## 3 Optimizing Light Distributions  
In this section, the data acquired from the studies in all three papers in this series will be brought together to achieve a simple, optimized light distribution. As a starting point, \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Urban** & **Rural** & **Motorway** \\ \hline Median Horiz. & \(-0.83^{\circ}\) & \(-1.02^{\circ}\) & \(-2.31^{\circ}\) \\ \hline Std (\(\sigma\)) Horiz. & \(6.91^{\circ}\) & \(6.60^{\circ}\) & \(5.78^{\circ}\) \\ \hline Median Vert. & \(-0.81^{\circ}\) & \(-0.74^{\circ}\) & \(-0.28^{\circ}\) \\ \hline Std (\(\sigma\)) Vert. & \(2.74^{\circ}\) & \(2.70^{\circ}\) & \(2.90^{\circ}\) \\ \hline \(d_{med}\) & \(84.8\) m & \(92.9\) m & \(229.0\) m \\ \hline \(d_{med-\sigma}\) & \(19.4\) m & \(20.2\) m & \(21.6\) m \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Fixation data for the different road categories during nighttime driving. Figure 6: Fixation data while driving through curves with a radius between 150 m and 250 m. Data digitalized from Shibata[19] are marked by red crosses. In the false colour representation shown, the darker blues correspond to low fixation numbers, while the lighter yellows correspond to higher fixation numbers. the gaze data acquired in this part of the paper series are taken and compared to the object data from part two, _Analysis of Real-World Traffic Data in Germany_. The main concept is that areas that are shown to contain many \"important\" traffic objects, such as other cars, pedestrians, or cyclists, should receive a lot of \"attention\", which in this study is represented by fixations. Areas in which no such objects appear do not require fixations from the driver. To make the comparison, the normalized mean fixation distribution is subtracted from the normalized mean object distribution. With both distributions being normalized to their corresponding maximum, both data matrices have a minimum value of 0 and a maximum value of 1, meaning that the resulting modification matrix (Figure 7) has a minimum of \(-1\) for areas where only gazes but no objects were detected, 0 where equal amounts of objects and gazes were measured, and +1 where only objects and no fixations were found. This is visualized in Figure 7. Orange and yellow areas mark those areas in which more objects than fixations are recorded (positive values). Green areas show those parts in which roughly equal amounts of fixations and objects are found (values around 0) and blue areas show the parts in which more fixations than objects are detected (negative values). For the next step, the base light distribution from part one, _Idealized Baseline Headlight Distribution_, shown in Figure 8, is taken into account as well. As described in part one of this series, this headlight distribution was determined from detection tests under different horizontal angles under ideal conditions for the driver, including a completely straight road, no other traffic participants, no other lighting than the vehicle's headlights, and only one detection object that was placed along different detection angles. Multiplying the matrices represented by Figures 7 and 8, results in a matrix that takes the baseline light that is required to detect objects under certain angles and modifies it according to the frequency of both fixations and objects found in real-life traffic. Since the resulting light distribution, as evident from Figure 7, is not going to be symmetrical and will have some hotspots, the result will be mirrored and smoothed in both the vertical and horizontal directions by a moving mean smoothing filter over 10 values corresponding to 0.1\({}^{\circ}\) in order to generate a light distribution that fits for right-hand traffic as well as for left-hand traffic. The result of this is displayed in Figure 9.  
Figure 8: Baseline headlight distribution used as a starting point for the optimization of the headlight distribution in the present study.