# Exploring Deep Neural Networks in Simulating Human Vision through Five Optical Illusions
## 3 Results
### Poggendorff Illusion  
In the Poggendorff illusion [36] experiment, participants were asked to adjust the position of the lower line to visually align with the upper line, while observing different angles of the upper line and different widths of rectangular covering. The perceived position of each participant was recorded and averaged against the actual position. As shown in Figure 12A, the greater the angle between the upper line and the rectangular covering, the smaller the position deviation. As the width of the rectangular covering increases, the actual distance deviation at each angle fluctuates slightly, but the deviation at an angle of 15 degrees shows a more significant change. Overall, participants tend to adjust the line to the left to achieve visual alignment of the line. Figure 10: Distribution of perceived length in the Müller-Lyer illusion, class activation heatmap for perceived length testing, L2 distance changes at different network depths. (**A**) The difference between perceived length and actual label length as observed by subjects. Pink represents arrows pointing outward; light green denotes inward. The vertical axis shows the average actual difference. (**B**) Class activation heatmap of straight lines with inward and outward arrows under perceived length groups in DNNs. (**C**) The left graph shows representational similarity changes between perceived length groups and actual length groups at different depths in DNNs; the right graph denotes the control group. Based on the average deviation values of the position, we regarded them as the perceived images after user adjustment. Then we extracted feature vectors between the actual position images of the true lines and perceived images in the last convolutional layer of the 12 models, calculating Euclidean distances to construct a representational dissimilarity matrix (RDM) [25], as shown in Figure 12C. Surprisingly, all models showed high similarity along the diagonal. The difference was that each model's RDM near the diagonal presented multiple parallel lines of high similarity. Combined with the visualization heatmaps based on the CAM method (Figure 13) [26; 27], the VGG series and AlexNet all showed feature tendencies towards the lines, as did Inception_v3 and ResNet152. Other models tended to focus on the rectangle or the overall image. Correspondingly, those models focusing on line features in the RDM showed multiple clear parallel lines of high similarity apart from the diagonal, with lower similarity in other areas. In contrast, models not particularly focusing on line features in the RDM presented multiple areas of high similarity, with weaker similarity outside the diagonal. Although the high similarity of all models along the diagonal indicates human-like judgments of visual illusions, these differences reflect whether the models truly focus on and understand the visual illusion phenomena in the images. Additionally, in the Euclidean distance analysis at different depths (Figure 12B), as network depth increased, deeper networks typically showed lower similarity values compared to shallower networks, possibly indicating a more complex mechanism of judgment of visual illusions at deeper levels of the models. Figure 11: Representational dissimilarity matrix of perceived length groups and control groups in DNNs. **(A)** The horizontal axis represents straight lines with outward arrows; the vertical axis represents inward arrows. All line lengths correspond to their respective average perceived lengths, darker colors indicate higher representational similarity. **(B)** The horizontal axis denotes outward arrow lines; the vertical axis denotes inward. All line lengths correspond to their actual length labels, darker colors indicate higher representational similarity. Figure 12: Distribution of perceived angles in the Poggendorff illusion, the response of DNNs to visual illusions at different network depths, and the representational dissimilarity matrix in DNNs.