## 2 Materials and Methods
### Static and Dynamic Analysis of Gaze  
As shown in Figure 5, a static analysis was carried out based on visual properties, such as gaze fixation duration, dwell time, and the number of fixations. Fixation duration means the time required for a driver to gaze at each object and assess the situations while driving. For instance, Figure 5a suggests that a driver held his or her gaze at the traffic lights for three seconds on the vehicle. Figure 5b indicates the sum of fixation duration of each object which was used to analyze the dispersion and density of the drivers' gaze. Figure 5c demonstrates the number of fixations, which means how many times a driver gazed at a certain object, translating into the frequency of checks in its status.  
In addition, SGE, the quantity of information generated from the driver's gaze dispersed across AOIs while driving, was calculated to estimate the amount of information to initiate a visual search. Here, as SGE signified the probability distribution of an object  
Figure 4: Display by scenario shown to the participants. (**a**) navigation system; (**b**) intersection; (**c**) navigation system; (**d**) sudden brake; (**e**) intersection.  
Figure 5: The visual properties for static analysis. (**a**) fixation duration; (**b**) dwell time; (**c**) Number of fixation.  
that the driver observed while driving or of the one that was overlooked, gaze dispersion across the whole areas can be quantified using Shannon's Entropy, which is expressed by Equation (1) [32].  
\[\text{SGE}\ =\ -\sum_{i=1}^{n}(p_{i})\text{log}\ _{2}(p_{i}) \tag{1}\]  
Here, \(p_{i}\) refers to the probability of gaze at AOIs for the \(i\)th time, and in case the driver focused only on a certain object, it led to a low probability distribution, resulting in a low entropy value. This is because their gaze density was measured higher than that of the other drivers who inspected all the objects involved [33]. In other words, the higher the entropy value of a driver was, the more evenly were distributed their gaze points in visual search, signaling lesser dispersion. As mentioned before, a static analysis did not reflect the visual search patterns that could indicate how the driver controls the vehicle and assesses the situations by continuously shifting or moving their gaze while driving on a road. Therefore, we also carried out GTE, which is a dynamic analysis on gaze, to quantify the dependency of objects that exist subsequently to the object that the driver's gaze is currently on [34]. Here, GTE refers to an indicator of complexity of a gaze transition pattern with a transition matrix based on the conditional probability of shifting the gaze from one location to the next, as expressed by Equation (2) [35].  
\[\text{GTE}\ =\ -\sum_{i=1}^{n}\ p_{i}\ \sum_{i,j=1}^{n}(p_{i,j})\text{log}\ _{2}(p_{i,j})\ \ \ \ \ \ \left\{\begin{array}{ccc}i,\ j&=&1,\,2,\,3,\,\cdots n\\ &i\
eq j\end{array}\right. \tag{2}\]  
GTE literally means the transition entropy of a driver's gaze, \(i\) signifies an AOI that the driver looks at first, and \(j\) refers to an AOI that is currently observed. A higher GTE makes it more difficult to predict precisely where the eyes are looking as the sequence of gaze shifts was not predefined. For instance, at a place where there are many stimuli involved, such as intersection, drivers may engage in a visual search in a more complicated pattern than they do on an ordinary road to avoid any collision, possibly resulting in a higher GTE [36]. In this case, the search pattern of the generated gaze may differ depending upon the driving experience, and the difference between the groups according to driving experience was analyzed using \(t\)-test (\(\alpha=0.05\)).