# Upper Body Pose Estimation Using Deep Learning for a Virtual Reality Avatar
## 3 Pose Regression Methods
### Validation of the Pose Regression Model  
Our pose regression model optimizes to minimize the overall MSE in Equation (2). During training our model for 5 epochs and 150 iterations, the calculated MSE decreases gradually, as depicted in Figure 4. As can be seen in Figure 4, the graph illustrates the relationship between the number of iterations in the fifth epoch (horizontal axis) and the calculated mean squared error (MSE) (vertical axis). The MSE decreases as the number of iterations increases, indicating that our model's choice of optimization method was appropriate. Figure 5 compares the output of the predicted values to the ground truth of the right shoulder. The horizontal axis represents the number of iterations, while the vertical axis illustrates the mean absolute error (MAE) between the y values of the joint \(j_{7}\). From this comparison, it can be inferred that our model's prediction of joint \(j_{7}\) values is in close alignment with the ground truth, further validating the effectiveness of the chosen optimization method. As Figure 5 shows, the MAE decreases within an acceptable range and is small enough to be unnoticeable in practice. Overall, these results demonstrate the validity and accuracy of the proposed model.  
We validate our pose regression model by applying the pose regression model to both the training and test data and then calculate the MSE for the ground truth. The mean MSE of the joints is 0.0277 for the training data and 0.0448 for the test data. Table 1 shows the MSE of the joints; \(j_{4}\), \(j_{5}\), \(j_{6}\), \(j_{7}\), \(j_{8}\), and \(j_{9}\). Small MSEs for the test data indicate that our regression method yields accurate results.  
To conduct a comprehensive comparison between our method and the IK method, we calculate the MSE between the ground truth position of the joints and the output of the Final IK [42] method. The results of this comparison are presented in Table 2 and demonstrate that our method results in lower errors with an MSE of 0.0448, compared to the Final IK method with an MSE of 0.8066. Furthermore, Table 3 compares the MAE of the right shoulder joint from the test dataset using both our method and the Final IK method. The results indicate that our method surpasses the performance of the Final IK method.  
Figure 4: Mean squared error(MSE) of our pose regression model in the last (5 th) epoch.  
Figure 5: Mean absolute error(MAE) of the predicted values and the ground truth data of the right shoulder or joint \(j_{7}\) of the last (5 th) epoch.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Joints** & **MSE of Training Data (cm)** & **MSE of Test Data (cm)** \\ \hline \(j_{4}\) & 0.0245 & 0.0342 \\ \(j_{5}\) & 0.0387 & 0.0456 \\ \(j_{6}\) & 0.0336 & 0.0448 \\ \(j_{7}\) & 0.0267 & 0.3870 \\ \(j_{8}\) & 0.0242 & 0.3940 \\ \(j_{9}\) & 0.0382 & 0.4270 \\ \hline \hline \end{tabular}
\end{table}
Table 1: MSE values for \(j_{4}\), \(j_{5}\), \(j_{6}\), \(j_{7}\), \(j_{8}\), and \(j_{9}\).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Methods** & **MSE of Test Data (cm)** \\ \hline Final IK & 0.8066 \\ Ours & 0.0448 \\ \hline \hline \end{tabular}
\end{table}
Table 2: MSE values of the test data.  
For further evaluation, we employ the MPJPE (mean per joint position error) [43] metric, a widely accepted standard for evaluating human pose estimation. We evaluate the accuracy of the upper body tracking on a sample of 27,056 frames drawn from our train and test datasets each. Table 4 shows the calculated MPJPE metric by comparing the local positions of the joints in the reconstructed motion to those in the reference.