# Fast Point Cloud Registration Method with Incorporation of RGB Image Information
## 3 Experiment
### Experimental Results
#### 3.3.3 Point Cloud Registration  
To verify the effectiveness of this method, the point clouds in Section 3.1 were registered under the same experimental environment, and this method was compared with ICP and FR-ICP for analysis. In the experiments, two sets of alignment experiments of ICP were set up to measure the improvement in accuracy and speed of this method by iterating 50 times and 100 times, respectively, while keeping other parameters constant. In addition, only the initial alignment was used to measure the experimental metrics while maintaining the default parameters of FR-ICP. The experimental evaluation metric was RMSE, which indicates the sum of squared distances from the source point cloud to the corresponding point pairs of the target point cloud, and the smaller the sum of squared distances indicates the lower registration error of the point cloud. Registration time was also compared to measure the efficiency of the registration method, where RMSE is defined as  
\[\text{RMSE}=\sqrt{\frac{\sum_{i=1}^{M}\parallel Rp_{i}+t-q_{i}\parallel^{2}}{ M}} \tag{16}\]  
The registration results of the five sets of streamlined point clouds shown in the analysis of the experimental data are shown in Table 3, where the first column shows the five sets of streamlined point clouds to be registered, and each subsequent column shows the registration results of the ICP, FR-ICP, and our method, respectively. As can be seen from the table, the registration results of the ICP algorithm with 50 iterations on all five groups of point clouds showed significant deviations and fell into local optimum when registering the point cloud in Table 3e with the largest rotation angle, resulting in registration failure. When the number of iterations of ICP reached 100, registration improved, but registration failure still occurred in the results. In the registration results of five sets of point clouds, our method and FR-ICP had good registration performance, which was due to the fact that the initial alignment in this paper kept good initial positions between the point clouds to be registered and prevented the point clouds from falling into local optimum in the alignment. The registration results of the above five groups of point clouds were evaluated metrically, and the RMSE and speed of the registration experiments were compared, as shown in Table 4. The table shows the higher registration error of ICP in the above point clouds. Without considering the alignment failure, the RMSE of the point cloud in d reached 1.721/0.834, and ICP compromised the speed while improving the accuracy. In d, the accuracy of our method improved from 0.834 mm of ICP (iter 100) to 0.580, and the speed increased by 42%. Compared with FR-ICP, our method had equal accuracy and outperformed FR-ICP in terms of speed, due to the fact that our method had a better initial position at registration, which reduced the computational overhead in the fine registration stage. With comparable accuracy in a, the 18.87 s of our method compared to 61.84 s/36.75 s \begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Point Cloud**} & \multicolumn{3}{c}{**Number of Points**} \\ \cline{2-4}  & **Original Point Cloud** & **Pass-through Filter** & **Transition Down of Voxel Grid** \\ \hline \multirow{5}{*}{Source Point Cloud} & 157,551 & 153,265 & 33,094 \\  & 157,026 & 155,082 & 32,537 \\ \cline{1-1}  & 156,963 & 153,185 & 32,137 \\ \cline{1-1}  & 157,595 & 151,695 & 31,328 \\ \cline{1-1}  & 158,657 & 157,285 & 33,130 \\ \hline Target Point Cloud \({}^{*}\) & 158,032 & 154,905 & 32,735 \\ \hline \end{tabular} \({}^{*}\) Target point cloud unique in the experiment.  
\end{table} 
Table 2: Number of points in the point cloud of the 5 sets of instances after preprocessing. of ICP (iter 100)/FR-ICP, the improvement in speed reached 69%/48%. Based on the above observations, we can conclude that our method can solve the problem of point cloud registration easily falling into local optimum, and has advantages in speed and accuracy compared with traditional methods.