## 1 Introduction
In the aspect of visibility, the observers suggested that various colors or large-sized images could provide good visibility of HUD images. Their study also revealed a trade-off between visibility and visual clutter [13]. [PERSON] et al. discussed the key factors and methods of ergonomic design for HUDs. Their research recommended that visual comfort, information color, character font, font size, brightness, and contrast should be well considered to improve the visual effect of the display and ensure safe driving [14]. [PERSON] found that the human-technology interaction of HUDs can be optimized by applying the correct enhancement-contrast ratios to minimize visual distraction from visual saliency [15]. [PERSON] et al. indicated that the projected information on the HUD might interfere with the colors in the background, such as in a lower contrast condition. Therefore, they proposed a saliency method to evaluate the mutual effect of HUDs on various backgrounds. Additionally, it is better to avoid assigning a red color to emergency information on HUDs in vehicles due to the reduction of saliency [16]. [PERSON] analyzed the effects of HUD on the human visual system, including color vision deficiency and background illumination. His opinion pointed out that light colors and highly saturated colors might become confused with the translucent driving data and affect data perception [17]. [PERSON] et al. utilized an AR HUD to investigate the influence of HUD visualizations on drivers' situation awareness and perceptions. The results showed that situation awareness would reduce with increasing driving context complexity [18]. [PERSON] et al. measured two kinds of optical see-through head-mounted displays under various lighting conditions ranging from 0 to 20,000 lx and calculated the contrast ratios between rendered black (transparent) and white imagery to investigate the influence of environmental lighting on the user. Their results suggested that the optical see-through head-mounted displays needed further improvement for contrast when used in environments with higher illuminance levels [19]. [PERSON] et al. proposed a gamma-curve-basedvirtual image-boosting method with a measurement model to solve background color blending. Their model could determine the appropriate gamma value for virtual image boosting to improve image quality [20]. [PERSON] et al. carried out a color-matching experiment with background-correlated color temperature (CCT), luminance levels, and two stimulus types to investigate the impact of background CCT on AR color appearance. They found that the matched colors in AR would shift towards the background when the background color was inconsistent with the stimulus. In addition, the study recommended that perceptual weighting on the foreground and background in the additive function be modified to accurately predict the appearance [21]. [PERSON] et al. explored the color appearance in a color-matching experiment with combinations of mixed foreground and background colors and tested the applicability of the CAM16 color appearance model in an AR environment. From their results, the prediction of CAM16 was not ideal, and they suggested it should be improved by modifying it with the addition of chromatic simultaneous contrast to produce a better result [22]. [PERSON] and [PERSON] investigate the preferred tone curves and background lighting geometries of a see-through head-mounted LCD with five psychophysical experiments. They suggested both brightness and contrast should be heightened accordingly to increase the image quality of a see-through head-mounted LCD [23]. Although some related works focused on improving visibility [24], studying the characteristics [25], and finding the preferences of the tone reproduction curve [26] for transparent LCD and OLED under various ambient lighting conditions, there were still a few studies that aimed for a HUD, whose display theory and application were slightly different from those devices.