# Method

We first show the 3D bone structure in two rendering ways as in Figure [5,](#page-5-0) where the volume rendering can show the reconstructed surface and the maximum projection can indicate the restored density information. Then we summarize the evaluation metrics in Table [2](#page-6-0) to compare with other methods. We can see that *Oral-3D* has the best performance over other models. Comparing *Oral-3D* and Auto Encoder with the Residual CNN and GAN, we can see the importance of decoupling the back-projection and deformation process. To be noted, R2N2 achieves the worst performance, where the model only learns the shape of the oral cavity but loses details of teeth. This has indicated the defect when converting the PX image as a collection of multi-view images. Additionally, we see that Auto Encoder has the closest performance to *Oral*, although the latter has a more clear surface. This has proved the promotion brought by the adversarial loss.

In this paragraph, we show two of the most common cases in dental healthcare, *e.g.*, dental implants and tooth pulling, to see if *Oral-3D* can provide dentist useful reference. Both cases require to locate the operation location before the surgery. In the first row of Figure [6,](#page-5-1) three wisdom teeth can be seen clearly on both sides in PX. These features also present in the two sides of the reconstruction results. In the second row, the patient misses two teeth on both sides of the mandible. While the missing place can also be located

<span id="page-6-2"></span>![](_page_6_Figure_0.jpeg)

Figure 7: We show a workflow to apply *Oral-3D* to obtain the dental arch curve in real-world applications in this picture. We first take a picture of the patient's mouth and segment then dental area semi-automatically. Then we use a cubic function to the fit points sampled from the skeletonized image of the binary mask.

Table 2: Quantitative Evaluation of 3D Reconstruction

<span id="page-6-0"></span>

| Method                 | View | Prior | D-Net | PSNR (dB)  | SSIM (%)   | Dice (%)   | Overall |
|------------------------|------|-------|-------|------------|------------|------------|---------|
| Residual CNN           | 1    | No    | No    | 17.46±9.58 | 72.90±2.09 | 57.95±7.43 | 73.54   |
| GAN                    | 1    | No    | Yes   | 17.71±1.04 | 69.96±1.91 | 57.80±7.76 | 73.78   |
| R2N2                   | 3    | No    | No    | 18.06±0.94 | 71.94±1.36 | 57.71±6.52 | 73.32   |
| Oral-3D (Auto-Encoder) | 1    | Yes   | No    | 19.04±0.85 | 76.78±1.65 | 69.68±4.98 | 80.56   |
| Oral-3D (GAN)          | 1    | Yes   | Yes   | 19.22±0.83 | 78.27±1.74 | 71.28±4.69 | 81.89   |

<span id="page-6-1"></span>Table 3: Evaluation results of different combination of discrimination loss (DL), reconstruction loss (RL), and projection loss (PL).

|         | DL only | DL+PL | DL+RL                       | DL+RL+PL      |
|---------|---------|-------|-----------------------------|---------------|
| PSNR    | 8.06    |       | 18.06(+10.00) 19.14(+11.08) | 19.22(+11.16) |
| SSIM    | 46.61   |       | 73.02(+26.41) 78.41(+31.80) | 78.27(+31.66) |
| Dice    | 35.50   |       | 64.53(+29.03) 70.89(+35.39) | 71.28(+35.78) |
| Overall | 40.79   |       | 75.95(+35.16) 81.66(+40.87) | 81.89(+41.10) |

<span id="page-6-3"></span>Table 4: Evaluation results on real-world images

| Dataset     | PSNR       | SSIM       | Dice       |
|-------------|------------|------------|------------|
| Real        | 17.36±0.70 | 69.30±2.03 | 71.44±3.66 |
| Synthesized | 19.22±0.83 | 78.27±1.74 | 71.28±4.69 |

accurately in the reconstruction image.