Fig. 1. Point cloud distributions corresponding to different rotation parameters. (a) Correct registration;(b) incorrect registration 1; (c) incorrect registration 2; (d) point cloud distribution of correct registration; (e) point cloud distribution of incorrect registration 1; (f) point cloud distribution of incorrect registration 2

Fig. 2. Relationship between entropy change and rotation angle around z axis. 0° corresponds to space distribution of correct registration

Fig. 3. Three groups of point clouds before and after registration. (a) Dataset 1 before registration; (b) dataset 2 before registration; (c) dataset 3 before registration; (d) dataset 1 after registration; (e) dataset 2 after registration; (f) dataset 3 after registration

Fig. 4. Registration errors caused by view change and structural similarity and symmetry. (a) Incorrect registration caused by view change and structural symmetry; (b) incorrect registration caused by structural similarity; (c) incorrect translation caused by structural similarity; (d) rotation error caused by structural symmetry

Fig. 5. Registration error and time in terms of different tG. (a)(b) S2-S3 of dataset 1; (c)(d) S2-S3 of dataset 2; (e)(f) S1-S2 of dataset 3

Fig. 6. Density change experiments corresponding to different sampling ratios

Table 1. Basic information of datasets

Table 2. Distances between adjacent station positions and registration order

Table 3. Registration error

Table 4. Registration results of dataset 1

Table 5. Registration results of dataset 2

Table 6. Registration results of dataset 3

Table 7. Registration mean root errors corresponding to different tilted angles