# Geometric Detail-Preserved Point Cloud Upsampling via a Feature Enhanced Self-Supervised Network
## 4 Experimental Results and Analysis
### Results of Point Cloud Upsampling  
**Results from testing on ESB dataset. ** Figure 8 validates the performance of our proposed point cloud upsampling method on mechanical CAD models sourced from the ESB dataset. Initially containing 512 points (first column), the point clouds are effectively upsampled to 1024 points (second column) and 2048 points (third column). This quadrupled point density not only enhances the clarity of the point cloud details but also brings the points closer to the geometric surface, ensuring a uniform distribution. Notably, the upsampling process preserves intricate manufacturing details, such as holes, as evident in the bearing seat point clouds presented in Figure 8a. These features remain clear, smooth, and well defined throughout the process. For a deeper understanding of our method, Figure 9 compares the existing point clouds in the ESB dataset (ground truth; GT) with the upsampling results obtained in this paper. In the last column, the red points represent the GT point clouds (2048 points), while the black points represent the upsampling results. A coordinate comparison reveals a consistent topological structure between the two point clouds. As can be seen in the second column, the point clouds upsampled using SSPU-FENet show a uniform arrangement, preserving sharp and boundary features. We also compute the Hausdorff distance (HD) between the GT and upsampled point clouds. For the exhaust elbow point cloud in Figure 9a, the average HD is 6.4242, with a minimum distance of 0.0702 and a maximum distance of 17.0627. Similarly, for the bearing-type part point cloud in Figure 9b, the  
Figure 8: Part results tested in the ESB dataset. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Supervised?** & **Perturbation Learning** & **Params (M)** & **Time (ms)** \\ \hline PU-Net [6] & Yes & No & 3.00 & 4.55 \\ PU-GAN [17] & No & Yes (fixed, 1D) & 2.07 & 7.08 \\ PU-GCN [14] & Yes & No & 0.29 & 5.51 \\ Dis-PU [7] & Yes & No & 3.99 & 12.77 \\ PC2-PU [24] & Yes & No & 1.71 & 4.19 \\ GC-PCU [16] & Yes & Yes (adaptive, 2D) & 5.01 & 858.9 \\ SPU-Net [19] & No & No & 0.68 & 130.9 \\ SAPCU [25] & No & No & 26.48 & 11,607.0 \\ \(S^{3}\) U-PVNet [11] & No & No & 19.64 & 1047.0 \\ SSPU-FENet & No & Yes (adaptive, 3D) & 8.71 & 900.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Comparison of model and time complexity. average HD is 9.7770, with a minimum distance of 0.7280 and a maximum distance of 20.1450. Additionally, the average point-to-face (P2F) distance for the bearing-type part is 3.8090. These metrics further validate the accuracy and precision of our upsampling method. **Results from tested point clouds collected in ModelNet40 and PU-GAN with various numbers of points. ** First, it is important to note that the number of points in a point cloud model can vary significantly. Therefore, it is crucial to assess the sampling effectiveness of our method across various point counts. To validate our approach, we randomly select models from the ModelNet40 dataset [23] and present the results in Figure 10. When dealing with sparse point clouds having diverse point inputs, our SSPU-FENet outperforms other methods, such as PU-Refiner [26] and PUFA-GAN [27]. Notably, even with a minimal input of 256 points, our method generates high-quality upsampled point clouds with well-defined boundaries and reduced blurring compared to PU-Mask [12]. Additionally, we observed that unsupervised methods exhibit varying upsampling effects when the input point clouds are sparse. For example, SPU-Net [19] produces some outliers at the edges of the upsampled point clouds. Similarly, SAPCU [25] generates some points to gather together.