# A Comparative Study of Weighting Methods for Local Reference Frame
## 4 Experimental Results and Analysis  
### Test on the Six Datasets  
The experimental results of the six datasets are listed in Table 2. For the Retrieval dataset, the 6 noise-free models are transformed to get 6 scenes by artificially setting the ground-truth transformation. Then the 6 scenes are down-sampled (sampling rate of 7/10), and Gaussian noise (standard deviation of \(0.3 pr\)) is added to them. The aim is to create a combination of nuisances. The other datasets are real data obtained by laser scanning devices, so no additional operation is implemented on them. In addition, we recommend that readers first see Section 4.4 to know which weighting method makes the distant points contribute more to the covariance matrix and which weighting method makes them contribute less to the covariance matrix. From Table 2, we can see that, on the Retrieval dataset, GF(\(\sigma=0.8\)) obtains the best performance, followed by GF(\(\sigma=1\)), GF(\(\sigma=0.6\)), BSC, and SHOT. TOLDI achieve relatively poor performance. For this dataset, the weighting method is used to reduce the effect of Gaussian noise and point density variation. Because there is no clutter, occlusion, and missing region, the contributions of the distant points do not need to be declined. Therefore, the weights of the distant points should be increased. However, as can be seen from the calculated results, EM and GF(\(\sigma=1\)) obtain inferior performance. This indicates that too large contributions of the distant points would also degrade the repeatability of the LRF, even without the effect of clutter, occlusion, and missing region. On the Laser Scanner and LiDAR Registration datasets, GF(\(\sigma=0.4\)), TOLDI, SHOT, and BSC have relatively good performance, whereas EM obtains poor performance. Both of the two datasets are high-quality, so they are less contaminated by noise. In this case, the contributions of distant points ought to be controlled properly, as will be shown in Section 4.3. Furthermore, their contributions should be weakened to improve the robustness to clutter, occlusion, and missing regions as well. The is the reason why GF(\(\sigma=0.4\)) and TOLDI achieve good performance, while EM and GF(\(\sigma=1\)) obtain poor performance on the two datasets. For the Kinect and Kinect Registration datasets, the ranking of all the methods changes significantly. The three best methods are GF(\(\sigma=0.8\)), GF(\(\sigma=1\)), and EM, while TOLDI gets a relatively poor performance. In addition to shape incompleteness (i.e., occlusion, clutter, and missing regions), the two datasets are also rather sparse (i.e., the point density variation is obvious) and noisy. Especially for point density variation, the contributions of the distant points should be increased, as will be shown in  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Retrieval** & \begin{tabular}{c} **Laser** \\ **Scanner** \\ \end{tabular}  & **Kinect** & **Space Time** & \ \begin{tabular}{c} **LiDAR** \\ **Registration** \\ \end{tabular}  & \begin{tabular}{c} **Kinect** \\ **Registration** \\ \end{tabular}  \\ \hline EM & 0.4992 & 0.0998 & **0.2040** & 0.2507 & 0.1079 & 0.0949 \\ SHOT & 0.5121 & 0.1360 & 0.1903 & 0.2517 & 0.1330 & 0.0905 \\ BSC & 0.5121 & 0.1360 & 0.1903 & 0.2517 & 0.1330 & 0.0905 \\ TOLDI & 0.4445 & **0.1386** & 0.1605 & 0.2458 & 0.1391 & 0.0792 \\ GF(\(\sigma=0.2\)) & 0.1930 & 0.0936 & 0.0468 & 0.2189 & 0.1234 & 0.0350 \\ GF(\(\sigma=0.4\)) & 0.4056 & 0.1338 & 0.1414 & 0.2478 & **0.1420** & 0.0751 \\ GF(\(\sigma=0.6\)) &Section 4.3. TOLDI is sensitive to point density variation, so it exhibits poor repeatability, even under the case with clutter, occlusion, and missing regions. For the Space Time dataset, the four methods (GF(\(\sigma=0.6\)), GF(\(\sigma=0.8\)), SHOT, and BSC) achieve relatively good performance, among which GF(\(\sigma=0.6\)) is the best one. In this dataset, besides clutter and occlusion, noise and outliers are the main nuisances.