## 6 Discussion
The final architecture of the SCN-EXT network was determined according to the capacity and DoF of the original SCN network. The SCN network was fine-tuned to detect 19 cephalometric landmarks in the ISBI public database. The LA and SC components utilized there were used as the basis in our work. The goal on the private AUDAX database was to localize 72 cephalometric landmarks; therefore, we modified the architecture of the SCN network only slightly, namely, such that the LA and SC components were able to process inputs with 72 channels. The SCN network that aimed for a detection of 19 cephalometric landmarks (ISBI database) had 6.20 M trainable parameters, while the DoF increased to 7.90 M in the case of detecting 72 landmarks (AUDAX database). The SCN-EXT architecture was determined by a simple experiment on the AUDAX database (see Section 5.1). We varied the number of replicates, \(J\), of the LA and SC components, and monitored the MRE by cephalometric landmarks' detection. Much simpler LA and SC components were applied than in the original SCN. Finally, we chose the SCN-EXT architecture with \(J=6\) repetitions of both components with respect to the hypotheses set out in this study. The SCN-EXT network had 6.88 M trainable parameters when detecting 72 landmarks (AUDAX database), while the DoF decreased to 4.16 M if this architecture was adapted for the ISBI database (i.e., reducing the number of channels). It can be noticed easily that the SCN-EXT network had, on both databases, much fewer trainable parameters than the original SCN. In order to compare the results of our proposed SCN-EXT method with the results of related works, we reimplemented the SCN method and the method by [PERSON] et al. [8] successfully. We also implemented the method by [PERSON] et al. [9], but the results, obtained with our implementation of this method, differed greatly from those reported (see the previous section). We deduced that a reason for the failure to reproduce the method is as follows: the method by [PERSON] et al. [9] models each landmark as a graph node. Each node is associated with the landmarks' positions and a feature vector that is extracted from a processed image at that position. The feature vector processing is conducted by using the HRNet18 backbone convolutional network. This method consists of two stages. The first stage estimates a global perspective transformation to align the mean positions of landmarks, constructed from the training data with the specific image. Afterwards, the second stage refines local landmark locations. The estimated global perspective transformation did not improve the landmarks' locations regularly, but, rather, it distorted them. A network that predicted nine free parameters of the perspective transformation matrix was described in [9] explicitly. However, [PERSON] et al. argued in [15] that such approach is unreliable and difficult to train perspective transformations. Therefore, they suggested applying the four-point estimation approach instead. It is unclear, though, how this four-point estimation would be applied for the landmark detection. The reason for the ineffectiveness of this method was, consequently, sought in the poorly estimated perspective transformations. As mentioned in the Introduction, the method by [PERSON] et al. [11] does not scale well to a larger number of cephalometric landmarks and training images. The authors validated their approach on the ISBI public database (i.e., on 19 landmarks and 150 testing images). They reported that a registration of a single testing image to training images was completed in approximately 20 min. In the AUDAX database, there were 3130 training images per one fold. We estimated that registration in this case would require about 20 times more processing time, i.e., about 400 min per one testing image. In total, this would mean 3 folds \(\times\) 1565 images \(\times\) 400 min per image = 1,878,000 min, or around 1304 days, to carry out the registration. The latter, of course, is not acceptable, so we have not implemented this method.