## 5 Results
### AUDAX Private Database  
The effectiveness of our proposed SCN-EXT method was also assessed on the AUDAX private database. On this database, we applied the threefold validation technique, where there were 1565 images in each fold and 72 cephalometric landmarks in each image. The results obtained on the individual folds were merged, and, afterwards, summarized with various statistics calculated over all images and over all cephalometric landmarks. We calculated the mean radial error and the 50 th and 90 th percentiles of the radial error. The spatial resolution for the AUDAX database is not known; therefore, all results are given in pixels. The calculated metrics are gathered in Table 6. In addition to our proposed SCN-EXT detection method, this table also presents the results of our implementations of two state-of-the-art methods. The methods in the table are arranged according to the decreasing value of the MRE metric. Based on publicly available information, we also reimplemented the method by [PERSON] et al. [9], but, with the calculated MRE of about 34 pixels and the median radial error around 25 pixels, we found that our attempt was completely unsuccessful. The effectiveness of the methods in Table 6 was also assessed with the nonparametric [PERSON]'s statistical test [14] at a 0.05 significance level. The calculated p-value was equal to 0, which indicates that not all the methods' medians are equal. The proposed SCN-EXT method had the lowest mean rank of 1.88, followed by the SCN method with the mean rank of 1.94, and the method of [PERSON] et al. [8] had the highest mean rank of 2.18. Let us evoke that the lower mean rank correlates with the lower radial error, and, consequently, with the higher effectiveness of the method. Subsequently, we conducted a multiple comparison test of mean ranks, i.e., a pairwise comparison of methods. This analysis pointed out that all three compared methods have significantly different mean ranks. On this basis, we argue that our proposed approach has proven overall to be the most effective detection method on the challenging AUDAX database. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**MRE (mm)**} & **SDR (\%)** & **SDR (\%)** & **SDR (\%)** & **SDR (\%)** \\  & & **2 mm** & **2.5 mm** & **3 mm** & **4 mm** \\ \hline SCN [10]\(\dagger\) & 1.41 \(\pm\) 1.40 & 74.84 & 81.42 & 86.89 & 94.47 \\ [PERSON] et al. [9] & 1.43 \(\pm\) N/A & 76.57 & 83.68 & 88.21 & 94.31 \\
**SCN-EXT** & **1.47 \(\pm\) 1.44** & **74.53** & **82.21** & **87.21** & **93.68** \\ [PERSON] et al. [8] & 1.48 \(\pm\) N/A & 75.05 & 82.84 & 88.53 & 95.05 \\ [PERSON] et al. [8]\(\dagger\) & 1.65 \(\pm\) 2.22 & 71.79 & 80.32 & 86.21 & 93.84 \\ [PERSON] et al. [11] & 1.54 \(\pm\) N/A & 74.00 & 81.30 & 87.50 & 94.30 \\ [PERSON] et al. [5] & 1.92 \(\pm\) 1.24 & 66.11 & 72.00 & 77.63 & 87.42 \\ SCN [10]\(\ddagger\) & N/A & 73.33 & 78.76 & 83.24 & 89.75 \\ [PERSON] et al. [5] & N/A & 62.74 & 70.47 & 76.53 & 85.11 \\ \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 5: Effectiveness of the cephalometric landmark detection methods on the public ISBI database: testing set 2. See Table 4 for denotations. In the sequel, we extracted the metrics from the obtained results only for those 19 landmarks that are also annotated in the public ISBI database. The mean and standard deviation of the radial error was calculated for each landmark and each compared method separately over all images (i.e., 4695 images). These metrics are accumulated in Table 7. The effectiveness of the methods was then assessed by [PERSON]'s statistical test (0.05 significance level), and by a multiple comparison test of mean ranks.