# Vertebral Center Points Locating and Cobb Angle Measurement Based on Deep Learning
## 1 Introduction  
Scoliosis is a physical condition characterized by a lateral curvature of the spine, usually defined as a curve on a standing radiograph of the spine measuring at least 10\({}^{\circ}\)[1]. Adolescent Idiopathic scoliosis is the most common form seen in clinical practice, accounting for nearly 80% of cases. The prevalence is estimated to be 1.3/1000 in children under 8 years of age and 1.8/1000 in children over 8 years of age [2]. This condition can lead to a variety of problems, including obvious body shape deformities, decreased chest volume, impaired spinal movement and breathing, decreased trunk balance, increased incidence of back pain, serious aesthetic problems, activity limitation and decreased quality of life [3; 4; 5]. The traditional method of diagnosing a curved spine determines the end verteba on the X-ray film, draws the line at the corresponding end verteba, and measures the spine curvature according to the drawn lines. This method is time-consuming, laborious, and vulnerable to the professional level of the medical surveyors, subjective factors, and other influences, leading to specific discrepancies in the results. In recent years, with the rapid development of deep learning and image processing, scoliosis measurement methods have also advanced significantly. [PERSON] et al. [6] proposed a method of Cobb angle measurement that employed Canny edge detection, fuzzy Hough (FHT) and spine edge structure detection. The peak value in Hough space was selected and the line that coincided with the upper and lower edges of the verteba was determined according to the constraint conditions of the shape of the verteba, and, finally, the Cobb angle was calculated. [PERSON] et al. [7] proposed a method to calculate Cobb angle. Firstly, the end vertebrae (the verteba with the greatest inclination in the scoliosis) are manually selected and then denoised and histogram equalized. Then thecanny edge detection operator is applied to the enhanced image to detect the edge of the vertebrae used to measure the Cobb angle. Finally, the line detection is carried out through Hough transform and the Cobb angle is calculated. [PERSON] et al. [8] employed intervertebral distance and positioning to differentiate cervical vertebrae from the spine. The X-ray image is preprocessed through histogram equalization, Canny edge detection, etc. Then the C3-C7 cervical region of interest (ROI) was manually selected. After the generalized Hough transform (GHT) and fuzzy C-means clustering, the center points of vertebrae are detected, and the center points of the intervertebral disc between vertebrae are obtained. The distance between two adjacent vertebrae was calculated and their centroids were found, thus obtaining the region of each vertebra. Affine transformation was then carried out on the lines passing through the centroid and connecting the two vertebrae, and vertical separation lines were found on these centroids, finally obtaining the boundary of the vertebra. [PERSON] et al. [9] segmented each column of pixel points of the preprocessed spine x-ray by the thresholding, extracted the contour using Canny edge detection, calculated the vertebral center points, and fitted the spine curve. [PERSON] et al. [10] proposed a Cobb angle measurement method which requires users to select vertebrae from the upper to the lower vertebrae via mouse operation. For each selected vertebra, a 150 \(\times\) 150-pixel rectangle for each selected vertebra created and sent to the DNN for predicting the slope of the vertebra. Subsequently, the tilt angle of the two end vertebrae are then detected and the sum of the absolute values of the tilt angles is calculated as the Cobb angle. [PERSON] et al. [11] calculated Cobb angle using a key point detection method. They proposed Structured Support Vector Regression (S2 VR), which directly estimates corner coordinates and Cobb angles by expressing prediction as a multi-output regression task. The Cobb angle measurement method proposed by [PERSON] et al.