# Design of a Binocular Pupil and Gaze Point Detection System Utilizing High Definition Images
## 3 Experimental Results
The results show that the average accuracy for both eyes are smaller than \(1^{\circ}\) which is accepted well among eye tracker studies. The calculated mean square error (MSE) and root mean square error (RMSE) of the system is presented in Tables 4 and 5 respectively. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{3}{*}{**Users**} & **Right Eye** & **Right Eye** & **Euclidean** & **Left Eye \(x\)** & **Left Eye \(y\)** & **Euclidean** & **Mean Error** \\  & \(x\) **Axis** & \(y\) **Axis** & **Right Eye** & **Axis Error** & **Axis Error** & **Left Eye** & **of Both** \\  & **Error (\({}^{\circ}\))** & **Error (\({}^{\circ}\))** & **Error (\({}^{\circ}\))** & **(\({}^{\circ}\))** & **Error (\({}^{\circ}\))** & **Error (\({}^{\circ}\))** & **Eyes (\({}^{\circ}\))** \\ \hline User 1 & 0.50 & 0.55 & 0.81 & 0.31 & 0.31 & 0.49 & 0.65 \\ User 2 & 0.58 & 0.37 & 0.77 & 0.35 & 0.22 & 0.46 & 0.61 \\ User 3 & 0.50 & 0.39 & 0.69 & 0.99 & 0.81 & 1.43 & 1.06 \\ User 4 & 0.77 & 0.78 & 1.11 & 0.47
According to estimated gaze points of user 1, Figure 13 shows left and right eye tracking graphics on the stimulus signal. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Users**} & **Right Eye** & **Right Eye** & **Euclidean** & **Left Eye \(x\)** & **Left Eye \(y\)** & **Euclidean** & **Mean MSE** \\  & \(x\) **Axis** & \(y\) **Axis** & **Right Eye** & **Axis MSE** & **Axis MSE** & **Left Eye** & **of Both** \\  & **MSE (\({}^{\circ}\))** & **MSE (\({}^{\circ}\))** & **MSE (\({}^{\circ}\))** & **(\({}^{\circ}\))** & **(\({}^{\circ}\))** & **MSE (\({}^{\circ}\))** & **MSE (\({}^{\circ}\))** & **Eyes (\({}^{\circ}\))** \\ \hline User 1 & 1.064 & 1.953 & 2.533 & 0.154 & 0.180 & 0.335 & 1.434 \\ User 2 & 0.071 & 0.078 & 0.150 & 0.071 & 0.025 & 0.097 & 0.123 \\ User 3 & 0.164 & 0.110 & 0.275 & 0.968 & 0.963 & 1.930 & 1.102 \\ User 4 & 0.221 & 0.284 & 0.506 & 0.168 & 0.117 & 0.285 & 0.395 \\ User 5 & 0.830 & 1.881 & 2.710 & 0.943 & 0.183 & 1.127 & 1.918 \\ User 6 & 0.257 & 0.607 & 0.864 & 0.450 & 0.417 & 0.867 & 0.865 \\ User 7 & 0.184 & 0.247 & 0.432 & 0.229 & 0.360 & 0.589 & 0.510 \\ User 8 & 0.322 & 0.585 & 0.908 & 0.344 & 0.541 & 0.876 & 0.892 \\ User 9 & 0.741 & 4.577 & 5.316 & 0.320 & 1.577 & 1.897 & 3.606 \\ User 10 & 0.225 & 0.186 & 0.412 & 0.238 & 0.125 & 0.363 & 0.389 \\ User 11 & 0.136 & 0.158 & 0.294 & 0.222 & 0.241 & 0.464 & 0.379 \\ Average & 0.383 & 0.969 & 1.309 & 0.373 & 0.429 & 0.802 & 1.055 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Estimation results of gaze tracking mean square errors in degrees. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Users**} & **Right Eye \(x\)** & **Right Eye \(y\)** & **Euclidean** & **Left Eye \(x\)** & **Left Eye \(y\)** & **Euclidean** & **Mean Error** \\  & **Axis Error** & **Axis Error** & **Right Eye** & **Axis Error** & **Axis Error** & **Left Eye** & **of Both** \\  & **(mm)** & **(mm)** & **Error (mm)** & **(mm)** & **(mm)** & **Error (mm)** & **Eyes (mm)** \\ \hline User 1 & 6.06 & 6.75 & 9.85 & 3.76 & 3.77 & 5.95 & 7.90 \\ User 2 & 7.03 & 4.56 & 9.36 & 4.27 & 2.64 & 5.56 & 7.46 \\ User 3 & 6.12 & 4.80 & 8.47 & 12.10 & 9.85 & 17.42 & 12.94 \\ User 4 & 9.46 & 9.54 & 13.61 & 5.73 & 4.58 & 7.99 & 10.80 \\ User 5 & 8.60 & 11.92 & 16.05 & 8.32 & 4.30 & 10.23 & 13.14 \\ User 6 & 6.04 & 6.18 & 9.79 & 7.19 & 7.77 & 11.80 & 10.79 \\ User 7 & 3.62 & 4.07 & 6.22 & 4.31 & 5.05 & 7.33 & 6.77 \\ User 8 & 5.45 & 6.96 & 9.68 & 5.73 & 6.99 & 9.76 & 9.72 \\ User 9 & 12.48 & 19.85 & 25.78 & 5.54 & 10.09 & 12.57 & 19.17 \\ User 10 & 4.27 & 3.41 & 6.04 & 4.76 & 3.56 & 6.67 & 6.36 \\ User 11 & 3.52 & 3.64 & 5.66 & 4.64 & 4.71 & 7.24 & 6.45 \\ Average & 6.60 & 7.42 & 10.95 & 6.03 & 5.75 & 9.32 & 10.13 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Estimation results of gaze tracking accuracies in mm.