## 4 Experiments
### Experiments on Registration Effectiveness
#### 4.3.6 Comparison between Registration Efficiency of Point Cloud  
Based on our registration framework and our proposed feature descriptor, we compare the average registration time between our accurate transformation estimation and state-of-the-art transformation estimation, such as feature matching, clustering, ICP, RANSAC, etc., on the above three datasets. Table 4 shows the average registration time based on the kinds of transformation estimations. Meanwhile, we compare the average registration time between our feature descriptor and state-of-the-art feature descriptors via our registration framework and our accurate transformation estimation. The average registration time of point clouds based on the kinds of feature descriptors on the above three datasets is shown in Table 5.  
The results in Table 4 show that the registration time of our proposed transformation estimation approach is only slightly lower than that of feature matching and ICP-based estimation methods. Although our transformation estimate technique takes somewhat longer to register than feature matching-based estimation methods, it is due to the fact that our method relies on feature matching to create initial matched point pairs. Although this phase takes some time, it lays the groundwork for more precise transformation estimates in the next stage. On the other hand, although the ICP-based transformation estimation method outperforms our method in registration time, as shown in Table 2, this method has significant errors in estimating the transformation matrix. This means that although the ICP method has advantages in time efficiency, there are shortcomings in accuracy. In \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **Method** & **Average \(\theta_{r}\)** & **Average \(\theta_{t}\)** & **Average \(\theta\)** \\ \hline \multirow{8}{*}{Stanford 3D Scanning Repository} & Based on our proposed feature descriptor & 0.9482 & 1.9568 & 1.4525 \\  & Based on 3 DSC & 2.1493 & 2.7855 & 2.4674 \\  & Based on spin image & 5.9344 & 4.4502 & 5.1923 \\  & Based on PFH & 3.5537 & 4.6589 & 4.1063 \\  & Based on RoPS & 3.2145 & 2.1765 & 2.6955 \\  & Based on FPFH & 4.2305 & 4.7327 & 4.4816 \\  & Based on BRoPH & 0.7891 & 1.3907 & 1.0899 \\  & Based on KDD & 0.5853 & 1.7786 & 1.1820 \\ \hline \multirow{8}{*}{SpaceTime dataset} & Based on our proposed feature descriptor & 1.1584 & 1.7649 & 1.4617 \\  & Based on 3 DSC & 0.7723 & 1.3402 & 1.0563 \\  & Based on spin image & 2.6478 & 2.9788 & 2.8133 \\  & Based on PFH & 2.0926 & 2.8522 & 2.4724 \\  & Based on RoPS & 3.0344 & 2.2079 & 2.6212 \\  & Based on FPFH & 2.5698 & 3.2903 & 2.9301 \\  & Based on BRoPH & 0.9833 & 1.2749 & 1.1291 \\  & Based on KDD & 0.8478 & 1.5194 & 1.1836 \\ \hline \multirow{8}{*}{Kinect dataset} & Based on our proposed feature descriptor & 1.3739 & 2.7891 & 2.0815 \\  & Based on 3 DSC & 3.2455 & 4.3264 & 3.7860 \\ \cline{1-1}  & Based on spin image & 6.3421 & 4.8911 & 5.6166 \\ \cline{1-1}  & Based on PFH & 5.3244 & 4.9817 & 5.1531 \\ \cline{1-1}  & Based on RoPS & 5.3201 & 4.5927 & 4.9564 \\ \cline{1-1}  & Based on FPFH & 5.0134 & 5.0923 & 5.0529 \\ \cline{1-1}  & Based on BRoPH & 1.4505 & 3.0117 & 2.2311 \\ \cline{1-1}  & Based on KDD & 2.3315 & 4.8299 & 3.5807 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average registration errors for point cloud registration based on different feature descriptors. addition, it can be observed in Table 4 that when feature matching-based transformation methods are combined with ICP methods or clustering methods, their computation time increases, resulting in lower time efficiency than our methods. This may be because these combination methods require more computing resources and steps when processing complex data. Finally, the transformation approach based on clustering/RANSAC requires a significant number of iterative operations, which takes longer than our method. This further demonstrates that our accurate transformation estimation approach is time efficient while retaining excellent accuracy.