# VFLD: Voxelized Fractal Local Descriptor
## 4 Experimentation
### Evaluation of the Registration Pipeline on ScanNet
Next, we measured the mean of this distance over all  
Figure 18: ScanNet scenes splitting steps. (**a**) The initial scene is downsampled into a point cloud of 12,000 points. (**b**) The 2D minimum area rectangle including all the points is obtained. (**c**) This two-dimensional rectangle is divided into four equal parts. (**d**) Three more clouds are created by iterating clockwise from the leftmost cloud. the points in the cloud, and repeated these operations for each point cloud to be registered such that we ended up with an error rate for each cloud of the scene. Finally, we computed the mean of this error value over the clouds, thus obtaining a final error rate for the registration of the whole scene. After iterating over all the dataset, we obtained an error rate for each scene out of the 707 ones in ScanNet. For the comparison, we applied the same process with the FPFH implementation from the Open3D library. As in the experimentation procedure described in Section 4, the parameters for FPFH were set to 5 for radii of the normal estimation, and 10 for the radii of the feature computation. Furthermore, we also assessed the respective performance of VFLD and FPFH for registration on another type of environment. As explained, the point clouds were downsampled using uniform sampling such that each scene contained 12,000 points. In a second phase, we ran this evaluation process over ScanNet data but using voxelized downsampling. This other method gave us different environments from the first one, being much more equalized and aligned as we can see in Figure 19. The results of VFLD and FPFH for these two types of environments are shown in Figures 20 and 21, in which we show the number of scenes within a specific error rate interval. Note that the point clouds are normalized in the range 0-100 such that a 0.2 error means a 0.2% of the size of the maximum dimension of cloud. If we consider them in centimeters, an error of 0.2 would mean  
As we can see from the results in Figure 20, VFLD outperformed FPFH on the first setup, with a mean over all the ScanNet samples of 0.91 and a variance of 13.11, compared to a mean of 1.35 and a variance of 23.23 for FPFH, accounting for a mean decrease in the error rate of 33%. We can note that, for both descriptors, the error rate mean is increased by infrequent elevated values, leading to higher variances. These values generally correspond to scenes where the fragmentation process generates clouds with lower numbers of points (500 or less) due to differences in the layout of the rooms as shown in Figure 8. As the shapes of all the ScanNet scenes are unknown before running the process, some configurations may involve small clouds, leading to poorer performance for registration for both descriptors. Figure 21 shows the results for the voxelized environment. It is worth noting that both VFLD and FPFH showed poorer performance than their corresponding results for the first environment, with a mean of 12.81 and a variance of 227.14 for VFLD, and a mean of 3.45 and a variance of 67.48 for FPFH, denoting an error rate increase of 1408% for VFLD and 255% for FPFH. In this case, FPFH led to a better accuracy than VFLD, which is to be expected, as the fractal dimension relies on the clutter of the points to perform. The voxel grid downsampling process sets the points on planes, which significantly impacts VFLD performance.