## 4 Experimental Results and Comparisons

Table 4: Comparisons of the visible-light pupils’ center tracking errors between the YOLOv3-tiny and the previous ellipse fitting based designs. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{2}{c}{**Validation**} & \multicolumn{2}{c}{**Test**} \\ \cline{2-5}  & **Precision** & **Recall** & **Precision** & **Recall** \\ \hline YOLOv3-tiny (original) & 81.40\% & 83\% & 78.43\% & 81\% \\ \hline YOLOv3-tiny (one anchor) & 80.19\% & 84\% & 80.50\% & 83\% \\ \hline YOLOv3-tiny (one anchor/one way) & 79.79\% & 82\% & 76.82\% & 81\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance comparisons of visible-light pupil object detection among the three YOLO-based models. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Mean Errors** & **Variance** \\  & **(Pixels)** & **(Pixels)** \\ \hline YOLOv3-tiny (original) & 1.62 & 2.03 \\ \hline YOLOv3-tiny (one anchor) & 1.58 & 1.87 \\ \hline YOLOv3-tiny (one anchor/one way) & 1.46 & 1.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparisons of the visible-light pupils’ center tracking errors among the three YOLO-based models by using the datasets of person 1 to person 8 for the training mode. Table 7 describes the comparison of computational complexities among the three YOLOv3-tiny-based models. In Table 7, \"BFLOPS\" means billion float operations per second. Using a personal computer with an Nvidia GeForce RTX 2060 card, the processing frame rate of pupil tracking with YOLOv3-tiny-based models is up to 60 FPS. Using a personal computer with an Nvidia GeForce RTX 2080 card, the processing frame rate of pupil tracking with YOLOv3-tiny-based models is up to 150 FPS. Moreover, when using the NVIDIA XAVIER embedded platform [41], the processing frame rate of pupil tracking with YOLOv3-tiny-based models is up to 88 FPS. Figure 15 illustrates the calculation of the gaze tracking errors, and the expression of the calculation method is described in Equation (5) as follows:  
\[\theta=\tan^{-1}\frac{E}{D} \tag{5}\]  
In Equation (5), the angle \(\theta\) reflects the gaze tracking errors (i.e., degrees), E is the absolute error (by pixels) at the gaze plane, and D is the application distance between the user and the gaze plane, where D is set to 55 cm. For the evaluation of the gaze tracking errors, Figure 16a depicts four target markers used for calibration for the training mode, and Figure 16b presents five target points used for estimation for the testing mode. For the training mode, using the four target markers shown in Figure 16a, Table 8 lists the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Mean Errors** & **Variance** \\  & **(Pixels)** & **(Pixels)** \\ \hline YOLOv3-tiny (original) & 4.11 & 2.31 \\ \hline YOLOv3-tiny (one anchor) & 3.99 & 2.27 \\ \hline YOLOv3-tiny (one anchor/one way) & 4.93 & 2.31 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparisons of the visible-light pupils’ center tracking errors among the three YOLO-based models by using the datasets of person 9 to person 16 for the cross-person testing mode. Figure 15: Diagram of estimating gaze tracking errors. comparison of gaze tracking errors among the three applied YOLOv3-tiny-based models. After being joined with the calibration process, the average gaze tracking errors by the proposed YOLOv3-tiny-based pupil tracking models are less than 2.9 degrees for the training mode. Table 9 lists the comparison of the gaze tracking errors among the three YOLOv3-tiny-based models for the testing mode using the five target points shown in Figure 16b. In Table 9, the average gaze tracking errors by the proposed YOLOv3-tiny-based pupil tracking models are less than 3.5 degrees. Table 10 revealed the performance comparison among the different deep-learning-based gaze tracking designs. In general, the gaze tracking errors by the wearable eye tracker will be less than those by the non-wearable eye trackers.