# A Comparative Study of Weighting Methods for Local Reference Frame
## 4 Experimental Results and Analysis
### Test on the Six Datasets
For outliers, the weights of the distant points should be reduced, because outliers are far away from the local surface. Moreover, this is helpful in reducing the effect of clutter and occlusion. However, if the weights of the distant points are too small, the LRF is sensitive to noise. Hence, TOLDI and GF(\(\sigma=0.2\)) obtain the worst performance. Based on the above discussion, we can know that no weighting method is always the best for all the datasets, because different datasets contain different kinds of nuisances, and the levels of nuisances are also different. Additionally, BSC is totally equivalent to SHOT, because the two methods always achieve the same results on the six datasets. Repeatability of LRF Under Different Levels of Occlusion, Clutter, and Partial Overlap, as Well as Varying Support Radii  
The calculated results under the four nuisances are shown in Figure 3. The three terms (including occlusion, clutter, and varying support radii) are tested on the Laser Scanner dataset. The term (partial overlap) is tested on the LiDAR Registration dataset. For the Laser Scanner dataset, we compute the percentages of occlusion and clutter of each model-scene pair. Then, according to the degree of occlusion, all the model-scene pairs are grouped into 6 clusters, and according to the degree of clutter, they are separated into 7 groups. The partition intervals for occlusion are respectively less than 65%, [65%, 70%), [70%, 75%), [75%, 80%), [80%, 85%) and [85%, 90%), and those for clutter are respectively less than 65%, [65%, 70%), [70%, 75%), [75%, 80%), [80%, 85%), [85%, 90%) and [90%, 95%). For the LiDAR Registration dataset, we compute the degree of overlap of each view pair. Only the view pairs with overlap being more than 0.3 are applied for the experiments. Then, these view pairs are divided into 7 groups according to the degree of overlap, and the partition intervals are (0.3, 0.4], (0.4, 0.5], (0.5, 0.6], (0.6, 0.7], (0.7, 0.8], (0.8, 0.9] and (0.9, 1], respectively. On the test for varying support radii, the radius is set from \(5 pr\) to \(30 pr\) with a step of \(5 pr\). As we can see from Figure 3a,b, with the increase of occlusion and clutter, the repeatability of the LRF decreases on the whole. In Figure 3c, the repeatability of the LRF increases as the overlap increases. TOLDI, SHOT, BSC, and GF(\(\sigma=0.4\)) are the best methods under different degrees of occlusion, clutter, or overlap. This indicates that reducing the contributions of the distant points indeed work to enhance the robustness to occlusion, clutter, and missing regions. We can also see that when the degree of occlusion, clutter, or overlap increases, the four methods are always the best. In other words, we do not need to further reduce the weights of the distant points when the degree of occlusion, clutter, or missing regions becomes larger. The weights of the distant points just need to be properly reduced. However, from the results in Table 2, we can know that if the experiments are tested on Kinect and Kinect Registration datasets, which are pretty sparse and noisy, the best methods would be GF(\(\sigma=0.8\)), GF(\(\sigma=1\)) and EM. Therefore, the weighting method should be designed to first reduce the effect of other nuisances (e.g., noise and keypoint localization error). Then, if occlusion, clutter, and missing regions are present, the weighting method should be further adjusted to reduce the effect of these nuisances. In Figure 3d, TOLDI is the best method when the support radius is \(10 pr\) and \(15 pr\), whereas GF(\(\sigma=0.4\)) is the best method when the support radius is \(20 pr\) and \(25 pr\). No method is always the best for all the support radii. With the increase of the support radius, the occlusion and clutter near the keypoint are introduced into the local neighborhood. Therefore, the weights of the distant points need to be further reduced. Especially, when the support radius is \(30 pr\), GF(\(\sigma=0.2\)) is the best method, which largely reduces the weights of the distant points.