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Similar Symmetries: The Role of Wallpaper Groups in Perceptual Texture Similarity
School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland, UK
School of Life Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland, UK
* Author to whom correspondence should be addressed.
Received: 1 March 2011; in revised form: 15 April 2011 / Accepted: 19 May 2011 / Published: 25 May 2011
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.
Keywords: wallpaper groups; texture similarity; pattern recognition; texture classification
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MDPI and ACS Style
Clarke, A.D.F.; Green, P.R.; Halley, F.; Chantler, M.J. Similar Symmetries: The Role of Wallpaper Groups in Perceptual Texture Similarity. Symmetry 2011, 3, 246-264.
Clarke ADF, Green PR, Halley F, Chantler MJ. Similar Symmetries: The Role of Wallpaper Groups in Perceptual Texture Similarity. Symmetry. 2011; 3(2):246-264.
Clarke, Alasdair D. F.; Green, Patrick R.; Halley, Fraser; Chantler, Mike J. 2011. "Similar Symmetries: The Role of Wallpaper Groups in Perceptual Texture Similarity." Symmetry 3, no. 2: 246-264.