Similar Symmetries: The Role of Wallpaper Groups in Perceptual Texture Similarity

Alasdair D F Clarke,Fraser Halley,Patrick R Green,Mike J Chantler

doi:10.3390/sym3020246

Abstract

Periodic patterns and symmetries are striking visual properties that have been used decoratively around the world throughout human history. Periodic patterns can be mathematically classified into one 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. This study presents the results from a grouping experiment using stimuli from the different wallpaper groups. We find that while different images from the same wallpaper group are perceived as similar to one another, not all groups have the same degree of self-similarity. The similarity relationships between wallpaper groups appear to be dominated by rotations.

Highlights

IntroductionSymmetry and tilings have been used in art and architecture throughout human history [13]
Symmetry and tilings have been used in art and architecture throughout human history [13].Two-dimensional periodic patterns can be classied into 17 different wallpaper groups based on the Euclidean plane isometries that they possess
The aim of this study was to investigate the effect of symmetry on texture similarity judgements

Summary

Introduction

Symmetry and tilings have been used in art and architecture throughout human history [13]. Two-dimensional periodic patterns can be classied into 17 different wallpaper groups based on the Euclidean plane isometries (translations, reections, rotations and glides) that they possess. Moorish and Egyptian architecture (see Figure 1) and the art of M. The Alhambra palace contains examples of most, if not all, of the wallpaper groups [4,5]

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