# Vertebral Center Points Locating and Cobb Angle Measurement Based on Deep Learning
## 4 Results  
To evaluate the model performance and Cobb angle measurement results, we calculated the model parameters, mean absolute percentage error (MAPE), and FPS were evaluated on the 40 X-piece test-set. The results are summarized in Table 1. The MAPE was calculated as:  
\[\text{MAPE}=\frac{1}{Nn}\cdot\sum_{N}\sum_{n}|\frac{\theta_{gt}-\theta_{pred}}{ \theta_{pred}}|\cdot 100\% \tag{5}\]  
where \(N\) is the number of samples, \(n\) is the number of lateral curvatures in a sample, and \(\theta_{gt}\) and \(\theta_{pred}\) are the actual and predicted values of the Cobb angle, respectively.  
As shown in Table 1, the MAPE of the proposed method is comparable to the first two models, while the parameter quantity is significantly reduced and the frame per second (FPS) is higher.  
To demonstrate the impact of utilizing locating points and correction formula on measurement results, we relabeled the central point of the vertebrae in the dataset and only labeled 17 vertebrae for detection. As shown in Table 2, direct training and prediction of the central points of 17 vertebrae on the full spine X-ray resulted in large errors and low accuracy in selecting end vertebrae. Notably, the error corresponding to the proximal thoracic (PT) was the largest due to the similarity between cervical vertebrae characteristics and those of the detected thoracic and lumbar vertebrae, leading to the model detecting cervical vertebrae and causing significant deviation in end vertebrae selection, thereby affecting Cobb angle measurements. However, with the use of locating points and correction formula, accuracy rates were significantly improved. Thus, the proposed method of utilizing locating points can effectively minimize the impact of cervical vertebrae and other features on X-ray, while the use of empirical formula can enhance measurement accuracy.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Parameters (M)** & **MAPE (\%)** & **FPS (Hz)** \\ \hline Hourglass & 193.62 & 9.78 & 8.43 \\ HrNet & 242.60 & 10.03 & 6.65 \\ Proposed method & 13.46 & 9.24 & 14.44 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Comparison of detection results of spinal key points.  
Figure 7: Before and after correction.  
To further verify the effectiveness of the proposed method, we conducted reliability analysis on the above test-set. Table 3 records ICC (intraclass correlation coefficient) and MAD (mean absolute deviation) of the two surveyors. It can be seen that the intra-observer results of the two observers are 0.951 and 0.958 respectively, with MADs 2.24 and 2.16 respectively. The ICCs between the two measurements are 0.940 and 0.942, and the MADs are 2.61 and 2.55, respectively. These results demonstrate that manual measurement is reliable.  
Table 4 records the intra-group correlation coefficients between the automatic detection method in this paper and the results obtained by two surveyors using the manual measurement method. The analysis between automatic Cobb angle detection method and manual measurement yielded an ICC of 0.897 and 0.902, respectively, and a MAD of 3.13 and 3.04, respectively. This indicates that the automatic detection method has good reliability.