# Geometric Detail-Preserved Point Cloud Upsampling via a Feature Enhanced Self-Supervised Network
## 4 Experimental Results and Analysis
### Results of Point Cloud Upsampling
In addition, \(S^{3}\) U-PVNet [25] blurs some non-flat regions, as shown in Figure 11.  
Second, in Figure 12, we present the upsampling results on the PU-GAN dataset, where the density of the input point clouds (2048 points) is enhanced by a factor of 16\(\times\) using various methods, including PU-Net [6], PU-GAN [17], PU-GCN [14], Dis-PU [7], PC2-PU [24], and our SSPU-FENet. The first row of Figure 12a,b shows the detailed local parts of the upsampling results, and the second row shows the whole upsampling results. As can be seen from Figure 12, the other methods, while performing well in most regions, generate noisy points in non-flat regions (e.g., edge parts). For example, the bear point clouds generate noise points at the edges (red boxed parts in Figure 12a), and the point clouds of the legs of the dog are connected due to noisy points (red boxed parts in Figure 12b). This is mainly due to the fact that these methods (e.g., repulsion loss, direct addition of 1D or 2D noise perturbations) give a large repulsive force to the points in these regions, leading to the generation of noisy points. While SSPU-FENet adds learnable 3D noise perturbation parameters, and considers repulsion loss (uniform) in the loss function, thus maintains distinct features without points gathering together. Figure 9: Comparison results between the GT point clouds in the ESB dataset and our generated point clouds. Figure 11: Upsampling (4\(\times\)) the point clouds from PU-GAN’s dataset with 512, 1024, 2048, and 4096 input points. Figure 10: Upsampling (4\(\times\)) the point cloud Cup from ModelNet40 with 256, 1024, and 4096 input points. Third, we provide a detailed analysis using various evaluation metrics to further evaluate the performance of our proposed network. The results for 4\(\times\) and 16\(\times\) upsampling are summarized in Table 4. Upon examining the CD metric in both the 4\(\times\) and 16\(\times\) results, it becomes evident that the distance metrics of our method are closer to 0 compared to other methods. This observation indicates a lower degree of information loss, demonstrating the effectiveness of our approach in preserving the original geometry. Furthermore, according to the P2F evaluation metrics based on the 4\(\times\) upsampling results, the P2F value of PU-Net (supervised learning method with repulsion loss) is 4.3590, and the P2F value of PU-GAN (unsupervised learning method with addition 1D noise) is 3.6100; while the P2F value of our SSPU-FENet is only 2.7034. This indicates that the points in our upsampled model are more closely aligned with the geometric surface. Taken together with the visual representations in Figure 12, it is clear that the SSPU-FENet proposed in this paper not only minimizes point reconstruction loss but also maintains point uniformity and sharp features, collectively leading to an enhanced upsampling effect. In addition, in terms of HD metrics, the results of this paper are only higher than the results of the 5\({}^{3}\) U-PVNet [25] method. This is due to the fact that the \(S^{3}\) U-PVNet [25] method adjusts the results through two processes of up- and downsampling (with high experimental complexity, as shown in Table 3), while this paper obtains the dense point clouds through only one process. Whereas the HD metrics reflect the maximum mismatch through the coordinates, the work is not an alignment, so a certain degree of error is acceptable. In summary, compared with visualization results and evaluation metrics, the method proposed in this paper generates more reasonable point positions than other methods.