## 3 Results
### Wrist Angle Prediction Using Machine Learning and a Single-Camera System (2 DML)  
When analyzing the results obtained from the single oblique camera for FE, several models (XGB regressor, RBF sampler and ridge regression, and the neural network) perform reasonably well (Table 5). The performance of the neural network achieved the lowest MAE for both flexion/extension and radial ulnar deviation angles. The overall best model with the lowest combined MAE resulted in flexion/extension MAE of 10.9\({}^{\circ}\) and a radial/ulnar MAE of 7.5\({}^{\circ}\) in shuffle 1. The MAE values in Table 5 for FE and RUD represent the most accurate individual model results. Again, the cubic regression model performed worse than the other models in all cases. Considering the other models for FE analysis, three models (XGB regressor, RBF sampler and ridge regression, and the deep neural network) have similar performance and are preferred to the other models. Turning to the RUD results, \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Feature** & **3 DML** & **3 DML** & **Radial-** & **2 DML** & **2 DML** & **Radial-** \\
**Importance Rank** & **Flexion/Extension** & **Ularar Deviation** & **Flexion/Extension** & **Ular Deviation** \\ \hline
1 & mcp2\_z & mcp2\_x & mcp3\_y & mcp2\_y \\
2 & mcp2\_x & mcp3\_x & centre\_wrist\_y & mcp5\_y \\
3 & centre\_wrist\_z & centre\_wrist\_x & mcp2\_y & mcp3\_x \\
4 & ulna\_z & ulna\_z & mcp3\_x & radial\_y \\
5 & mcp2\_y & ulna\_x & ulna\_y & mcp2\_x \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Top 5 features of importance for flexion/extension (FE) and radial/ulnar deviation (RUD) as determined from a multi-camera system (3 DML) and single-camera system (2 DML). \begin{table}
\begin{tabular}{l l l l l l l l l l l l} \hline \hline
**Model** & **Shuffle 1 MAE (\({}^{\circ}\))** & \multicolumn{2}{l}{**Shuffle 2 MAE (\({}^{\circ}\))**} & \multicolumn{2}{l}{**Shuffle 3 MAE (\({}^{\circ}\))**} & \multicolumn{2}{l}{**Shuffle 4 MAE (\({}^{\circ}\))**} & \multicolumn{2}{l}{**Mean MAE \(\pm\) SD (\({}^{\circ}\))**} \\ \hline  & FE & RUD & FE & RUD & FE & RUD & FE & RUD & FE & RUD \\ \hline Linear & 10.4 & 7.2 & 13.7 & 8.0 & 11.7 & 8.2 & 11.0 & 6.5 & \(\begin{array}{l}11.7\pm\\ 1.4\ (\text{B})\end{array}\) & \(\begin{array}{l}7.5\pm\\ (\text{B})\end{array}\) & \(\begin{array}{l}0.8\\ \\ \end{array}\) \\ \hline Quadratic & 8.7 & 5.8 & 10.6 & 9.4 & 11.3 & 7.4 & 10.2 & 6.1 & \(\begin{array}{l}10.2\pm 1.1\\ (\text{B},\text{C})\end{array}\) & \(\begin{array}{l}7.2\pm\\ (\text{B},\text{C})\end{array}\) \\ \hline Cubic & 36.2 & 21.8 & 83.3 & 74.1 & 142.9 & 134.2 & 40.8 & 28.3 & \(\begin{array}{l}76\pm\\ (\text{A})\end{array}\) & \(\begin{array}{l}50\\ (\text{A})\end{array}\) & \(\begin{array}{l}65\pm\\ (\text{A})\end{array}\) \\ \hline XGB Regressor & 7.8 & 6.2 & 8.4 & 6.3 & 9.0 & 5.9 & 9.5 & 6.1 & \(\begin{array}{l}8.7\pm\\ (\text{B},\text{C})\end{array}\) & \(\begin{array}{l}6.1\pm\\ (\text{B},\text{C})\end{array}\) \\ \hline Support Vector & 6.6 & 5.6 & 9.4 & 6.2 & 7.5 & 4.9 & 8.2 & 5.2 & \(\begin{array}{l}7.9\pm\\ (\text{B},\text{C})\end{array}\) & \(\begin{array}{l}1.2\\ (\text{C})\end{array}\) \\ \hline RBF Sampler & 10.3 & 6.8 & 10.9 & 7.2 & 11.4 & 7.5 & 11.0 & 6.3 & \(\begin{array}{l}10.9\pm\\ 0.5\ (\text{B},\text{C})\end{array}\) & \(\begin{array}{l}7.0\pm\\ (\text{B},\text{C})\end{array}\) \\ \hline Neural & 5.9 & 5.2 & 8.0 & 6.1 & 7.6 & 5.2 & 7.4 & 5.4 & \(\begin{array}{l}7.2\pm 0.9\\ (\text{C})\end{array}\) & \(\begin{array}{l}5.5\pm\\ (\text{C})\end{array}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Mean absolute error (MAE) plus/minus standard deviation (SD) results from testing data of predicted flexion/extension (FE) and radial/ulnar deviation (RUD) angle using a multi-camera system across four shuffles. Mean MAE values that do not share a letter are significantly different from one another. both the cubic and XGB regressor demonstrate poor results. The others show superior performance; however, the neural network noticeably has the lowest MAE.