## 4 Experiments and Discussion
### Landmark Detection Results  
#### 4.3.1 ISBI Test Dataset  
The results for ISBI public data are presented in Tables 1 and 2. Table 1 presents the SDR, and Table 2 presents the MRE results. \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**SDR (Successful Detection Rate)**} \\ \hline
**Anatomical Landmarks** & \multicolumn{2}{c}{**2 mm (\%)**} & \multicolumn{2}{c}{**2.5 mm (\%)**} & \multicolumn{2}{c}{**3 mm (\%)**} & \multicolumn{2}{c}{**4 mm (\%)**} \\ \hline  & **Testset1** & **Testset2** & **Testset1** & **Testset2** & **Testset1** & **Testset2** & **Testset1** & **Testset2** \\ \hline
1. sella turcica & 98.7 & 99.0 & 98.7 & 99.0 & 99.3 & 99.0 & 99.3 & 99.0 \\
2. nasion & 86.7 & 89.0 & 89.3 & 90.0 & 93.3 & 92.0 & 96.0 & 99.0 \\
3. orbitale & 84.7 & 36.0 & 92.0 & 61.0 & 96.0 & 80.0 & 99.3 & 96.0 \\
4. porion & 68.0 & 78.0 & 78.0 & 81.0 & 84.7 & 86.0 & 93.3 & 93.0 \\
5. subspinale & 66.0 & 84.0 & 76.0 & 94.0 & 87.3 & 99.0 & 95.3 & 100.0 \\
6. supramentale & 87.3 & 27.0 & 93.3 & 43.0 & 97.3 & 59.0 & 98.7 & 82.0 \\
7. pogoonion & 93.3 & 98.0 & 97.3 & 100.0 & 98.7 & 100.0 & 99.3 & 100.0 \\
8. menton & 94.0 & 96.0 & 98.0 & 98.0 & 98.0 & 99.0 & 99.3 & 100.0 \\
9. gnathion & 94.0 & 100.0 & 98.0 & 100.0 & 98.0 & 100.0 & 99.3 & 100.0 \\
10. gonion & 62.7 & 75.0 & 75.3 & 87.0 & 84.7 & 94.0 & 92.0 & 98.0 \\
11. lower incisal incision & 92.7 & 93.0 & 97.3 & 96.0 & 97.3 & 97.0 & 99.3 & 99.0 \\
12. upper incisal incision & 97.3 & 95.0 & 98.0 & 98.0 & 98.7 & 98.0 & 99.3 & 98.0 \\
13. upper lip & 89.3 & 13.0 & 98.0 & 35.0 & 99.3 & 69.0 & 99.3 & 93.0 \\
14. lower lip & 99.3 & 63.0 & 99.3 & 80.0 & 100.0 & 93.0 & 100.0 & 98.0 \\
15. subnasale & 92.7 & 92.0 & 95.3 & 94.0 & 96.7 & 95.0 & 99.3 & 99.0 \\
16. soft tissue pogoonion & 86.7 & 4.0 & 92.7 & 7.0 & 95.3 & 13.0 & 99.3 & 41.0 \\
17. posterior nasal spine & 94.7 & 91.0 & 97.3 & 98.0 & 98.7 & 100.0 & 99.3 & 100.0 \\
18. anterior nasal spine & 87.3 & 93.0 & 92.0 & 96.0 & 95.3 & 97.0 & 98.7 & 100.0 \\
19. articulate & 66.0 & 80.0 & 76.0 & 87.0 & 83.0 & 93.0 & 91.3 & 97.0 \\ \hline Average: & 86.4 & 74.0 & 91.7 & 81.3 & 94.8 & 87.5 & 97.8 & 94.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Successful Detection Rate (SDR) Results on Testset1 and Testset2 of range 2 mm, 2.5 mm, 3 mm, 4 mm. We compare our detection results with other benchmarks' results. Table 3 shows the comparison. Figure 8 shows one of the examples of our results. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Anatomical Landmarks** & \multicolumn{2}{c}{**Mean Radial Error (mm)**} \\ \hline  & **Testset1** & **Testset2** \\ \hline
1. sella turcica & 0.577 & 0.613 \\
2. nasion & 1.133 & 0.981 \\
3. orbitale & 1.243 & 2.356 \\
4. porion & 1.828 & 1.702 \\
5. subspinale & 1.752 & 1.253 \\
6. supramentale & 1.136 & 2.738 \\
7. pogonion & 0.836 & 0.594 \\
8. menton & 0.952 & 0.705 \\
9. gnathion & 0.952 & 0.594 \\
10. gonion & 1.817 & 1.431 \\
11. lower incisal incision & 0.697 & 0.771 \\
12. upper incisal incision & 0.532 & 0.533 \\
13. upper lip & 1.332 & 2.841 \\
14. lower lip & 0.839 & 1.931 \\
15. subnasale & 0.853 & 0.999 \\
16. soft tissue pogonion & 1.173 & 4.265 \\
17. posterior nasal spine & 0.819 & 1.028 \\
18. anterior nasal spine & 1.157 & 0.995 \\
19. articulate & 1.780 & 1.310 \\ \hline Average: & 1.077 & 1.542 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results on Testset1 and Testset2 of mean radial error.