## 6 Discussion
The remaining methods from Table 4 were around 40% behind the SCN method in terms of effectiveness, and were, therefore, not included in the comparison on the private AUDAX database. First, let us analyze the results on the ISBI public database. The effectiveness of the proposed SCN-EXT method is comparable to the effectiveness of state-of-the-art cephalometric landmark detection methods. The SCN-EXT is, on testing set 1, less effective by about 8.65% than the best method by the authors [PERSON] et al. (2019), and on testing set 2 by about 4.26% than the best SCN method (see Tables 4 and 5). We were unable to reproduce the results of (2019), because important implementation details are missing in this method's presentation. Undoubtedly, one of the reasons for the lower effectiveness of our SCN-EXT method is that the architecture was established by using the AUDAX database (and not the ISBI data on which the method was actually applied). It should be noted that the DoF of the SCN-EXT method was almost one-third smaller than the DoF of the SCN method. It can also be seen on testing set 2 that the SCN and SCN-EXT methods have very similar SDR metrics. A great similarity between the methods was also perceived on testing set 1. A reason for the higher MRE of the SCN-EXT method is, therefore, attributed to those landmarks for which the SDR was \(>\)4 mm (i.e., incorrectly detected landmarks were detected more erroneously than in the SCN method). Finally, let us emphasize that the ISBI database is a small database with a small learning set (150 images), and with only 250 testing images divided into two sets. Let us continue with an analysis of the results on the AUDAX private database. This database is very challenging, as it contains 4695 (testing) images, divided into 3 folds, in 287 very different sizes. A goal was to localize 72 cephalometric landmarks in each image. Spatial image resolution data were not available. To the best of our knowledge, this is the first such public or private database with a large number of X-ray images and a larger number of landmarks on which the cephalometric landmark detection methods have been verified. Taking into account all 72 cephalometric landmarks, our proposed SCN-EXT method proved to be superior compared to other state-of-the-art methods. It was more effective than the second-ranked SCN method by about 2.68% (see Table 6). The differences and rankings were confirmed statistically significantly by the nonparametric Friedman's test, and by the multiple comparison test of mean ranks. If we took into consideration from the set of all cephalometric landmarks only those 19 landmarks that were also annotated in the ISBI public database, then the SCN-EXT method this time again proved to be statistically significantly the best method. It surpassed the second-best SCN method by about 2.92% (see Table 7). A similar conclusion was drawn if we compared methods at the level of an individual cephalometric landmark. In this case, the SCN-EXT method was demonstrated to be the more effective method on 15 out of the 19 landmarks, and the second best on 4 landmarks. Afterwards, we arranged the detection effectiveness for the mentioned 19 landmarks with respect to the detection effectiveness for all 72 landmarks on the AUDAX database, where only our SCN-EXT method was observed. It was discovered that as many as 6 landmarks ranked among the top ten (even in the top three, see Table 8), 10 landmarks among the top twenty, and 15 landmarks among the top thirty-five most accurately detected cephalometric landmarks. The less accurately localized were the landmarks point A, orbitale, point B, and porion, as the least accurately detected landmark in 52 nd place. On this basis, we argue that the ISBI database consists of 19 relatively easier to detect cephalometric landmarks. On the other hand, the AUDAX database can be said to contain at least 33 cephalometric landmarks, which are more difficult to localize than landmarks in the ISBI database.