## 4 Experiments
### Experiments on Registration Effectiveness
#### 4.3.5 Comparison between Registration Effectiveness of Point Clouds  
As a result, we compare our feature descriptor to state-of-the-art feature descriptors using our registration framework. The average registration errors of point clouds in our dataset are shown in Table 3. It clearly shows that the average registration error for point clouds in the Standford 3D Scanning Repository via our proposed feature descriptor is moderate, lagged by BRoPH and KDD, and the average registration error for point clouds in the SpaceTime dataset via our proposed feature descriptor is also moderate, lagged by 3 DSC, BRoPH, and KDD. However, in the Kinect dataset, pairwise registration based on our proposed feature descriptor obtains the least registration error, which means it achieves the best registration effectiveness. The deep-seated reason is that the sampling quality or noise level of the three datasets is different, and our proposed feature descriptor has a greater robustness to noise. The point clouds in the 3D Scanning Repository are scanned with a Cyberware 3030 MS scanner, which is a swept-stripe laser triangulation range scanner with a higher sampling quality; the point clouds in the SpaceTime dataset are captured by a SpaceTime Stereo scanner with a high sampling quality, and point clouds are scanned by a low-cost Microsoft Kinect scanner with a low sampling quality. Different sampling qualities of the scanner decide the noise level of captured point clouds, with higher sampling quality resulting in less noise, and vice versa. Point clouds in the 3D Scanning Repository and the SpaceTime dataset have lower noise, so feature descriptors  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dataset** & **Method** & **Average \(\theta_{r}\)** & **Average \(\theta_{t}\)** & **Average \(\theta\)** \\ \hline \multirow{6}{*}{Stanford 3D Scanning Repository} & Based on our proposed transformation estimation & 0.9482 & 1.9568 & 1.4525 \\  & Based on feature matching & 9.4399 & 7.3246 & 8.3823 \\  & Based on clustering & 4.3431 & 6.5498 & 5.4465 \\  & Based on ICP & 9.8769 & 9.6781 & 9.7775 \\  & Based on feature matching + clustering & 1.4501 & 2.0906 & 1.7704 \\  & Based on feature matching + ICP & 7.9139 & 6.2305 & 7.0722 \\  & Based on RANSAC & 3.7798 & 2.1909 & 2.9854 \\ \hline \multirow{6}{*}{SpaceTime dataset} & Based on our proposed transformation estimation & 1.1584 & 1.7649 & 1.4617 \\  & Based on feature matching & 8.2308 & 6.5423 & 7.3866 \\  & Based on clustering & 4.5671 & 4.7348 & 4.6510 \\  & Based on ICP & 8.5521 & 7.2261 & 7.8891 \\  & Based on feature matching + clustering & 2.1989 & 2.1091 & 2.154 \\  & Based on feature matching + ICP & 3.2239 & 4.0121 & 3.618 \\  & Based on RANSAC & 3.3201 & 3.2271 & 3.2736 \\ \hline \multirow{6}{*}{Kinect dataset} & Based on our proposed transformation estimation & 1.3739 & 2.7891 & 2.0815 \\  & Based on feature matching & 10.8911 & 10.0919 & 10.4915 \\ \cline{1-1}  & Based on clustering & 6.2237 & 8.3211 & 7.7274 \\ \cline{1-1}  & Based on ICP & 12.3002 & 10.0809 & 11.1906 \\ \cline{1-1}  & Based on feature matching + clustering & 2.3271 & 3.1633 & 2.7452 \\ \cline{1-1}  & Based on feature matching + ICP & 4.0212 & 3.7751 & 3.8982 \\ \cline{1-1}  & Based on RANSAC & 3.9432 & 3.5872 & 3.7652 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Average registration errors for point cloud registration based on different transformation estimations.  
such as 3 DSC, BRoPH, and KDD are more advantageous, and the registration effectiveness based on these feature descriptors are naturally higher than the registration effectiveness based on our proposed feature descriptor. However, with the increase in noise in point clouds, the advantage of our proposed feature descriptor in point cloud registration also emerges, which is due that the mean operation in the process of producing covariance filters out of most of the noise-damaged samples, making our feature descriptor very robust to noise and achieving the highest registration performance in the Kinect dataset.