## 2 Materials and Methods  
A total of 333 individuals who visited the Korea University Ansan Hospital for orthodontic evaluation between 2014 and 2019 were enrolled in this study. Cephalometric radiograph images were used for clinical examination, and 159 and 174 patients were indicated for orthognathic surgery and orthodontic treatment, respectively (Table 1). The datasets were randomly split. Forty cases were used solely to evaluate the model, while the training and validation sets were comprised of the remaining 293 cases. The training set consisted of 220 cases and the validation set consisted of 73 cases. This research protocol was approved by the Institutional Review Board, Korea University Ansan Hospital (no. 2020 AS0062). In the data pre-processing step, 50 landmarks were detected using an automated landmark detection method using the VGG16 model. All cephalometric radiographs were aligned using the Frankfort-horizontal plane, and a minimum box containing all 50 landmarks was selected (Figure 1). Following this, a square box was selected as the lower part where the main structures including the maxilla and mandible could be included. The data were cropped by giving a margin of 10%. The data size was down-sampled to a \(256\times 256\) pixel size. The three deep learning models used in this study were Modified-Alexnet, MobileNet, and Resnet50 (Figure 2). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Orthodontic Treatment** & **Orthognathic Surgery** & **Total** \\ \hline Number of patients & 159 & 174 & 333 \\ Number of females/males & 88/71 & 93/81 & 181/152 \\ Mean age (SD) & 22.7 (5.8) & 23.4 (4.9) & 23.1 (5.1) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of the samples. Figure 1: (**a**) Landmarks used in this study: 1, sella; 2, nasion; 3, porion; 4, orbitale; 5, basion; 6, articulare; 7, pterygomaxillary fissure; 8, anterior nasal spine; 9, posterior nasal spine; 10, A point; 11, B point; 12, PM; 13, pogonion; 14, gnathion; 15, menton; 16, maxillary incisor tip; 17, maxillary incisor root; 18, mandibular incisor tip; 19, mandibular incisor root; 20, maxillary first molar distal; 21, mandibular first molar distal; 22, antegonali notch; 23, corpus left; 24, gonion; 25, ramus down; 26, condylion; 27, R3; 28, R1; 29, glabella; 30, soft tissue nasion; 31, nasal bridge point; 32, dorsum of nose; 33, pronasale; 34, columella; 35, subnasale; 36, soft tissue A; 37, labrale superius; 38, upper lip; 39, stomion superius; 40, upper embrasure; 41, lower embrasure; 42, stomion inferius; 43, lower lip; 44, labrale inferius; 45, soft tissue B; 46, soft tissue pogonion; 47, soft tissue pgnathion; 48, soft tissue menton; 49, submandibular point; and 50, cervical point. (**b**) Minimum box selection including all landmarks. (**c**) Square box selection including the inferior part and down-sampling. Modified-Alexnet combined the separated modules in the basic Alexnet for ease of implementation, and had an input image size of \(227\times 227\) pixels [25]. MobileNet and Resnet50 had a default size of \(224\times 224\) pixels for the input image [26]. Modified-Alexnet used He-normal initialization as the initial weight, and MobileNet and Resnet50 used the weight provided by ImageNet as the initial weight. The training was conducted using the stochastic gradient descent (SGD) optimizer [1; 27]. The initial learning rate was set at 0.002 and the batch size was set at 32. A total of 150 epochs were performed, and the learning rate was adjusted to a 0.1 factor when the validation loss value did not improve more than 1e-6 during 20 epochs. At the  
Figure 2: The three deep learning models used in this study were (**a**) Modified-Alexnet, (**b**) MobileNet, and (**c**) Resnet50. point when validation accuracy no longer increased significantly, the study was terminated and the model was evaluated.