## 5 Results
### AUDAX Private Database
In the table next to the MRE value, we wrote in parentheses the order of methods with respect to the mean rank (value 1 indicates the most effective and value 3 the least effective method), where we denoted by an asterisk whether the differences in results are statistically significant. Our proposed method proved to be the most accurate by 15 landmarks and the second best by 4 landmarks, which is notably better than the compared methods. Improvements were statistically significant for six landmarks. Finally, we calculated the MRE over all 19 landmarks (see the row \"all landmarks\" in the table). The effectiveness of our proposed detection method was statistically significantly higher by at least 3% than for the compared methods. The SCN method was shown to be the second most effective, followed by the method by [PERSON] et al. [8]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **MRE (px)** & **PCTL\({}_{50}\) (px)** & **PCTL\({}_{90}\) (px)** \\ \hline
**SCN-EXT** & **11.26 \(\pm\) 17.51** & **6.52** & **24.13** \\ SCN [10] \(\dagger\) & 11.57 \(\pm\) 18.71 & 6.70 & 25.10 \\ [PERSON] et al. [8] \(\dagger\) & 12.19 \(\pm\) 15.02 & 8.36 & 25.00 \\ \hline \hline \multicolumn{4}{l}{\(\dagger\)—Our implementation of the method.} \\ \end{tabular}
\end{table} 
Table 6: Effectiveness of the better cephalometric landmark detection methods on the private AUDAX database. The column MRE denotes the mean and standard deviation of the radial error, while columns PCTL\({}_{50}\) and PCTL\({}_{90}\) denote the 50 th (i.e., median value) and 90 th percentiles of the radial error, respectively. All values are in pixels. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Landmark** & **SCN-EXT (px)** & **SCN [10] \(\dagger\) (px)** & **[PERSON] et al. [8] \(\dagger\) (px)** \\ \hline \(-\)1i–Lower incisal incisior & \(\mathbf{5.06\pm 7.34^{(1)}}\) & \(5.09\pm 7.48^{(2)}\) & \(7.45\pm 7.72^{(3)}\) \\ +1i–Upper incisal incisior & \(\mathbf{4.55\pm 6.72^{(1)}}\) & \(4.55\pm 6.83^{(2)}\) & \(8.33\pm 7.77^{(3)}\) \\ ANS–Anterior Nasal Spine & \(\mathbf{8.96\pm 10.88^{(1,*)}}\) & \(9.35\pm 11.55^{(2)}\) & \(12.16\pm 19.39^{(3)}\) \\ Ar–Articulate & \(\mathbf{8.07\pm 9.38^{(1,*)}}\) & \(8.44\pm 9.69^{(2)}\) & \(9.56\pm 8.14^{(3)}\) \\ Gm–Gathion & \(\mathbf{7.11\pm 6.08^{(1,*)}}\) & \(7.29\pm 6.22^{(2)}\) & \(8.04\pm 6.17^{(3)}\) \\ Go–Gonion & \(9.40\pm 8.50^{(2)}\) & \(11.05\pm 10.15^{(3)}\) & \(8.81\pm 7.11^{(1)}\) \\ Li\({}^{\prime}\)–Lower lip & \(\mathbf{4.51\pm 6.77^{(1)}}\) & \(4.66\pm 12.77^{(2)}\) & \(7.01\pm 6.80^{(3)}\) \\ Ls\({}^{\prime}\)–Upper lip & \(\mathbf{4.49\pm 6.30^{(1)}}\) & \(4.63\pm 8.68^{(2)}\) & \(7.16\pm 6.50^{(3)}\) \\ Me–Menton & \(\mathbf{6.77\pm 6.52^{(1,*)}}\) & \(6.94\pm 6.63^{(2)}\) & \(7.86\pm 6.17^{(3)}\) \\ N–Nasion & \(7.31\pm 10.21^{(2)}\) & \(\mathbf{7.29\pm 10.24^{(1)}}\) & \(9.12\pm 10.09^{(3)}\) \\ Or–Orbitale & \(12.22\pm 14.29^{(2)}\) & \(\mathbf{12.15\pm 14.20^{(1)}}\) & \(12.62\pm 11.92^{(3)}\) \\ Pg–Pogoon & \(\mathbf{7.17\pm 9.34^{(1)}}\) & \(7.24\pm 9.49^{(2)}\) & \(9.62\pm 8.98^{(3)}\) \\ Pg\({}^{\prime}\)–Point Soft Pogoonion & \(\mathbf{9.02\pm 15.80^{(1)}}\) & \(9.30\pm 31.05^{(2)}\) & \(9.88\pm 10.73^{(3)}\) \\ PNS–Posterior Nasal Spine & \(\mathbf{9.14\pm 7.64^{(1)}}\) & \(9.31\pm 7.87^{(2)}\) & \(11.65\pm 8.61^{(3)}\) \\ Po–Portion & \(\mathbf{13.44\pm 15.34^{(1)}}\) & \(13.89\pm 16.21^{(2)}\) & \(14.89\pm 12.43^{(3)}\) \\ S–Sella Turcica & \(\mathbf{4.85\pm 3.58^{(1,*)}}\) & \(4.99\pm 3.76^{(2)}\) & \(5.20\pm 3.60^{(3)}\) \\ Sn\({}^{\prime}\)–Subnasale & \(\mathbf{5.68\pm 5.35^{(1,*)}}\) & \(5.84\pm 6.77^{(2)}\) & \(8.02\pm 6.12^{(3)}\) \\ SS–Subspinale (Point A) & \(\mathbf{11.02\pm 12.70^{(1)}}\) & \(11.28\pm 13.41^{(2)}\) & \(14.16\pm 12.37^{(3)}\) \\ SM–Supramentale (Point B) & \(12.88\pm 17.02^{(2)}\) & \(\mathbf{12.92\pm 16.90^{(1)}}\) & \(14.08\pm 15.03^{(3)}\) \\ \hline All landmarks & \(\mathbf{7.98\pm 10.57^{(1,*)}}\) & \(8.22\pm 12.82^{(2)}\) & \(9.77\pm 10.29^{(3)}\) \\ \hline \hline \end{tabular}
\end{table}