# Exploring Deep Neural Networks in Simulating Human Vision through Five Optical Illusions
## 3 Results
### Muller-Lyer Illusion  
After collecting data on participants' perceived lengths of lines in the Muller-Lyer illusion [35], we quantified the degree of visual illusion, which is the difference between the perceived length and the actual length. As shown in Figure 10A, significant differences in the degree of visual illusion were observed between inward-pointing arrows (represented by light green bar graphs) and outward-pointing arrows (represented by pink bar graphs) under different length standards. Specifically, the visual illusion caused by outward-pointing arrows was positive, whereas that by inward-pointing arrows was negative. This means that visually, lines with outward-pointing arrows seemed shorter than their actual length, while lines with inward-pointing arrows appeared longer. In other words, to visually match the actual length standard, lines with outward-pointing arrows needed to be adjusted longer than their actual length, and those with inward-pointing arrows shorter.  
We calculated the Euclidean distance between the feature vectors of the perceived lines of inward and outward-pointing arrows after adjustment by users and constructed a representational dissimilarity matrix (RDM) [25], as shown in Figure 11A. The horizontal axis of the RDM represents lines with outward-pointing arrows, and the vertical axis represents lines with inward-pointing arrows. All lines correspond to the average perceived lengths after adjustment, meaning the perceived lengths visually equaled the actual lengths. The results showed that DenseNet169/201, VGG16/19 exhibited high similarity at the diagonal, indicating these networks' highly similar representations of perceived lines with inward and outward-pointing arrows, reflecting a human-like performance in the visual illusion of length variation. In Figure 11B, a control group was similarly set up, with the axes still representing lines with outward- and inward-pointing arrows. However, here, the line lengths corresponded to actual length labels, e.g., a length label of 200 indicating an actual length of 200. Interestingly, apart from ResNetv2_50, other networks that showed human-like visual illusions exhibited shifts above the diagonal. This indicates that even with lines of the same length, the addition of opposite arrows led the models to make different length judgments, i.e., produce visual illusions. This further confirms the human-like perception performance of the models at the diagonal in Figure 11A. Under variations in network depth (Figure 10C), the perceived lines matched the actual lengths of the control group (right side), generally maintaining a similar trend, further indicating the models' human-like perception in visual illusions.  
When applying the visual CAM method [26; 27], models that exhibited visual illusions were observed in Grad-CAM and Grad-CAM++ to focus on features of both the line itself and the arrows (Figure 10B). The focus was mainly on the overall or partial features of the arrows and the line, with some attention to the line in the middle area. In contrast, models that did not exhibit visual illusions mostly focused only on the arrows or the line and the overall features of the image. This difference indicates the cause of the models' perception of the Muller-Lyer illusion.