# Geometric Detail-Preserved Point Cloud Upsampling via a Feature Enhanced Self-Supervised Network
## 4 Experimental Results and Analysis
### Ablation Studies  
**Analysis of the size of the neighboring range. ** The neighborhood size significantly influences the performance of local feature encoding and feature learning in point cloud upsampling, as shown in Figure 6, with a point cloud of 512 points as network input and the average results of upsampling on different ratios (\(4\times,8\times,16\times\)) as the output. An analysis of the chamfer distance (CD) and Hausdorff distance (HD) reveals that a reduction in these distances corresponds to an enhancement in upsampling quality. Notably, the optimal results are attained at a neighborhood size of 32. Additionally, the point-to-face distance (P2F) represents the importance of a smaller distance, indicating a closer approximation to the geometric surface. Specifically, a neighborhood size of 32 yields the lowest average distance, approximately 1.9. The Jensen-Shannon divergence (JSD) metric provides insights into distribution disparities, while the two uniform metrics assess point alignment, all converging to their minimal values at a neighborhood size of 32. Moreover, whether using 512, 1024, or 4096 points as network input for upsampling, it shows that a neighborhood size of 32 still gives the best results in terms of evaluation metrics; e.g., for 1024 points as network input for \(4\times\) upsampling, a neighborhood size of 32 yields the lowest average distance under the P2F metric, 1.9011, and a neighborhood size of 16 yields the distance 3.5910. In summary, this particular setting is crucial for achieving efficient and superior results in point cloud upsampling. For fewer or more points as input, we need to recompute the size of this neighborhood. **Analysis of network modules. ** Table 2 shows the average metric results on different upsampling ratios (\(4\times,8\times,16\times\)) when inputting point clouds with 512 points to the three distinct networks for upsampling, which are SSPU-FENet, SSPU-FENet without the FEM (where the coordinates are directly fed into the network), and SSPU-FENet without the NPM. The results show that SSPU-FENet exhibits the lowest values across all metrics, clearly demonstrating the significance of each component in enhancing point cloud upsampling. Meanwhile, Figure 7 shows a visualization of the results. When the FEM is omitted, a  
Figure 6: Comparison of the average performance of different upsampling ratios under different neighborhood sizes. noticeable increase point-to-face distance (P2F) is observed, rising from 1.9052 (Figure 7b) to 1.9210 (Figure 7a). This indicates that some of the interpolated points (mainly edge and corner points) have not been placed in the proper positions and they are too close to the current center point. It leads to a degradation in upsampling quality. Furthermore, the exclusion of the NPM also results in a significant deterioration of performance. Specifically, the chamfer distance (CD) increases from 0.1148 to 0.2206, indicating a decrease in the accuracy and precision of the upsampled point cloud. In summary, the modules of SSPU-FENet play a pivotal role in ensuring the effectiveness of point cloud upsampling. The integration of both the FEM and NPM is crucial for achieving optimal results. **Analysis of model and time complexity. ** In Table 3, a comprehensive comparison of various network models is presented, emphasizing key aspects such as network type, network parameter size, inference time, and the incorporation of feature perturbation learning. A method like PU-GAN [17] employs fixed-value perturbation learning, leading to faster inference speeds despite its unique architecture as a generative adversarial network. Conversely, the GC-PCU [16] model employs adaptive perturbation learning, resulting in an increase in both parameters and inference time compared to PU-GAN or non-perturbation methods. As for the proposed SSPU-FENet, it is specifically designed to preserve sharp features and enhance feature capabilities.