## 5 Results
### ISBI Public Database  
Initially, the effectiveness of our proposed SCN-EXT method, designed primarily for cephalometric landmark detection, was assessed on the ISBI public database. We used the prescribed methodology and established metrics [5]. The mean and standard deviation of the radial error were calculated over all 19 cephalometric landmarks and over all testing images. In addition, the successful detection rate (SDR) metric was evaluated for the four prescribed classes. The results for testing set 1 are gathered in Table 4, while Table 5 summarizes the obtained results for testing set 2. The effectiveness of the state-of-the-art methods were added to the tables as well. Implementations of these methods were not publicly available; therefore, we just summarized the results published by the authors of the methods. We reimplemented only two state-of-the-art methods successfully. The remaining methods were either basically too ineffective (e.g., methods [6,7]), or it was very difficult to scale them to the problem of 72 cephalometric \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **MRE (mm)** & **SDR (\%)** & **SDR (\%)** & **SDR (\%)** \\  & & **2 mm** & **2.5 mm** & **3 mm** & **4 mm** \\ \hline [PERSON] et al. [9] & \(1.04\pm\) N/A & 88.49 & 93.12 & 95.72 & 98.42 \\ SCN [10] \(\dagger\) & \(1.08\pm 1.08\) & 87.30 & 91.40 & 94.25 & 97.33 \\ [PERSON] et al. [11] & \(1.08\pm\) N/A & 86.40 & 91.70 & 94.80 & 97.80 \\
**SCN-EXT** & \(\mathbf{1.13\pm 1.11}\) & \(\mathbf{85.61}\) & **90.60** & **93.96** & **97.44** \\ [PERSON] et al. [8] & \(1.17\pm\) N/A & 86.67 & 92.67 & 95.54 & 98.53 \\ [PERSON] et al. [8] \(\dagger\) & \(1.30\pm 2.07\) & 83.65 & 90.70 & 94.81 & 97.86 \\ [PERSON] et al. [5] & \(1.67\pm 1.48\) & 73.68 & 80.21 & 85.19 & 91.47 \\ SCN [10] \(\ddagger\) & N/A & 73.33 & 78.76 & 83.24 & 89.75 \\ [PERSON] et al. [5] & N/A & 71.72 & 77.4 & 81.93 & 88.04 \\ \hline \hline \end{tabular} N/A—Data not available. \(\dagger\)—Our implementation of the method. \(\ddagger\)—Results reported just for the merged testing set 1 and 2.  
\end{table} 
Table 4: Effectiveness of cephalometric landmark detection methods on the public ISBI database: testing set 1. The column MRE denotes the mean and standard deviation of the radial error, while the SDR columns denote the successful detection rate (in %) for the four specified classes. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method** & **MRE (px)** & **PCTL50 (px)** & **PCTL50 (px)** & **Trainable** \\ \hline SCN \(\dagger\) & 11.56 & 6.70 & 24.91 & 7.90 M \\ \hline SCN-EXT, \(J=1\) & 12.35 & 7.21 & 26.44 & 1.15 M \\ \(\ldots\)\(J=2\) & 11.80 & 6.90 & 25.25 & 2.29 M \\ \(\ldots\)\(J=3\) & 11.57 & 6.75 & 24.72 & 3.44 M \\ \(\ldots\)\(J=4\) & 11.56 & 6.73 & 24.68 & 4.58 M \\ \(\ldots\)\(J=5\) & 11.54 & 6.69 & 24.57 & 5.73 M \\ \(\ldots\)\(J=6\) & **11.36** & **6.66** & **24.31** & **6.88 M** \\ \(\ldots\)\(J=7\) & 11.42 & 6.67 & 24.30 & 8.02 M \\ \(\ldots\)\(J=8\) & 11.35 & 6.54 & 24.20 & 9.17 M \\ \(\ldots\)\(J=9\) & 11.26 & 6.57 & 24.05 & 10.31 M \\ \(\ldots\)\(J=10\) & 11.48 & 6.60 & 24.48 & 11.46 M \\ \hline \hline \end{tabular} \(\ddagger\)—Our implementation of the method.  
\end{table} 
Table 3: Effectiveness of different SCN-EXT architectures on cephalometric landmark detection on fold 1 of the AUDAX private database. The column MRE denotes the mean and standard deviation of the radial error, while columns PCTL50 and PCTL50 denote the 50 th (i.e., median value) and 90 th percentile of the radial error, respectively. All values are in pixels (“px”). The column “trainable” presents the number of trainable parameters in millions. landmarks' detection (e.g., method [11]), or method descriptions were not comprehensive enough to be able to reproduce them accurately (e.g., method [9]). Additionally, the results of our methods' implementations are presented in the tables, where they are marked by \(\dagger\) next to the method name. The methods in both tables are arranged according to the decreasing value of the MRE metric.