the pose generated in the case of failure is worse than the ICP. The author proposes an NDT algorithm with trilinear interpolation to solve this problem. This algorithm has a higher success rate than the classical NDT algorithm, but it takes a longer time. To speed up NDT registration, [PERSON] et al. [68] encapsulated SSE-friendly and multi-threaded NDT, which can run up to 10 times faster than its original version in PCL. In addition, three methods for neighbor voxel search are provided, including KDTREE, DIRECT1, and DIRECT7. [PERSON] et al. [69] added semantic labels to point clouds by calculating the smoothness of point clouds. Point clouds without semantic labels are discarded and do not take part in registration. Point clouds with distinct semantic labels are separately registered by NDT. Experimental analysis has shown that the algorithm improves the speed and robustness of registration. [PERSON] et al. [70] developed an NDT registration algorithm with variable voxel size that considers the local density in the process of dividing a large voxel into several small voxels and gathers the sparse point cloud as a large voxel. The point cloud is densely dispersed into multiple small voxels to solve the problem that most sparse points cannot be used due to the difference in the number of point clouds caused by the fixed voxel size and enhance the accuracy of registration. [PERSON] and [PERSON] [71] converted the reference point cloud into a disclike distribution suitable for the point cloud structure, addressing the effect of the thick distributions whose mass centers are hanging in the air on NDT registration. [PERSON] and [PERSON] [72] introduced a multi-layer-based transformation algorithm for the normal distribution. The algorithm automatically calculates the cell size by looking at the boundary of the point cloud, and then the point cloud is subdivided into 8n cells, where n represents the level of the layer. In addition, the method uses the Mahalanobis distance function as the score function to replace the original Gaussian probability function and optimization using the [PERSON] and Levenberg-Marquardt methods. Compared with the NDT algorithm, this method has longer-distance measurement capability and a faster convergence speed. Later, [PERSON] and [PERSON] [73] added a feature extraction module to the above algorithm, namely MLNDT based on feature extraction, which further improved the efficiency and robustness of the registration algorithm. [PERSON] and [PERSON] [74] presented the KLNDT algorithm to solve the problems of the fixed number of layers and the limited number of optimization iterations in MLNDT. The algorithm searchesthe key layer and registers in the key layer until the termination criterion is satisfied. Experiments show that KLNDT has a higher success rate and accuracy than MLNDT. [PERSON] and [PERSON] [75] presented PNDT, defined the probability of point samples, and calculated the mean and covariance according to the probability. Compared with the classical NDT, PNDT point cloud registration accuracy is higher. [PERSON] et al. [76] used semantic information extracted from point clouds to enrich NDT features and combined NDT histogram descriptors for loop closure detection. This method has higher accuracy than non-semantic NDT methods. [PERSON] et al. [77] proposed a weighted normal distribution transform (weightedNDT) method, which reflects the static probability of each point as a weight. Compared with his dynamic target removal method, the weightedNDT algorithm has higher classification accuracy and lower scanning matching error. [PERSON] et al.