# A Fast Point Clouds Registration Algorithm for Laser Scanners
## 3 Experimental Results
### Evaluation
Through the above experiments and the determination of the ERMSE values, we compared the magnitude of RMSEs and ERMSEs for the four methods as shown in Figure 11. Here, ICP uses the right vertical coordinate and SAC-IA+ICP, 3 DHoPD+ICP, and our method use the left vertical coordinate. Figure 11 shows that the ERMSE error is slightly lower than RMSE, and agree with the change trend of RMSE. Table 5 shows the final RMSE, \(\beta\), and ERMSE values of ICP, SAC-IA+ICP, 3 DHoPD+ICP, and our method for the six models, and the best results are highlighted in bold font. From the experiment results, we can see that ICP cannot be used for models with large initial pose deviations, while SAC-IA+ICP, 3 DHoPD+ICP, and our method can be used for all the models, and their registration accuracies are both quite high. Table 6 shows the registration time of each algorithm for the six models in the conditions. We can see that our approach is the most efficient. The total registration time of our method for the six models is only about 1/25 of SAC-IA+ICP method and 1/2 of 3 DHoPD+ICP method. To get the reason of the performance in details, we compared the operating time of ICP registering, and before this step, between 3 DHoPD+ICP method and ours. For the model of Bunny, the ICP registering time of our method is four orders of magnitude lower than that of the 3 DHoPD+ICP method, while the preparing time is  
Figure 10: Analysis of registration resultsby iterative closest point (ICP), sample consensus initial alignment (SAC-IA+ICP), 3D histograms of point distributions ICP (3 DHoPD+ICP) and our method. (**a**) Bed, (**b**) Motorbike, (**c**) Piano, (**d**) Dragon1, (**e**) Dragon2, (**f**) Bunny. about 0.4 s higher than it. This result indicates that for the entire point clouds registration process, optimizing feature descriptors is a more effective way. The registration results of each algorithm are shown in Figure 12. In the experiments, the source point clouds are in green, the target point clouds are in red, and the registered point clouds are in blue. It can be seen from the results that the ICP has a large registration error for the point cloud with large initial positions, and the registration of Bed, Motorbike, Piano, and Dragon1 point are failed. The SAC-IA-IA+ICP algorithm, the 3 DHoPD+ICP algorithm, and our method have nearly the same registration results for the six models, which are all registered successfully. On the other hand, our approach has the least registering time, showing a higher efficiency. Hence, this algorithm has a significant improvement over others. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **ICP** & **SAC-IA+ICP** & **3 DHoPD+ICP** & **Ours** \\ \hline
**Bed** & 30.208 & 14.266 & 1.043 & **0.662** \\
**Motorbike** & 3.099 & 7.191 & 0.689 & **0.56** \\
**Piano** & 22.33 & 13.16 & 0.732 & **0.583** \\
**Dragon1** & 4.776 & 17.426 & 1.385 & **0.38** \\
**Dragon2** & 1.014 & 18.538 & 1.751 & **0.696** \\
**Bunny** & 1.745 & 19.342 & 1.462 & **0.613** \\
**Total** & 63.172 & 89.923 & 7.062 & **3.494** \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Registration time for six models of each algorithm/s. Figure 11: Root mean square error (RMSE) and effective root mean square error (ERMSE) of ICP, SAC-IA+ICP, 3 DHoPD+ICP, and our method.