# A Fast Point Clouds Registration Algorithm Based on ISS-USC Feature for the 3D Laser Scanner
## 4 Experimental Results and Analysis
### Experimental Procedure  
In order to verify the advancement and effectiveness of the improved voxel filter, the traditional ICP algorithm, the ICP algorithm with voxel filter and the ICP algorithm with the improved voxel filter are used for registration comparison of the four models. The standard to measure the registration accuracy uses the _getFitnessScore_ in PCL, which is the average of the squared distances of all corresponding points after registration. The smaller the value is, the smaller the error is, which is defined as:  
\[getFitnessScore=\frac{\sum_{i=1}^{N}{(p_{i}-q_{i})^{2}}}{N} \tag{11}\]  
where \(p_{i}\) is any point in the source point clouds \(P\), \(q_{i}\) is the corresponding point in the target point clouds \(Q\), and \(N\) is the corresponding point pairs after the completion of ICP fine registration iteration based on KD tree. Table 3 shows the registration results of the three algorithms for the four models. Figure 10 shows the comparison curves of registration time and registration error of three algorithms under four model conditions. In the figure, the left axis is the registration time, and the right axis is the registration error. It can be seen that the registration time of the traditional ICP algorithm is longest, and the registration accuracy is sometimes high and sometimes low with the change of the model. For the ICP algorithm with voxel filter, the registration is faster after down-sampling, but the registration accuracy is significantly reduced. For the ICP algorithm with improved voxel filter, not only the registration time is reduced, but the registration accuracy can be stable in a higher range. The results of this registration comparison show that the improved voxel filter can more accurately represent the original data, which has stronger enhancement to the extraction of key points, coarse registration and fine registration. The more accurate the data, the faster the registration speed will be. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**ICP**} & \multicolumn{2}{c}{**ICP+ Voxel Filter**} & \multicolumn{2}{c}{**ICP+ Improved Voxel Filter**} \\ \cline{2-6}  & **Time** & \begin{tabular}{c} **Registration** \\ **Error** \\ \end{tabular} & **Time** & \
\begin{tabular}{c} **Registration** \\ **Error** \\ \end{tabular} & **Time** &
\begin{tabular}{c} **Registration** \\ **Error** \\ \end{tabular} \\ \hline Bunny & 50.451 & 6.62234 \(\times\)\(10^{-5}\) & 2.210 & 1.96057 \(\times\)\(10^{-4}\) & 3.283 & 4.37225 \(\times\)\(10^{-6}\) \\ Armadillo & 45.606 & 4.15124 \(\times\)\(10^{-5}\) & 3.162 & 2.2289 \(\times\)\(10^{-5}\) & 3.017 & 2.24228 \(\times\)\(10^{-5}\) \\ Dragon & 40.574 & 9.28518 \(\times\)\(10^{-3}\) & 6.246 & 9.12843 \(\times\)\(10^{-3}\) & 6.202 & 3.91463 \(\times\)\(10^{-3}\) \\ Drill & 4.558 & 1.754 \(\times\)\(10^{-5}\) & 0.087 & 2.30307 \(\times\)\(10^{-5}\) & 0.043 & 2.28272 \(\times\)\(10^{-5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Registration results of the three algorithms for the four models. Figure 9: Feature points plot extracted from Drill1 and Drill2 models. (**a**) Drill1 model. (**b**) Drill2 model. In order to verify the validity and accuracy of the proposed algorithm, three other algorithms are designed for comparative experiments under the same conditions. The three other algorithms are: the 3 DSC + RANSAC + ICP algorithm without improved voxel filter, the 3 DSC + RANSAC + ICP with improved voxel filter and the USC + RANSAC + ICP algorithm without improved voxel filter. In the process of RANSAC coarse registration, adding a pre-exclusion step can immediately filter out the wrong hypothetical poses, thereby saving more time to generate more other possibly correct hypothetical poses and reducing the time of coarse registration. The distance threshold \(\varepsilon_{RANSA}\) is the judgment criterion for interior point, but the selection of its value will affect the registration accuracy.