## 3 Proposed Methods
### Calibration and Gaze Tracking Processes  
Before using the wearable eye tracker to predict the gaze points, the gaze tracking device must undergo a calibration procedure. Because the appearance of each user's eye and the application distance to the near-eye camera are different, the calibration must be done to confirm the coordinate mapping scheme between the pupil's center and the outward scene, after which the wearable gaze tracker can correctly predict the gaze points correspond to the outward scene. Figure 11 depicts the used calibration process of the proposed wearable gaze tracker. The steps of the applied calibration process are described as follows:  
At the first step, the system collects the correspondence between the center point coordinates of the pupils captured by the nearfield eye camera and the gaze points simulated by the outward camera. Before calibration, in addition to recording the positions of the center points of the pupil movement, the trajectory of markers captured by the outward camera must also be recorded. Figure 12 shows the trajectory diagram of tracking the pupil's center with the nearfield eye image for calibration. In addition, Figure 12 reveals the \begin{table}
\begin{tabular}{c c c c} \hline  & & \multicolumn{2}{c}{**Actual Values**} \\ \cline{3-4}  & & **Positives** & **Negatives** \\ \hline \multirow{2}{*}{Predictive values} & \multirow{2}{*}{Positives} & True Positives & False Positives \\  & & (TP) & (FP) \\ \cline{2-4}  & &
\begin{tabular}{c} \end{tabular} & True Negatives \\ \hline \multirow{2}{*}{Predictive values} & \multirow{2}{*}{Negatives} & False Negatives & True Negatives \\  & & (FN) & (TN) \\ \hline \end{tabular}
\end{table} 
Table 2: Confusion matrix for classification. Figure 11: The used calibration process of the proposed wearable gaze tracker. corresponding trajectory diagram of tracking four markers' center points with the outward image for calibration. In Figure 12, the yellow line indicates the sequence of the movement path of gazing the markers, and the red rectangle indicates the range of the eye movement. In Figure 13, when the calibration process is executed, the user gazes at the four markers sequentially from ID 1, ID 2, ID 3, to ID 4, and the system records the coordinates of the pupil movement path while watching the gazing coordinates of the outward scene with markers. Then, the proposed system performs the coordinate conversion to achieve the calibration effect. The pseudo-affine transform is used for the coordinate conversion between the pupil and the outward scene. The equation of the pseudo-affine conversion is expressed as follows:  
\[\left[ \begin{array}{c}X\\ Y\end{array} \right]\ =\ \left[ \begin{array}{ccc}a_{1}&a_{2}&a_{3}&a_{4}\\ a_{5}&a_{6}&a_{7}&a_{8}\end{array} \right]\left[ \begin{array}{c}X_{p}\\ Y_{p}\\ X_{p}Y_{p}\\ 1\end{array} \right], \tag{3}\]  
where \((X,Y)\) is the outward coordinate of the markers' center point coordinate system, and \((X_{p},Y_{p})\) is the nearfield eye coordinates of the pupils' center point coordinate system. In (3), the unknown transformation coefficients of \(a_{1}\)-\(a_{8}\) need to be solved by the coordinate values computed and estimated from \((X,Y)\) and \((X_{p},Y_{p})\). In order to carry out the calculation of the transformation parameters of \(a_{1}\)-\(a_{8}\) for calibration, Equation (4) describes the pseudo-affine transformation with four-points calibration, which is used to solve the transformation  
Figure 12: Diagram of tracking pupil’s center with the nearfield eye camera for calibration. Figure 13: Diagram of tracking four markers’ center points with the outward camera for calibration 1 When the user gazes at the marker ID1 for calibration. 2 When the user gazes at the marker ID2 for calibration. 3 When the user gazes at the marker ID3 for calibration. 4 When the user gazes at the marker ID4 for calibration. coefficients of the coordinate conversion. The equation of the pseudo-affine conversion with four-point calibration is expressed as follows:  
\[\left[