# Design of a Binocular Pupil and Gaze Point Detection System Utilizing High Definition Images
## 3 Experimental Results  
Figure 10 shows the measurement of the luminosity in the experimental environment. The luminosity of the room was measured with Extech LT300 light meter (FLIR Systems, Wilsonville, OR, USA) and its value was observed to be 505 lux. The experiment was tested with a desktop computer containing a 3.4-GHz Intel(r) core(tm) i7-3770 K CPU and 16 GB of RAM. The monitor resolution was 1280 \(\times\) 1024. In addition, an 850-nm illuminator group was used. The camera was positioned right below the center of the monitor, and the illuminator was also positioned below the center of the monitor. The distance (\(L\)) between the monitor and the user was roughly 700 mm. We tested our gaze tracking system with 11 participants \begin{table}
\begin{tabular}{c c c} \hline \hline
**Initial Parameters** & **Value** & **Unit** \\ \hline Stimulus center \(x\)-coordinate (_xCenter_) & 640 & pixel \\ Stimulus center \(y\)-coordinate (_yCenter_) & 512 & pixel \\ Stimulus radius (_A_) & 256 & pixel \\
33 Angular frequency (_w_) & 2 \(\times\)\(\pi\)\(\times\) 0.1 & rad/s \\ Progress start time (\(t_{0}\)) & 0 & s \\ Refresh rate of monitor (_rt_) & 16.6 & ms \\ Phase (\(\theta\)) & 0 & rad \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Moving target initial values. Figure 10: The luminosity measurement of the experimental environment. whose ages were between 25 and 40. We performed the experiments with minimum 400 images per participant. Experimental results showed that the system can process 2046 \(\times\) 1086 pixel images at 40 fps. Performance of the system compared to 640 \(\times\) 480 pixel eye trackers, is approximately 280 fps as shown in Figure 11.  
To estimate eye gaze points, first users were asked to look at calibration points. Nine calibration points are not visible to users on the user screen simultaneously. When calibration starts, the first calibration point is seen on the screen. Then, users have to press PC mouse to see other calibration points. After nine points calibration ends up, users track at least one cycle movement of the moving target stimulus. Afterwards, we estimate that system accuracy is offline. Figure 12 shows gaze point estimation geometry of our stimulus. In general, the difference between the estimated (_Sx, Sy_) and the actual (_S_') gaze point coordinates is expressed as the error amount of the gaze tracking system as shown in Equation (14). Here, \(\theta\)  
Figure 11: The system performance. fps: frames per second. Figure 12: Gaze point estimation geometry on the user screen. corresponds to error amount, \(L\) is the user to screen distance and \(E(S_{x,y})\) is Euclidean distance between estimated gaze point and the actual user screen coordinates. Equation (15) depicts absolute distance (\(D\)) of the estimated gaze position (\(Sx\), \(Sy\)) from stimulus center coordinates in pixel. Equations (16) and (17) are estimated gaze point (\(Sx\), \(Sy\)) \(x\)-axis deviation (\(E_{dx}\)) and \(y\)-axis deviation (\(E_{dy}\)) from gazed point (\(S^{\prime}\)) actual coordinates. Finally, Equation (18) gives the expression of Euclidean error \(E(S_{x,y})\) between estimated gaze point and actual user screen coordinates. \[\theta=arctan\left(\frac{E\big{(}S_{x,y}\big{)}}{L}\right) \tag{14}\]  
\[D\big{(}S_{x,y}\big{)}=\sqrt{\left|Sx-640\right|^{2}+\left|Sy-512\right|^{2}} \tag{15}\]  
\[E_{dx}=\frac{\left|Sx\times 256-Sx\times D\right|}{D} \tag{16}\]  
\[E_{dy}=\frac{\left|Sy\times 256-Sy\times D\right|}{D} \tag{17}\]  
\[E\big{(}S_{x,y}\big{)}=\sqrt{E_{dx}{}^{2}+E_{dy}{}^{2}} \tag{18}\]  
To calculate the accuracy of the system in degrees, the error amount in pixels requires conversion to mm unit. For this conversion, we multiplied pixel size of our monitor (0.29 mm) with the errors \(E_{dx}\) and \(E_{dy}\). Then the \(x\)-axis, \(y\)-axis and Euclidean errors in degrees are calculated with Equations (19)-(21). Figure 10:0  
Figure 10:1  
Figure 10:2  
Eleven users participated in our system test and the calculated accuracy of the system is presented in Tables 2 and 3.