## 3 Results and Discussion  
### Result of Image Completion  
We applied the trained GAN using the proposed method to the actual tooth image completion. Overall, it took 4 days for training: Steps 1 and step 2 required 1 day each, and step 3 took 2 days. We used a personal computer with an i7-6700 (3.4 GHz) processor, 24 GB of RAM, and an RTX 2080 Ti GPU. The figures below show some examples of the results (Figure 15).  
Figure 14: Image generated after the last training step.  
Figure 15: _Cont_.  
We used the structural similarity index (SSIM) [26] and peak signal-to-noise ratio (PSNR) [27] to quantitatively measure the training result of a GAN. The SSIM is a measure of the difference between the ground truth image and the image being compared. The value closer to 1 indicates better results. The PSNR is a measure of the sharpness and uses the difference in noise between the ground truth image and the restored image. The table below presents the accuracy measured by the SSIM (Table 1), which we classified according to the mask ratios to assess the effect on the image completion. The closer the value is to 1, the better the result.  
For a more intuitive explanation of the SSIM, images with values of 0.75-0.95 among those used in the experiments are shown at 0.05 intervals (Figure 16). The left side shows the ground truth images, and the right side shows the restored images. From a value of 0.85 and above, we can see the edge lined up, and a value above 0.9 is similar to that of the ground truth images.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Mask** & **Incisor** & **Canine** & **Premolar** & **Molar** \\ \hline
0–10\% & 0.921 & 0.918 & 0.911 & 0.923 \\
10–20\% & 0.915 & 0.911 & 0.906 & 0.913 \\
20–30\% & 0.885 & 0.883 & 0.879 & 0.894 \\
30–40\% & 0.819 & 0.822 & 0.839 & 0.859 \\ \hline \end{tabular}
\end{table}
Table 1: Evaluation using structural similarity index (SSIM).  
Figure 15: Some examples of generated images.  
The following is the result measured based on the PSNR (Table 2). Higher values indicate better results. The images used in the experiment are 16.42 at minimum and 28.27 at maximum.  
As with the SSIM, among the images used in the experiment, images with a PSNR of 16-28 are shown at three intervals (Figure 17). The edges on the left are the ground truth images and the images on the right are the generated images. When the PSNR is less than 20, we can see that the edge is broken or missing. A small amount of noise occurs from above 22, although this is similar to the ground truth images.  
Figure 16: Images of various structural similarity index (SSIMs).  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Mask** & **Incisor** & **Canine** & **Premolar** & **Molar** \\ \hline
0–10\% & 26.68 & 24.42 & 24.71 & 26.27 \\
10–20\% & 25.82 & 24.19 & 23.69 & 25.07 \\
20–30\% & 22.72 & 22.57 & 21.62 & 23.33 \\
30–40\% & 19.49 & 19.78 & 19.71 & 21.93 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Evaluation based on PSNR.  
Figure 17: Images of various PSNRs.  
In this study, we used images with an SSIM of over 0.9 and a PSNR of over 22 for 3D reconstruction. Overall, when the mask size is less than 10%, 95% of the images obtained are available for 3D reconstruction. It took 0.1 s for an image completion, and we used 100 slices of both the maxilla and mandible. We conducted the image completion five times per slice. Therefore, the entire image completion process took approximately 100 s.