Similar Symmetries and the Effect of Scale

• Main Authors: A D F Clarke, P R Green, M J Chantler
• Format: Article
• Language: English
• Published: SAGE Publishing 2011-04-01
• Series: i-Perception
• Online Access: https://doi.org/10.1068/i196

Tilings and symmetries are striking visual properties that have been used decoratively around the world throughout human history. Tiled patterns can be mathematically classified into 1 of 17 different wallpaper groups, and while computational models have been developed which can extract an image's symmetry group, very little work has been done on how humans perceive these patterns. We will give an overview of the results from two experiments which investigate the role wallpaper groups of two-dimensional patterns have on their perceived similarity. The first experiment involved participants grouping a set of 85 tiled patterns into subsets based on perceptual similarity. We find that patterns with the same wallpaper group are classified as similar more frequently than would be expected by chance and patterns with similar numbers of symmetries are viewed as similar. However, a simple linear-regression model fails to account for most of the variance. The second experiment looks at the interaction between scale (tile size) and wallpaper group and how they influence perceptual similarity. The empirical data are then compared with a computational model.