## 3 Experiments and Results
### Experimental Results on MU-GAN  
To verify the robustness of the proposed network, a small hole in each model from different parts of the complete CHarts model is generated for testing. Figure 7 shows the complete results of the input data. Our network has more reasonable repair results on both the head with more feature points and the body with fewer feature points. Specifically, we extract the hole region patches from the three different scales generated by MU-GAN; the final complete point cloud is generated by merging the hole region patches with the incomplete point cloud. By this method, not only the holes are filled, but also the high-fidelity features of the model are preserved. The final result is not affected by the downsampling at different scales because the combination of different scales of features can effectively retain more features of the original model. To prove that the MU-GAN can retain the original structure and feature well for different hole sizes, a series of experiments are conducted. As shown in Figure 8, for Output-2, the output is realistic enough for small holes, while the output is not completed for large  
Figure 7: Experimental results of different CHarts models with small holes. Output-2, Output-4, and Output-8 denote the point cloud generated from \(P_{1}\), \(P_{2}\), and \(P_{3}\) separately. The text continues here. holes (e.g., rows 2 and 3). To overcome the problem that more information is not available for large holes, the features obtained by the three different scales should be merged to repair the incomplete model. The results show that the method can retain the structure information of the input point cloud well under different missing ratios. The MU-GAN can further improve the high-quality output for filing the missing region from the compact latent feature to low-level features. To evaluate the performance of the proposed method and verify the necessity of multi-scale, the values of CD and EMD are compared between the single-scale upsampling GAN (SU-GAN) and MU-GAN, respectively. What needs to be explained is that the single scale means the \(P_{1}\), which is the downsampled two ratios from the original point cloud \(P\). As illustrated in Figure 9, the values of CD and EMD are both the lowest when the missing ratio of the input point cloud is 3%. The reason is that the holes are so small that the surface of the point cloud is semantically reasonable. Additionally, we notice that the input point cloud is the best in terms of CD and EMD for 3% missing data. However, the completed point cloud is sufficiently realistic from our visual inspection in Figure 8 (row 1), while they might not be exactly aligned in every detail. As the proportion of missing data increases, our method outperforms the input point cloud and SU-GAN. For the missing ratio up to 15%, the performance of MU-GAN is improved by 34.15% and 22.44% for the CD and EMD, which is compared with that of SU-GAN. It shows that MU-GAN has a good restoration result and strong robustness for the CHarts model with different hole sizes. Figure 8: Experimental results of one CHarts model with different hole sizes, and the size increases from top to bottom. The missing ratios of the model are 3%, 5%, 10%, and 15%, respectively. In the following, we compare our method to several existing methods [18; 37; 42] and present both quantitative and qualitative comparisons on the CHarts test dataset. Table 1 represents the results of the quantitative comparison. The CD and EMD values of different parts vary within a small range, sand it verifies the robustness of our model. Compared with other methods, the MU-GAN achieves the lowest EMD and CD. The CD and EMD values of RL-GAN and PU-Net are higher than the traditional method because the input point clouds of RL-GAN have a fixed size of 2048, and their repair results are too sparse and cannot generate dense point clouds. PU-Net is an upsampling network rather than a GAN network, so it cannot patch the holes completely.