Human Visual Perception of Two-Dimensional Symmetry

Most literature on symmetry perception has focused on bilateralreflection symmetry with some suggesting that it isthe only type of symmetry humans can perceive (Wilson &Wilkinson, 2002). Using image stimuli generated from themathematically well-defined seventeen wallpaper groups, thisstudy demonstrates that humans can discriminate various symmetriesfound in 2D wallpaper patterns (Liu, Hel-Or, Kaplan,Van Gool, et al., 2010). Furthermore, the results demonstratethe features which contribute to wallpaper pattern perception.All wallpaper groups but one were found to be reliably distinguishable(p < 0:05). Additionally, as wallpaper patterns canbe arranged in a hierarchy, we propose a metric to quantify thesimilarity of their perception using the shortest path in this hierarchy.This subgroup distance was found to be a factor in alikely model of pattern perception.