# Exploring Deep Neural Networks in Simulating Human Vision through Five Optical Illusions
## 3 Results
### Hermann Grid Illusion  
The strength of the Hermann grid illusion is categorized into three clarity levels: clear, weak, and none. The illusion is associated with four colors, as well as five point sizes and five color gradient depths (ranging from white to black). The gradient depth is denoted from \(\mu(1)\) to \(\mu(5)\) to show the depth of the color of the point. \(\mu(1)\) is white and \(\mu(5)\) is black. As shown in Figure 7A, the results indicate that the perception of flickering dots is the most intense within the white gradient depths from \(\mu(1)\) to \(\mu(3)\). Flickering dots are perceived at the \(\mu(1)\) depth in all four colors. As gradient intensity increases, the perception of flickering dots gradually weakens, with green grids showing the most significant perception from  
Figure 6: Class activation heatmaps of 12 DNNs for 3 depths of green. Each model corresponds to Grad-CAM/Grad-CAM++ and their guided backpropagation, with red class activation heatmaps provided in Figure A1. \(\mu(1)\) to \(\mu(3)\). Additionally, an increase in the dot size also leads to a weaker perception of flickering dots. Participants report that the perception of \"Weak\" flickering dots resembles that of gray dots, but less clear than the \"Clear\" level. Figure 7: Behavioral data distribution of the Hermann grid, perceptual testing in DNNs. (**A**) Distribution of the intensity of flickering dots in the Hermann grid for different colors as perceived by subjects. (**B**) Representational similarity changes in the model for the Hermann grid based on \(\mu(1)\)/Dot_size(6), under different grid colors and gradient depth changes. Subsequently, 12 deep neural networks (DNNs) processed these four colors of grid images, and experiments were conducted. Using the \(\mu\)(1) depth (dot size 6) of the four colors as a baseline, the L2 distance of feature vectors was calculated for other gradient depths and dot size combinations of the same color compared to the baseline. As illustrated in Figure 7B, all 12 models initially showed an upward trend as the gradient intensified from white to black. However, a downward trend subsequently appeared in gray grids across all models. Generally, as gradient depth increased and white transitioned to black, the similarity decreased, i.e., L2 distance increased, usually in a monotonic presentation. However, it was observed that the trend was not unidirectional (only increasing or decreasing) but exhibited a more complex pattern with increasing gradient depth. The downward trend suggests that the models might have made judgments similar to flickering dots, and the slope of the decline could reflect the perception intensity of flickering dots. It is evident from the graph that the flickering dot perception was most pronounced in gray grids, while green and red grids (to a lesser extent) also showed similar perceptions. In contrast, blue grids showed almost no perception of flickering dots. Specifically, Inception_v4 displayed a decreasing and then increasing trend in green grids, possibly indicating a judgment similar to \"Clear\" but weaker than black flickering dots. A similar trend was also observed in the gray grids of DenseNet121 [31] (dot sizes 7 and 8) and ResNetv2_101. Under different dot sizes, the trend showed a positive correlation; the larger the dot size, the weaker the perception of flickering dots. Overall, the 12 models exhibited diverse perceptions of flickering dots in the four colors of grids, with most models showing weaker perception (lower slope). In the DenseNet series, flickering dot perception in gray, red, and green grids was more marked. We then developed a representational dissimilarity matrix (RDM) for each color grid, as depicted in Figures 8A and A2-A4, following the [PERSON] method (2013) [25]. Analysis of these RDMs revealed structural similarities across the four color grids, with distinct variations in representational similarity across different gradient depths.