# VFLD: Voxelized Fractal Local Descriptor
## 4 Experimentation
### Evaluation of the Registration Pipeline on ScanNet  
As mentioned before, one of the most common applications for three-dimensional description methods is 3D registration. This is related to computing the transformation between two point clouds that depict parts of the same environment with an overlap between them. By doing so in a loop, a 3D reconstruction of a complex scene can be obtained. Figure 17: Accuracy (top) and precision–recall (bottom) curves for different state-of-the-art methods for ModelNet (leftmost) and Simple Figures (rightmost) datasets. (**a**) ModelNet accuracy; (**b**) Simple Figures accuracy; (**c**) ModelNet precision–recall; (**d**) Simple figures precision–recall. Specifically, an input sequence is composed of a range of point clouds captured in the same environment. Consequently, there must be an overlap between two consecutive clouds. The method starts with two correlated point clouds. A uniform sampling filter is then used to reduce the number of points of both clouds. The next step typically involves a keypoint detector, but we decided not to include one to avoid the point selection process impacting the final result. The descriptors are then extracted for all the points of both subsampled clouds and the corresponding points computed using the nearest neighbor method in the descriptor space. The correspondences are forwarded to RANSAC (RANdom SAmple Consensus) [37], which computes the transformation of the second cloud with respect to the first one. The corresponding cloud is transformed and joined to the first cloud. Finally, ICP (Iterative Closest Point) [38] can be used to further refine the computed transformation. In our case, we did not involve ICP in our experiments. Whilst ICP is a common step in the registration pipeline, we opted to omit it because if is were included, it would be harder to discern whether VLFD is working properly or, in contrast, whether it is ICP providing such accuracy. This process was applied iteratively to all the clouds in the sequence, finally achieving a three-dimensional reconstruction of the environment. We applied this registration process to the ScanNet dataset. As explained in Section 4.1, ScanNet is not intended to perform registration, as it only provides point clouds of complete rooms. Consequently, we were obliged to split the point clouds performing the following procedure. First, we started by transforming the scene into a point cloud, and downsampling it to make it treatable. The point clouds were downsampled using uniform sampling such that each one ended up with 12,000 points. Subsequently, we flattened the point cloud in two dimensions by removing the z-axis, finding the minimum area rectangle, including all these 2D points. We then split this rectangle in four equal quarters, creating four different point clouds. We then iterated clockwise through these point clouds starting from the leftmost one, and generated for each pair of consecutive clouds a new one, made of half of the first one and half of the second one. Finally, we ended up with seven overlapping point clouds obtained from the initial scene. These steps are described in Figure 18.  
At this point, we were then able to run a registration pipeline on these clouds, as there were overlapping areas. We applied the registration process described earlier in this Section to every set of point clouds obtained from each ScanNet scene. The parameters for VFLD were the best values found in the previous experimentation, namely, 18 as the number of radii, 1 as the starting radius, 0.5 as the radius increment, and 5 as \(nIters\). All the point clouds were normalized such that the minimum and maximum dimensions were 0 and 100. In order to accurately evaluate the efficiency of VFLD for registration, we determined an error rate with the following procedure. For each point in the cloud being registered, we computed the Euclidean distance between the new point after registration, and its corresponding initial true position.