## 2 Experiment 1
### Results and Discussion
#### 2.2.2 Psychological Scale Fitting  
In order to accurately compare the gloss perception differences between real and virtual materials, it is necessary to obtain the mathematical expressions of the gloss psychometric scales in both environments. Therefore, linear regression is executed using the analysis data based on MLDS. The fitting results of the real group are presented in Figure 4a. In the low-gloss area (between approximately 0 and 30 GU), the slope of the psychometric scale is initially large and gradually tends to ease. Subjects are able to perceive large areas covered by highlights in the mirror reflection direction when observing stimuli in this range. At this stage, subjects rely solely on judging the glossiness based on the brightness of highlights. It is noteworthy that surfaces with higher glossiness are characterized by a higher overall brightness. In the intermediate range from 30 GU to 65 GU, the perceived glossiness changes of the subjects appear to be more linear, increasing at a constant and low slope. This stage can be regarded as a transition between the two nonlinear change areas at both ends. The basis for the subjects to judge the glossiness changes from the overall brightness of the material surface in the mirror reflection direction to the clarity of the reflected image. Due to the mixed cue, it becomes difficult for observers to decide which type of visual information is more credible. Therefore, the weight distribution of each cue becomes relatively balanced in this area. In the high-gloss area (above 65 GU), the change in perceived glossiness begins to proceed in a nonlinear mode again. The material surface in this range of glossiness can already reflect clear images, and subjects pay more attention to judging the level of glossiness based on the clarity of reflected images or the sharpness of highlight edges. Figure 3: The results of the psychological scale were obtained by MLDS analysis. (**a**) The relationship between real-world glossiness and relative perceived glossiness. (**b**) The relationship between PBR smoothness parameters and relative perceived glossiness. The black dashed line in the figure is a reference, indicating the relative perception intensity that theoretically corresponds to no psychological perception influence. Figure 4b displays the fitting results of the Virtual group. There is a significant difference in the final form of the psychological scale between the virtual group and the real group, with the overall three-stage change observed in the Real group not appearing in the Virtual group. The change in relative perception glossiness of the Virtual group is very consistent from the beginning to the end, which is in contrast to the Real group. The linear regression equation for the Real group is presented in Equation (1), where x represents the real-world glossiness, and y represents the relative perception glossiness. The fitted model (\(p<2.2\times 10^{-16}\)) has very strong explanatory power for the original data (\(r^{2}=0.9619\)). The gray band-shaped area in the figure is a confidence interval with a confidence level of 99%. The overall change shows a very obvious three-stage growth, which is consistent with [PERSON] et al. 's [28] similar results. \[\text{y}=\frac{1}{10000}\Big{(}0.0235\text{x}^{3}-2.817\text{x}^{2}+184.027 \text{x}-977.183\Big{)}, \tag{1}\]  
The linear regression equation for the Virtual group is presented in Formula (2), where x represents the PBR smoothness value, and y represents the relative perception glossiness. The regression results (\(p<2.2\times 10^{-16}\)) also have a high degree of interpretability, with all fitted items showing a very high level of significance (\(r^{2}=0.9619\)). Based on Equation (2), it can be observed that as PBR smoothness increases, the impact of the cubic term with equal weight becomes more significant. On the other hand, the linear term only has a significant effect at very low gloss levels, indicating that it approximates linear changes only in the low glossiness area.