## 6 Discussion  
In this study, we upgraded the state-of-the-art SCN neural network to the SCN-EXT network by adding the \(J\) repetitions of both the local appearance (LA) component and the spatial configuration (SC) component into the original SCN architecture. All \(J\) replicates of each component were summed up simply, and both sums were, finally, combined by using the Hadamard product. By modifying the architecture in this way, we increased the capacity, as the new SCN-EXT network is able to learn \(J^{2}-1\) more transformation functions than the basic SCN network. It is completely trivial that if we add \(J\) copies of LA and SC components, then the capacity of such a modified network will, of course, increase compared to the capacity of the original SCN network (if the same LA and SC components are utilized). However, the contribution of our approach is that by \(J\)-times repeating and merging the simpler LA and SC components, we can maintain approximately \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Landmark** & **MRE (px)** & **PCTL50 (px)** & **PCTL50 (px)** \\ \hline \(\text{Ls}^{\prime}\)–Upper lip) & 4.49 \(\pm\) 6.30 & 3.14 & 8.49 \\ \(\text{Li}^{\prime}\)–Lower lip) & 4.51 \(\pm\) 6.77 & 3.30 & 8.53 \\ \(\text{+11-Upper incisal incisor}\) & 4.55 \(\pm\) 6.72 & 3.00 & 8.30 \\ \(\text{Pn}^{\prime}\)–Pronasale & 4.61 \(\pm\) 7.13 & 3.46 & 9.20 \\ \(\text{S-Sella Turica}\) & 4.85 \(\pm\) 3.58 & 3.97 & 9.67 \\ \(\text{APocc-Anterior point of}\) & 4.95 \(\pm\) 5.27 & 3.66 & 9.60 \\ \(\text{occlusion}\) & 4.97 \(\pm\) 4.61 & 3.90 & 9.97 \\ \(\text{Si-Floor of Sella}\) & 5.06 \(\pm\) 7.34 & 3.55 & 9.90 \\ \(\text{B}^{\prime}\)–Point Soft B & 5.22 \(\pm\) 6.69 & 3.64 & 10.06 \\ \(\text{Sn}^{\prime}\)–Subnasale & 5.68 \(\pm\) 5.35 & 4.41 & 11.58 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Ten cephalometric landmarks from the AUDAX database detected most accurately by the SCN-EXT method. For denotations, see Tables 2 and 6. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Landmark** & **MRE (px)** & **PCTL50 (px)** & **PCTL50 (px)** \\ \hline \(\text{SOr}\)–Supraorbitale & 15.81 \(\pm\) 20.29 & 7.99 & 43.83 \\ \(\text{ZyO}\)–\(\text{Zy Orbit Ridge}\) & 16.90 \(\pm\) 15.79 & 11.84 & 38.37 \\ \(\text{Te}\)–Temporale & 17.03 \(\pm\) 18.05 & 12.39 & 35.41 \\ \(\text{Ir}\)–Point Ir & 17.09 \(\pm\) 17.22 & 12.15 & 37.25 \\ \(\text{R1-R1}\) & 17.25 \(\pm\) 14.82 & 13.25 & 35.61 \\ \(\text{Gn}^{\prime}\)–Point Soft Gnaathion & 18.59 \(\pm\) 22.10 & 10.95 & 46.41 \\ \(\text{GI}^{\prime}\)–Glabella & 19.21 \(\pm\) 20.64 & 11.91 & 46.66 \\ \(\text{R3-R3}\) & 19.58 \(\pm\) 16.82 & 14.69 & 41.66 \\ \(\text{Rh}\)–Rhinion & 24.08 \(\pm\) 33.69 & 10.49 & 81.31 \\ \(\text{Th}^{\prime}\)–Throat & 60.15 \(\pm\) 76.76 & 28.97 & 177.48 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Ten cephalometric landmarks from the AUDAX database detected least accurately by the SCN-EXT method. For denotations, see Table 6.  
the same DoF of the new SCN-EXT network as has the original SCN network with the more complex LA and SC components, while we simultaneously increase the capacity and learning ability of the SCN-EXT, respectively. The latter is especially acute if processing and memory resources are limited; namely, training the large models (i.e., with large DoF) requires powerful computing units, a large learning set, and a large primary memory. This research was focused on the problem of detecting many cephalometric landmarks on diverse lateral skull X-ray images. The SCN-EXT network was designed primarily for this purpose. We have shown experimentally (see the Section 5) that the SCN-EXT network components learn well to predict landmark locations. In our current solution, we do not supervise a training by forcing individual components to learn how to localize a specific subset of landmarks. The latter would be achieved, for example, by adding the \(L1\) regularization term for sparsity into the training, which could be one of the future research guidelines.