## 2 Materials and Methods
### Data Preprocessing  
_The Creation of Supervised Data_  
A large amount of supervised data is required to create a CNN model [19]; however, the dataset of lumbar spine oblique X-ray images at various angles needed for this study was not publicly available. Therefore, in this study, lumbar spine X-ray images of arbitrary angles were pseudo-fabricated from CT images, and these images were used as the supervised data.  
The procedure for creating supervised data using the software shown in Figure 1 is summarized below:  
1. Specify the center of the spinal canal and the spinous process in the axial section image of the third lumbar vertebra, thereby creating a reference line for the angle;
2. The axial section image is converted to a coronal section image, and the range is set so that the first to the fifth lumbar vertebrae are included in the image;
3. Cut out the set area in the plane perpendicular to the created reference line;
4. Create a pseudo X-ray image containing three-dimensional information by adding together the images cut out in step 3 to an arbitrary extent;
5. Visually adjust the maximum and minimum pixel values of the image to create an image with contrast similar to the actual X-ray image;  
\begin{table}
\begin{tabular}{c c} \hline
**Environment** & **Contents** \\ \hline Software & MATLAB 2022a (Mathworks) \\ OS & Windows 10 \\ CPU & Intel Core i9-10980 XE 3.5 GHz \\ RAM & DDR4 2666 Mhz 64 GB \\ GPU & NVIDIA RTX P5000 16 GB \(\times\) 4 \\ \hline \end{tabular}
\end{table}
Table 1: Software and specifications of the computer used in this study.  
Create and save an image according to the procedure described up to step 5, rotated in 5\({}^{\circ}\) increments from \(-60^{\circ}\) to 60\({}^{\circ}\) relative to the reference angle.  
The selection of the range from \(-60^{\circ}\) to 60\({}^{\circ}\) relative to the reference angle (0\({}^{\circ}\)) for generating lumbar spine X-ray images was primarily based on the typical clinical angles used in lumbar oblique radiography. This range was chosen to encompass the angles most commonly utilized for diagnostic accuracy, as angles beyond 60\({}^{\circ}\) often result in a lateral view, which was not the focus of this study. Consequently, the study limited its scope to 60\({}^{\circ}\) to maintain relevance to standard oblique imaging practices. The above procedure was applied to all CT images, and 25 lumbar spine X-ray images were created per CT image per patient. An example of the images produced is shown in Figure 2.  
In creating the supervised data, a line connecting the center of the spinal canal and the spinous process was used as the reference line, and the imaging angle of the pseudo X-ray image was defined by how many degrees it was tilted from that line. This enabled the generation of a large amount of supervised data with clear imaging angles.  
Since this method created a pseudo X-ray image from a CT image, there was a possibility that there may be some differences from the actual X-ray image. However, considering that the purpose of this study was to estimate the shooting angle, the pseudo X-ray images were considered to be sufficiently useful. In addition, this method allowed the generation of a large amount of supervised data, which was necessary for the training of the CNN model.  
Figure 1: Example of implementation for creating a supervised image. The green line represents the corrected 0\({}^{\circ}\) based on the CT image. The yellow dashed lines indicate the range used for generating the pseudo X-ray image, while the solid yellow line denotes the center of this range.  
A dedicated program was developed to generate the supervised data. This program read CT images and automatically generated pseudo X-ray images at specified angles. The implementation screen of the program is shown in Figure 1. The program was developed using MATLAB. The development of the program enabled the efficient creation of a large amount of supervised data.