# Exploring Deep Neural Networks in Simulating Human Vision through Five Optical Illusions
## 2 Materials and Methods
### Optical Illusions  
Optical illusions are a key research topic in the field of visual perception, helping us understand the workings and limitations of the human visual system. In this study, to broaden the spectrum of investigated phenomena and contribute to a more comprehensive understanding of visual illusions, we employed five classic visual illusions: color assimilation, the Hermann grid illusion, the Muller-Lyer illusion, the Zollner illusion, and the Poggendorff illusion (Figure 2). The color assimilation illusion, as shown in Figure 2A, showcases the influence of adjacent colors on our visual perception. This phenomenon is exemplified by the appearance of squares in three distinct hues against a striped background. Conversely, the Hermann grid illusion, presented in Figure 2B, features a grid pattern interspersed with white dots. At the grid intersections, ephemeral dots emerge, unveiling our visual system's approach to light contrast and edge delineation. The Muller-Lyer illusion (Figure 2C) employs lines terminated by differing arrow configurations to illustrate the impact of contextual indicators on length perception, whereby the inclusion of varied arrows modifies the perceived length of a line. Similarly, the Zollner illusion (Figure 2D) induces a perception of misalignment in lines obscured by rectangles, underscoring our visual system's challenges in discerning line orientation and parallelism. The Poggendorff illusion (Figure 2E), meanwhile, engenders a distorted perception of line angles contingent on arrow placement, shedding light on our visual processing of spatial positioning and alignment. By studying these illusions, we can gain a deeper understanding of the mechanisms of human visual perception and its similarities and differences with DNNs, especially in terms of color, brightness contrast, size, and spatial relationship processing. Based on the variable factors of these five visual illusions, we set the parameters for each (Figure 2, Table 1). For color assimilation, we used 12 colors based on the RGB color wheel, with backgrounds of alternating black, gray, and white stripes which generate three hues of original color(three different depths) for the square colors, totaling 36 stimuli. In the Hermann grid illusion, we set five sizes of white dots (6-10) and five grayscale levels (\(\mu\) = 1-5) from white to black, and four grid colors (red, green, blue, gray), totaling 100 stimuli. For the Muller-Lyer illusion, we set lines of 200 to 380 pixels (20 increments) with matching inward and outward arrows, totaling 20 stimuli. The Zollner illusion had seven rectangle widths (120-240, interval = 20) and five angles (15\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), 60\({}^{\circ}\), 75\({}^{\circ}\)), totaling 35 stimuli. In the Poggendorff illusion, we set six angles (30\({}^{\circ}\), 40\({}^{\circ}\), 45\({}^{\circ}\), 55\({}^{\circ}\), 60\({}^{\circ}\), 75\({}^{\circ}\)), three arrow spacings (15, 25, 35), and line positions in three areas (\(\frac{1}{3}\), \(\frac{1}{2}\), \(\frac{2}{3}\)) (Figure 2E), totaling 54 stimuli. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Illusion** & **Independent Variable** & **Perception** & **Total** \\ \hline Color Assimilation & Color(12)/Depth(3) & Ranking & 36 \\ Hermann-grid illusion & Color(4)/Dot\_size(5)/Gradient\_depth(5) & Option & 100 \\ Müller-Lyer illusion & Line\_length(10) & Adjustment & 20 \\ Zöllner illusion & Angle(5)/Rectangle\_width(7) & Adjustment & 35 \\ Poggendorff illusion & Angle(6)/Arrow\_space(3)/Position(3) & Adjustment & 54 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The setting of the illusion’s experiment  
Figure 2: Experiments with human subjects based on 5 geometric visual illusions. (**A**) Color assimilation: 12 colored squares in alternating black, gray, and white striped backgrounds, divided into 3 depths. The task is to rank the similarity in color between the 3 depths and the square. (**B**) Hermann grid: Flickering dot illusion with a black background and grid.