# Characterization of Driver Dynamic Visual Perception Under Different Road Linearity Conditions
## 4 Model Construction
### Modeling of Pupil Diameter over Time at Different Road Sections  
The trend of pupil diameter change over time and the fitted curves of drivers in different driving scenarios (straight ahead, turning, climbing, downhill) are shown in Figure 7, which clearly reflect the influence of the complexity of the driving task on the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Section of Road** & **Average Fixation Duration Model** & \(\mathbf{R^{2}}\) \\ \hline Straight Movement & \(y=1.62437\times 10^{-5}\mathrm{t}^{3}-0.00204\mathrm{t}^{2}+0.0772\mathrm{t}+0.46727\) & 0.843 \\ Turn & \(y=6.0543\times 10^{-6}\mathrm{t}^{3}-7.72704\times 10^{-4}\mathrm{t}^{2}+0.02957 \mathrm{t}+0.12151\) & 0.701 \\ Climbing & \(y=2.43225\times 10^{-6}\mathrm{t}^{3}-2.98094\times 10^{-4}\mathrm{t}^{2}+0.01557 \mathrm{t}+0.47329\) & 0.815 \\ Downhill & \(y=9.01659\times 10^{-6}\mathrm{t}^{3}-0.00112\times 10^{-4}\mathrm{t}^{2}+0.04226 \mathrm{t}+0.23338\) & 0.731 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Model of changes in average fixation duration under different road segments. driver's cognitive load. The fitted model showed better fitting results. The specific fitting parameters are shown in Table 4. The models for the number of fixations under different road sections and their fitting results are listed in Table 4.  
For the straight road section, the fitting model is:  
\[\mathrm{y}=1.35886\times 10^{-5}\mathrm{t}^{3}-0.00168\mathrm{t}^{2}+0.06018 \mathrm{t}+2.3468 \tag{5}\]  
The R\({}^{2}\) value of this model is 0.813, indicating that the model fitted the data well. The fitted curve for the straight ahead section was smooth, with a smoother change in pupil diameter. This indicated that, in straight driving, the driver's cognitive load was low, and the driving task was mainly focused on lane keeping, with relatively little attention demand and low environmental complexity. As a result, the pupil diameter changed more slowly and remains in a relatively stable range. For the turning section, the fitting model is:  
\[\mathrm{y}=2.67826\times 10^{-5}\mathrm{t}^{3}-0.00326\mathrm{t}^{2}+0.11417 \mathrm{t}+3.71775 \tag{6}\]  
The R\({}^{2}\) value of this model was 0.772, and the relatively low fitting effect indicated that the pupil diameter fluctuates more in the turning scene and the accuracy of the fitted model was low. At the beginning of the turn, the pupil diameter rose rapidly, which indicated that the driver's cognitive load increased significantly when facing the tasks of path selection,  
Figure 7: Model of pupil diameter under different road sections: (**a**) straight ahead; (**b**) turning; (**c**) climbing; (**d**) downhill. speed control, and environment judgment. With the completion of the turning task, the cognitive load gradually decreased and the pupil diameter gradually stabilized. For the climbing section, the fitting model is:  
\[\mathrm{y}=5.1995\times 10^{-6}\mathrm{t}^{3}-6.16309\times 10^{-4}\mathrm{t}^{2}+ 0.02224\mathrm{t}+3.235289 \tag{7}\]  
The R\({}^{2}\) value of the model was 0.794, which indicated a better fitting effect for the climbing section. When going uphill, the pupil diameter rose slowly, which reflected the driver's high demand for power control and speed adjustment at the beginning of the ramp. As the driver gradually adapted to the on-ramp environment, the cognitive load decreased and the pupil diameter stabilizes. For the downhill section, the fitting model is:  
\[\mathrm{y}=1.8722\times 10^{-7}\mathrm{t}^{3}-4.36681\times 10^{-4}\mathrm{t}^{2 }+0.028\mathrm{t}+3.56532 \tag{8}\]  
The R\({}^{2}\) value of the model was 0.753, and the relatively low fitting effect reflected the high volatility of the data in the downhill section, which lead to the poor accuracy of the model.