## 4 Discussion
used a three-axis gyroscope to measure thumb supination and reported that patients with carpal tunnel syndrome had less range of motion than healthy individuals [28; 29]. In the present study, thumb supination was measured by directly fixing an angle sensor to the dorsal base of the thumb with tape, and the resulting angles were used as true values. The angles of radial abduction and palmar abduction, obtained simultaneously, were also considered true values. In this study, the angle sensor was used as the true value and combined with MediaPipe and machine learning to achieve a very high estimation accuracy for radial abduction and palmar abduction, a result consistent with the results of previous studies [19]. The differences in the validation MAE values for radial abduction, palmar abduction, and pronation can be attributed to the accuracy of the angle sensor, for which the values are as follows: X- and Y-axes--0.2\({}^{\circ}\) and \(Z\)-axis--1\({}^{\circ}\). The lower accuracy for the \(Z\)-axis measurements likely contributed to the higher MAE observed for palmar abduction, a movement involving \(Z\)-axis motion. In contrast, radial abduction and pronation, which are primarily associated with X- and \(Y\)-axis motions, showed similar levels of accuracy, consistent with the sensor's specifications. Residual plots are crucial for evaluating regression models by clarifying issues related to assumptions and detecting outliers. In the residual plots for all the ML models in this study, a wide spread of residuals was observed across all angles, with no systematic deviations. The residual plots demonstrated that the residuals were centered around zero, indicating that the models performed reliably across the dataset. However, a small number of outliers were observed. This may be due to the limitations of the MediaPipe library in capturing thumb motion, a potential cause of which is the camera's position (at a 45\({}^{\circ}\) angle from the palmar side), which could make it difficult to accurately capture depth information when the thumb faces the camera. To address these issues, future studies could incorporate additional parameters or utilize multi-angle camera setups to improve the accuracy of motion capture and reduce the occurrence of outliers. Feature importance represents the contribution of a feature when a model makes a prediction. SHAP values explain the effect of a specific feature having a certain value compared with a prediction made when that feature has a baseline value. The features listed on the \(y\)-axis are those considered by the model in its estimation process. Their position on the \(y\)-axis reflects their importance, with the higher-ranked features exerting a more significant influence on the output of the angle estimation model. As reported in previous research, norm_tip_size had the highest feature importance and SHAP value for radial abduction and palmar abduction. Norm_tip_size is a normalized value calculated by dividing the area of the parallelogram formed by the thumb and the second metacarpal by the square of the length of the index finger. Because the length of the index finger does not change with movement, normalizing based on this length accounts for variations in the distance between the camera and the subject. Additionally, the area of the parallelogram decreases when the abduction angle is between 0 and 45 degrees and increases again when it exceeds 45 degrees. This demonstrates that the relationship between the parallelogram area and the rotation angle changes depending on the angle. Previous research has shown that high estimation accuracy can be achieved by setting appropriate parameters during machine learning estimation [19]. In this study, the correlation coefficients for pronation were 0.85, 0.85, 0.92, 0.91, and 0.94 for the five methods employed, namely linear regression, ElasticNet, SVM, random forest regression, and LightGBM, respectively. These values are lower than those observed for radial and palmar abduction.