# VFLD: Voxelized Fractal Local Descriptor
## 5 Conclusions and Future Work  
In this work, we proposed VFLD, a Voxelized Fractal Local Descriptor. It computes a descriptor for each point in a point cloud, exploiting the fractal dimension of its neighboring points. The descriptor was evaluated using two different datasets and largely outperformed FPFH in terms of descriptiveness, reaching more than 60% accuracy considering an error below 1 (as it can be seen in Figure 11). Regarding the robustness to Gaussian noise and point cloud density, these properties are derived from the nature of the box-counting method for calculating the fractal dimen  
Figure 22: Registration results of two different environments using VFLD as the descriptor of choice for the feature-matching step. Four different clouds are shown for each example; each one is of a different color. (**a**–**d**,**h**–**k**) are color images from a sequences of the dataset, and (**e**–**f**,**l**–**n**) are the tridimensional reconstruction of the scene achieved using the proposed VFLD. sion. Since the occupancy of the space around the point is counted, this calculation is not affected by Gaussian noise up to a certain level. The same property applies to the point density since the occupancy calculation gives the same results with one point somewhere in space as with several points. On the other hand, our proposal showed poorer performance on simple and planar surfaces. This is understandable, however, as these parts are considered uninteresting, and any other descriptor will likely struggle. Regarding the computation time, the algorithm is not as efficient as its competitors. We measured the time it took to process a single point cloud with 3000 points using the methods involved in the experiments, with the results being as follows: FPFH delayed 16.34 ms, VFLD took 29,413.02 ms, 3 DSC runtime was 7259.01 ms, and PFH computed for 15,686.68 ms. The runtimes were measured in the same computer with all the optimizations (OMP and CUDA, Open3D and PCL 1.8 implementations) enabled for the descriptors that supported them. As can be seen, our approach clearly performed worst. However, this is to be expected, as we straightforwardly implemented the theoretical basis. Nonetheless, the main bottleneck points of our method are two. On the one hand, the fractal dimension should be computed for a set of radii, while, on the other hand, the fractal dimension computation (box-counting) method also requires several iterations. This is performed for a single point. Thus, the process is also repeated for each point in a point cloud. A significant speedup may be achieved if these processes run in parallel. Further improvement could be obtained by leveraging a GPU-CUDA implementation. As a summary, in comparison with FPFH, which is the main competitor of our approach regarding non-learning 3D feature descriptors, our approach provides a more powerful descriptor. Regarding registration tasks, two public datasets of point clouds captured with commercial sensors were put to the test. First, with VFLD, about 58% of the scenes in ScanNet yielded an equivalent error of under 2 cm in a room with 10-m walls. FPFH only achieved 18% for the same error threshold. In addition, the qualitative analysis of VFLD in the ViDRILO dataset (Kinect v1 sensor with no processing of the point clouds) also reported sound quality of three-dimensional reconstruction of the scenes. VFLD was reportedly also more tolerant to noise. Our approach also provides 18 components in its descriptor (FPFH has 33), which makes any pipeline involving it inherently faster without further optimizations. As the downside, it can be mentioned that, in its actual implementation, VFLD requires more computation time that its competitor. As a future work, we plan to tackle the optimization of the method so that it is competitive in terms of runtime. As mentioned, one weakness of the registration pipeline is that we did not use a keypoint detector.