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Symmetry 2011, 3(2), 246-264; doi:10.3390/sym3020246

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

1
School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland, UK
2
School of Life Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland, UK
*
Author to whom correspondence should be addressed.
Received: 1 March 2011 / Revised: 15 April 2011 / Accepted: 19 May 2011 / Published: 25 May 2011
(This article belongs to the Special Issue Symmetry Processing in Perception and Art)
Download PDF [6643 KB, 26 May 2011; original version 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 wallpaper groups; texture similarity; pattern recognition; texture classification
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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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.

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