# VFLD: Voxelized Fractal Local Descriptor
## 4 Experimentation  
In order to test the suitability of VFLD, we carried out an extensive set of tests. The experimentation involved two different datasets and was always compared with the Fast  
Figure 4: Diagram of the VLFD generation process. Figure 5: Visualization of the steps that comprise the computation of the descriptor. (**a**) The surrounding points at different radii are obtained. Two radii are used in this example for visualization purposes. (**b**) Box-counting is used to obtain the leaf size and the occupied boxes on each subset. Four iterations are visualized. (**c**) The log–log curve is generated for the data obtained, and a line is fitted. Its slope is the fractal dimension. Figure 3: Plot of the computed fractal dimension for \(nIters=\{3,5,7,15\}\) for a random set of points. This is a log–log plot in which the X-axis refers to the inverse of the voxel size in the box-counting method, while the Y-axis is the number of occupied boxes. Note the difference in the slope (FD, fractal dimension) of the fitted line when \(nIters\) is set too high. Point Feature Histogram (FPFH), which is widely used in the context of 3D data feature description. The aim of the experiments was to set the optimal values for the parameters of the proposal. We followed the testing protocol proposed in [29]. For each point cloud of the dataset, a random translation and rotation were applied, thus providing two versions of the same point cloud. One is the target cloud \(PC_{t}\) and the other the modified cloud \(PC_{m}\). We computed the accuracy and the precision-recall curve in order to quantify the descriptiveness of the method. Accuracy measures the percentage of correct matches out of the total number of matches (both correct and incorrect). It is a global metric that evaluates how well the descriptor performs in making matches across all possible cases. It indicates what percentage of the matched points between the two transformed clouds are correct, that is, how many of the total generated matches are truly valid. Precision focuses on how many of the predicted correct matches are actually correct. It evaluates the quality of the correct matches predicted by the system. It indicates what percentage of the matches predicted as valid are actually correct. A high precision value means that the descriptor is good at avoiding false positives (incorrect matches predicted as correct). Recall measures the system's ability to find all the correct matches, i.e., how many of the true correct matches have been identified by the descriptor. Recall tells us what percentage of the true correct matches (all points that should correspond between the two point clouds) were successfully identified by the descriptor. A high recall value indicates that the descriptor has a high capacity for detecting correct matches, although it may also generate some incorrect matches (false positives)  
To test our system, we implemented the following protocol. For each point, we obtained the corresponding descriptor using the feature description method under consideration. As a result, two sets of descriptors were computed: one for the target cloud \(PC^{t}\), and one for the modified cloud \(PC^{m}\). Then, for each feature \(f^{t}\) in \(PC^{t}\), the nearest \(f^{m}_{1}\) and the second nearest \(f^{m}_{2}\) features of \(PC^{m}\) were obtained. We then computed the ratio between the distances \((|f^{t}-f^{m}_{1}|)/(|f^{t}-f^{m}_{2}|)\). If the resulting ratio was under a threshold \(\tau\), the two features \(f^{t}\) and \(f^{m}_{1}\) were considered a match. Furthermore, if the distance between the 3D points of the features that match was under another threshold \(\rho\), the match was considered a true match. Otherwise, it was taken as a false match. Precision was computed as the number of correct matches with respect to the matches. Additionally, the recall was the number of correct matches with respect to those points. We used the metrics to construct the precision-recall curves (PRCs).