## 5 Results
### SCN and SCN-EXT Architecture Determination  
Our research is based on the SCN neural network. The implementation of this network is, to the best of our knowledge, not publicly available; therefore, based on the available information, we recreated the SCN network ourselves. We tested our own implemented SCN on the public ISBI database by using the (hyper)parameters reported in [10]. The SCN network had the following architecture. The local appearance component had 4 layers and 128 filters with \(3\times 3\) kernels. The spatial configuration component used a downsampling factor of 16 and included 128 filters of \(11\times 11\). In total, this network had around 7.90 million (M) trainable parameters. The SCN network with the described architecture was referred to in the sequel as \"our implementation of the method\".  
Our proposed SCN-EXT solution is a generalization of the SCN architecture, with \(J\)-times repetition of local appearance and spatial configuration components (see Section 3.2). We determined the most acceptable SCN-EXT architecture by using the following simple experiment. This experiment was conducted on the AUDAX private database, whereas folds 2 and 3 formed the training set, while fold 1 was utilized as the testing set. According to the presented theory in Section 3, we integrated \(J\) repetitions of both components of the SCN network into the SCN-EXT network. If we had employed our fine-tuned SCN for this purpose, then the memory requirements would have become so high (even at small values of \(J\)) that this problem could not be solved with today's available hardware. Therefore, we utilized the following simplified SCN architecture for this experiment: (i) local appearance component: 4 layers and 32 filters with \(5\times 5\) kernels; and (ii) spatial configuration component: a downsampling factor equal to 16 and 32 filters with \(11\times 11\) kernels. Afterwards, the SCN-EXT networks were constructed by changing the number of repetitions of SCN network components, whereas parameter \(J\) was varied between 1 and 10 with step 1. It should be stressed that for \(J=1\), we are dealing with the original SCN network.  
The results obtained by using different SCN-EXT architectures are summarized in Table 3. The number of repetitions (\(J\)) of the SCN architecture components is written next to the method name. For comparison, we also added in this table the results of the fine-tuned SCN architecture (see the first line). Three metrics are shown based on the radial error. All metrics were evaluated across all 72 cephalometric landmarks and across all 1565 testing images. The values are given in pixels, where a lower value indicates the more effective method. We added a number of trainable parameters in the last column. Marked in bold is the SCN-EXT architecture, i.e., SCN-EXT (\(J=6\)), which was used in all subsequent experiments. We chose this network because it is a good compromise between effectiveness and training time. At the same time, this network is similar to the fine-tuned SCN with respect to the DoF (see the \"trainable\" column). As both networks have similar DoFs, in fact the SCN-EXT network (\(J=6\)) has even 1 M lower DoF, all differences in the results can be attributed to changes in the CNN architecture, and not to a raw increase of the DoF (as in the case if we would utilize SCN-EXT with \(J=9\)).