## 4 Discussion  
When using the low-cost four camera system with only open-source CV algorithms (Objective 1), large errors occurred when the markers were outside the field of view of the camera, distorted, or blurred within the camera view, resulting in inaccurate marker tracking. If the 3D marker location was inaccurate, the coordinate system vectors and resulting angles generated would also be inaccurate. The DLC/Anipose combination resulted in high errors (99\({}^{\circ}\) FE; 25\({}^{\circ}\) RUD) probably because the rotation matrices depended on accurate marker locations; if the joint center established via the two different methods is different, then large offsets and distortions can occur [18]. In conclusion, the CV methods investigated in this study as part of the first objective generated poor wrist angle predictions. Machine learning (3 DML) offered substantial improvement for wrist angle predictions compared to the computer vision method (3 DCV). As displayed in Table 3, several models show promise at learning the inaccuracies and complex patterns associated with wrist movements. As noted in the results, the MAE of the 3 DML method was as low as 5.9\({}^{\circ}\) for FE and 5.2\({}^{\circ}\) for RUD. In addition, the standard deviation across shuffles for the MAE was between 0.2 and 1.6\({}^{\circ}\) for all models except the worst-performing model, the cubic regression. This small standard deviation demonstrates how well the model can generalize \begin{table}
\begin{tabular}{l c c c c c c c c c c} \hline \hline
**Model** & **Shuffle 1 MAE(\({}^{\bullet}\))** & **Shuffle 2 MAE(\({}^{\bullet}\))** & **Shuffle 3 MAE(\({}^{\bullet}\))** & **Shuffle 4 MAE(\({}^{\bullet}\))** & **Mean MAE \(\pm\) SD (\({}^{\bullet}\))** \\ \hline  & FE & RUD & FE & RUD & FE & RUD & FE & RUD & FE & RUD \\ \hline Linear Regression & 15.1 & 9.5 & 16.9 & 9.7 & 18.8 & 9.1 & 18.6 & 8.9 & 17.4 \(\pm\) & 9.3 \(\pm\) 0.4 \\  & & & & & & & & & 1.7 (B) & (B,C) \\ \hline Quadratic Regression & 14.2 & 9.0 & 24.5 & 12.5 & 17.7 & 10.3 & 15.9 & 8.8 & 18.1 \(\pm\) & 10.2 \(\pm\) \\  & & & & & & & & & 4.5 (B) & 1.7 (B,C) \\ \hline Cubic Regression & 28.9 & 13.4 & 89.0 & 75.6 & 68.5 & 56.2 & 57.0 & 40.7 & 61 \(\pm\) & 47 \(\pm\) 26 \\  & & & & & & & & & 25(A) & (A) \\ \hline XGB Regressor & 14.8 & 9.4 & 16.6 & 9.9 & 14.0 & 8.1 & 14.9 & 80 & \(\begin{array}{c}15\pm 1.1\\ (\text{B,C})\end{array}\) & 27 \(\pm\) 0.9 \\  & & & & & & & & & (B,C) \\ \hline Support Vector Regression & 13.8 & 8.8 & 16.9 & 9.7 & 18.4 & 8.9 & 17.8 & 8.8 & 16.7 \(\pm\) & 9.1 \(\pm\) 0.4 \\  & & & & & & & & 2.0 (B) & (B,C) \\ \hline RBF Sampler and Ridge Regression & 14.1 & 9.5 & 16.9 & 9.6 & 15.8 & 9.1 & 15.4 & 8.6 & 15.6 \(\pm\) & 9.2 \(\pm\) 0.5 \\ \hline Neural Network & 10.9 & 7.5 & 13.8 & 5.2 & 12.1 & 7.1 & 11.9 & 6.9 & 12.2 \(\pm\) & 6.7 \(\pm\) 1.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Mean absolute error (MAE) plus/minus standard deviation (SD) from testing dataset of predicted flexion/extension (FE) and radial/ulnar deviation (RUD) angles using a single-camera system across four shuffles. Mean MAE values that do not share a letter are significantly different from one another. to accurately predict wrist angle across a variety of subjects and arm orientations. The statistical analyses demonstrated that the worst prediction performance is associated with the cubic regression model. The accuracy of these models may be further improved with increased training data, and the methods described herein may provide the scaffolding for further development in the field of markerless motion capture. As expected, the 2D single-camera method (2 DML) (Table 5) was not as accurate when compared to the 3D multi-camera method (3 DML) (Table 3). Similar to the case of the multiple camera, cubic regression performed the worst. The observed drop in accuracy compared to the 3 DML method is probably because the 3D dataset provides marker depth to the system, which is important for predicting angles in multiple planes.