# A Comparative Study of Weighting Methods for Local Reference Frame
## 4 Experimental Results and Analysis
### Test on the Six Datasets
The occlusion and clutter that are far away from keypoint do not affect the repeatability of LRF. This explains why TOLDI, SHOT, BSC, and GF(\(\sigma=0.4\)) always achieve the best performance in Figure 3a,b when the degree of occlusion or clutter increases. Repeatability of LRF Under Different Levels of Gaussian Noise, Point Density Variation, Shot Noise, and Keypoint Localization Error  
In the experiments, the Retrieval dataset is applied. The four kinds of nuisances are respectively injected into the 6 noise-free scenes. The standard deviation of Gaussian noise is set as \(0.1 pr\), \(0.2 pr\), \(0.3 pr\), \(0.4 pr\), and \(0.5 pr\) to create noisy point clouds. The sampling rate is set as 9/10, 8/10, 7/10, 6/10, and 5/10 to simulate point density variation. The outlier ratio is set as 0.2%, 0.5%, 1%, 2%, and 5% to extract some points. These points are moved along their normal vectors by a magnitude of \(0.5\times R\) to create outliers. The Gaussian noise with a standard deviation of \(0.2 pr\), \(0.4 pr\), \(0.6 pr\), \(0.8 pr\), and \(1 pr\) is added to the scene keypoints to simulate keypoint localization error. The experimental results are illustrated in Figure 4.  
Figure 3: The repeatability of LRF obtained by the five weighting methods with respect to four kinds of nuisances, including (**a**) occlusion, (**b**) clutter, (**c**) partial overlap, and (**d**) varying support radii. As shown in Figure 4, for different nuisances, the best method is different. In terms of robustness to noise and keypoint localization error (Figure 4a,d), GF(\(\sigma=0.6\)), SHOT, and BSC achieve the best performance. It indicates that the contributions of distant points should be controlled properly for the two nuisances. Both contributing too many and too little will degrade the robustness of the LRF. In terms of robustness to point density variation (Figure 4b), GF(\(\sigma=0.8\)), GF(\(\sigma=1\)), and EM are the best methods. Therefore, the contributions of the distant points ought to be increased for point density variation. In terms of robustness to outliers (Figure 4c), GF(\(\sigma=0.2\)) is the best method. This indicates that the contributions of the distant points should be weakened for outliers. This conclusion is just opposite to that drawn in reference [20]. The experiments of reference [20] were performed on the datasets with noise. Their conclusion is probably unreliable because the applied datasets are not only affected by outliers. Based on the experimental results in Sections 4.2 and 4.3, we can conclude that when the weights of the distant points are too large (e.g., EM), the LRF is susceptible to occlusion, clutter, missing regions, noise, outliers, and keypoint localization error. However, when the weights of the distant points are too small (e.g., GF(\(\sigma=0.2\))), the LRF is sensitive to noise, point density variation, and keypoint localization error. Figure 4: The repeatability of LRF obtained by the five weighting methods with respect to four kinds of nuisances, including (**a**) Gaussian noise, (**b**) point density variation, (**c**) shot noise, and (**d**) keypoint localization error.