# Exploring Deep Neural Networks in Simulating Human Vision through Five Optical Illusions
## 3 Results
### Hermann Grid Illusion
Specifically, within the gray grid's RDM, we identified distinct rectangular areas showing heightened similarity at intermediate gradient depths, notably between \(\mu\)(3) and \(\mu\)(4). This pattern suggests that these gradient depths may trigger a flickering dot perception in the models. Interestingly, as representational similarity increased between \(\mu\)(4) and \(\mu\)(5), the models' flickering dot perception appeared to diminish, indicating a nuanced shift in perception with changing gradient conditions. For the blue grid, a high level of representational similarity was observed at shallower gradient depths, which might account for the reduced presence of flickering dots. Conversely, the other color grids exhibited fewer high-similarity areas at the shallowest gradients, \(\mu\)(1) and \(\mu\)(2). Specifically, models from the AlexNet [7] and VGG series [8] demonstrated increased similarity in the lower right corner of their RDMs, suggesting a potential decrease in sensitivity to color grid variations. Meanwhile, models from the DenseNet series [31] showed distinct low similarity regions in the lower left and upper right corners of the gray grid's RDM, indicating a more nuanced and differentiated processing of color grids across gradient depths. In Figure 8B, the feature tendencies of different models when processing Hermann grid illusion images are displayed [26; 27]. Through Grad-CAM analysis, it was found that VGG series models mainly focus on each intersection of the grid image, while models performing better in flickering dot perception, such as the DenseNet and Inception series, tend to focus more on the edges of the grid and show weaker feature preferences for the middle dots. In contrast, the AlexNet model's focal points are concentrated on the fence-like structures formed between the dots. When analyzed with Grad-CAM++, models that effectively identified flickering dots tended to focus on features of squares and intersections inside the grid, while those with weaker or no clear performance in perceiving flickering dots showed almost no significant changes. Subsequently, tests were conducted on the performance of flickering dot perception at different network depths, as shown in Figure 9. Using the image of \(\mu\)(1) depth with dot size 6 as a baseline, the impact of dot size changes at different network depths on L2 distance was calculated. The graph shows that--at the same network depth--changes in dot size had almost no effect on L2 distance. However, as network depth increased, the non-monotonic change trend became more pronounced in deeper networks, possibly reflecting a significance in processing similar to human perception of flickering dots at deeper network levels. Figure 8: RDMs of DNNs under different colored grids, class activation heatmap for the gray grid. **(A)** Horizontal and vertical axes represent four grid colors, each corresponding to a combination of dot size and gradient depth. Darker colors indicate higher representational similarity. **(B)** Class activation heatmap for gray, the most prominent color for flickering dots in DNNs. Class activation heatmaps for the other three colors are in Figures A2–A4. Figure 9: Perceptual performance of flickering dots at different network depths in DNNs.