## 1 Introduction  
Low back pain is a common health problem worldwide, with numerous studies finding that it is a leading cause of disability and has a significant socioeconomic impact, reducing the quality of life for many people [1; 2; 3]. Lumbar spondylosis and spondylisthesis are among the most common causes of low back pain [4; 5; 6]. Magnetic resonance imaging and X-ray images are used to identify lumbar spondylosis and spondylisthesis, and lumbar spine radiography is often used first [7; 8]. Among these, lumbar oblique radiography is often used to determine the presence of the aforementioned lumbar spondylosis and the morphology of the intervertebral joints, and the images obtained change depending on the angle at which the body is tilted [9; 10]. Therefore, since the optimal angle varies depending on the joint or area to be observed and the suspected pathological condition, if the angle can be instantly estimated from the obtained image, it is easier to determine whether the image is what is required at that time. In other words, there is a need for instantaneous estimation of whether the oblique angle is appropriate for post-imaging evaluation and whether re-imaging is necessary. Obtaining an appropriate lumbar oblique image is essential for accurate diagnosis and treatment decisions. However, it is difficult even for skilled radiological technologists to obtain the optimal angle in a single shot, and multiple shots are sometimes required. This leads to an increase in patient radiation exposure and prolongation of examination time, so improvements are needed. In addition, images taken at inappropriate angles may lead to a decrease in diagnostic accuracy and oversight, which may adversely affect the patient's treatment plan. In recent years, deep learning techniques have been used in the medical field [11; 12; 13; 14; 15; 16; 17], and there has been a lot of research related to the spine [18]. Deep learning has the potential to automate the estimation of optimal imaging angles by modeling the experience and knowledge of skilled radiologists. The development of such technology is expected to reduce the burden on radiological technologists and improve the efficiency of examinations, thereby contributing to improvements in the quality of medical care. To further elucidate the methodology of our study, it is crucial to explain the rationale behind employing two distinct convolutional neural network (CNN) models: one specialized for classification and another for regression. These models interact by initially using the classification model to categorize the images based on certain predefined criteria, which then guides the regression model to accurately estimate the imaging angles. In this study, we wanted to investigate the possibility of using a convolutional neural network (CNN) to estimate the angle of a lumbar oblique image. Since big data is needed to create a CNN model, in the case of this study, lumbar oblique X-ray images from various angles with known acquisition angles are required. In this study, however, we created lumbar spine X-ray images of arbitrary angles pseudo-created from computed tomography (CT) images, and we used these images to create the model and evaluate its accuracy. This makes it possible to generate a large number of images from various angles. This will ensure a large dataset necessary for training the CNN model. The purpose of this study is to create lumbar spine X-ray images of arbitrary angles pseudo-rectified from CT images and to estimate the angles of lumbar spine oblique images using a CNN trained by those images. The results of this study are expected to contribute to the optimization and efficiency of lumbar oblique imaging, thereby reducing the burden on patients and improving the quality of medical care. In addition, the method proposed in this study can be applied to images other than lumbar oblique images, and it is expected to contribute to the development of medical image analysis.