# A Fast Point Clouds Registration Algorithm for Laser Scanners
## 3 Experimental Results
### Selection of Main Parameters  
The algorithm in this paper changes the registration result by modifying the parameters. Through the registration error returned by the experimental results, we find that many parameters are related to the grid size of the point cloud. Root mean square error (RMSE) is the error measurement method often used in point cloud registration, which means the average of the sum of squared distances between the corresponding points of two point clouds. It is defined as  
\[RMSE=\sqrt{\frac{1}{N}{\sum}_{i=1}^{N}\left\|p_{i}-q_{j}\right\|^{2}},(1\leq j \leq M) \tag{12}\]  
where, \(p_{i}\) and \(q_{j}\) are nearest neighbors in pair, located in data \(P\) and \(Q\), respectively, and \(N\) and \(M\) represent the registration scales of \(P\) and \(Q\). The smaller the RMSE, the better the registration result.  
Table 1 shows the number of sampling points and ISS feature points under different grid sizes, the first two lines belong to source point cloud \(P\), the rest belongs to Q. In orderto reduce the running time of the algorithm, the number of sampling points is generally several thousand. Considering that too many feature points will increase the calculation time, and too few will affect the registration accuracy, the grid size is selected as 0.03 m.  
For the 3 DSC algorithm, the main parameters are \(R_{3 dsc\_frame}\), \(r_{min}\), and \(\rho_{i}\). \(R_{3 dsc\_frame}\) denotes the support radius for 3 DSC and is usually set to 10 times of the grid size. \(r_{min}\) is the minimal radius value for the search sphere, which is often set same scale with the grid size. \(\rho_{i}\) is the density of the corresponding local point, which is set one-tenth of \(r_{min}\).  
Table 2 shows the registration results of different \(\varepsilon_{runsac}\), when the initial value of \(\varepsilon_{icp}\) is 0.1 m. When \(\varepsilon_{transsac}\) = 0.3 m, the registration time is the least and the RMSE is also the smallest.  
Table 3 shows the registration results of different \(\varepsilon_{icp}\), when \(\varepsilon_{transsac}\) = 0.3 m. When \(\varepsilon_{icp}\) = 0.3 m, the RMSE is the smallest.  
Figure 9 shows the registration results of \"Bed\" with different grid sizes. It can be seen from the figure that as the grid size increases, the registration time and the number of ISS-3 DSC features continue to decrease, and the RMSE value is quite small in the range of 0.02 m to 0.04 m, so we set the grid size to be 0.03 m. More parameters are listed in Table 4.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Grid Size/m** & **0.01** & **0.02** & **0.03** & **0.04** & **0.05** \\ \hline
**Sample points (P)** & 36,415 & 11,174 & 5425 & 3190 & 2173 \\
**ISS feature points (P)** & 769 & 220 & 120 & 48 & 32 \\
**Sample points (Q)** & 38,213 & 11,727 & 5661 & 3394 & 2239 \\
**ISS feature points (Q)** & 879 & 252 & 112 & 54 & 34 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The number of sampling points and feature points under different grid sizes.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(\varepsilon_{input}\)/m & **0.02** & **0.05** & **0.08** & **0.1** & **0.2** & **0.3** & **0.4** & **0.5** & **0.6** \\ \hline
**Time/s** & 0.812 & 0.8 & 0.813 & 0.801 & 0.819 & 0.803 & 0.802 & 0.806 & 0.809 \\
**RMSE/m** & 0.091 & 0.091 & 0.081 & 0.078 & 0.078 & 0.07 & 0.07 & 0.07 \\ \hline \hline \end{tabular}
\end{table}
Table 3: \(\varepsilon_{transsac}\) = 0.3 m, the registration results of different \(\varepsilon_{icp}\).  
Figure 9: The result of registration under different leaf sizes.