## 4 Verification and Analysis
### Analysis of Experimental Data  
In order to test the algorithm's effectiveness in the laboratory scanning point cloud, the data from two groups of mechanical devices were collected using a portable three-dimensional scanner (PRINCE 335) with a reference distance of 300 mm and a field depth of 250 mm. The operating distance of the scanner from the scanned surface ranged from 200 to 450 mm, and the precision reached 0.01 mm + 0.025 mm/m by precise scanning. The number of collected workpiece point clouds was 853,105, and the collecting site and the collection point clouds are shown in Figure 7. The above figure is named Workpiece A, and the below figure, Workpiece B, to simplify the subsequent analysis. They are the same as the above for the algorithm settings. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Point Cloud** & **ICP** & **RANSAC** & **Depth Filtering-ICP** & **IWOA-RANSAC-ICP** \\ \hline Bunny & 745.52 & 1026.437 & 1652.41 & 1156.532 \\ Monkey & 2044.7 & 2806.24 & 3758.65 & 3025.42 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Registration time of these three methods (ms). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Point Cloud**} & \multirow{2}{*}{**Error**} & \multicolumn{4}{c}{\(\sigma_{MSE}\) (mm)} \\ \cline{3-5}  & & **ICP** & **RANSAC** & **Depth Filtering-ICP** & **Algorithm of This Paper** \\ \hline \multirow{3}{*}{Bunny} & x & 0.321532 & 0.161132 & 0.752535 & 0.125004 \\  & y & 0.247523 & 0.106212 & 0.532120 & 0.113524 \\  & z & 0.374156 & 0.264652 & 0.332154 & 0.154236  
Workpiece A has 853,105 points, which is reduced to 648,172 after downsampling. Workpiece B has 356,310 points, which is reduced to 175,640 after the same operation. Two groups of point clouds were processed by downsampling and translation rotation transformation, respectively, and then registered using the three algorithms mentioned above. The results of their registration using the four algorithms are shown in Figure 8.  
Figure 8: Results of workpiece point cloud registration. (**a**) Standard ICP algorithm; (**b**) Standard RANSAC algorithm; (**c**) Depth Filtering-ICP; (**d**) IWOA-RANSAC-ICP algorithm. Figure 7: Collected surface workpiece point clouds. (**a**) Experimental platform; (**b**) Point cloud data of workpiece A; (**c**) Point cloud data of workpiece B. The registration time of the point clouds of Workpieces A and B using the three algorithms are shown in Table 3 below. As can be seen from the above table, when the point cloud data increases significantly, the time of all the above four algorithms increases accordingly. For workpieces A and B, the time difference between the time required by the ICP algorithm and the time of the method designed in this paper is not large. Although the algorithm process in this paper is longer, it still maintains a good alignment speed and accuracy due to the better robustness of IWOA, and the RANSAC and Depth Filtering-ICP algorithms require a larger increase in time and a longer alignment time, which proves that the algorithms need to be further optimized. The mean square error of the point clouds of Workpieces A and B using the four algorithms is presented in Table 4 below. As can be seen from the above Figure 8, Tables 3 and 4, the standard ICP can roughly accomplish the registration of some point clouds with the same downsampling rate and maximum number of iterations throughout the test but is subject to poor registration accuracy, which may be attributed to the higher initial point-to-point requirements of ICP registration and the lower accuracy of subsequent registration in the case of a large initial point pair error. The standard RANSAC algorithm can obtain better results than the standard ICP algorithm in the registration of workpieces A and B.