{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T18:14:07Z","timestamp":1760984047011,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2011,5,25]],"date-time":"2011-05-25T00:00:00Z","timestamp":1306281600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.3390\/sym3020246","type":"journal-article","created":{"date-parts":[[2011,5,25]],"date-time":"2011-05-25T11:12:20Z","timestamp":1306321940000},"page":"246-264","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Similar Symmetries: The Role of Wallpaper Groups in Perceptual Texture Similarity"],"prefix":"10.3390","volume":"3","author":[{"given":"Alasdair D. F.","family":"Clarke","sequence":"first","affiliation":[{"name":"School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland, UK"}]},{"given":"Patrick R.","family":"Green","sequence":"additional","affiliation":[{"name":"School of Life Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland, UK"}]},{"given":"Fraser","family":"Halley","sequence":"additional","affiliation":[{"name":"School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland, UK"}]},{"given":"Mike J.","family":"Chantler","sequence":"additional","affiliation":[{"name":"School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, EH14 4AS, Scotland, UK"}]}],"member":"1968","published-online":{"date-parts":[[2011,5,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Abas, S.J., and Salman, A.S. (1994). Symmetries of Islamic Geometrical Patterns, World Scientific Publishing Company.","DOI":"10.1142\/9789814335942"},{"key":"ref_2","unstructured":"Rnning, F. (2011, May 23). Geometry and Islamic Patterns. Available online: http:\/\/people.exeter.ac.uk\/PErnest\/ pome24\/index.htm."},{"key":"ref_3","unstructured":"Tyler, C.W. (2011, May 23). The human expression of symmetry: Art and neuroscience. Available online: http:\/\/www.ski.org\/CWTyler_lab\/CWTyler\/Art%20Investigations\/Symmetry\/Symmetry.html."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"641","DOI":"10.1016\/0898-1221(86)90416-5","article-title":"Symmetry in moorish and other ornaments","volume":"12","author":"Grnbaum","year":"1986","journal-title":"Comput. Math. Appl."},{"key":"ref_5","first-page":"670","article-title":"What symmetry groups are present in the Alhambra?","volume":"53","author":"Grnbaum","year":"2010","journal-title":"Not. AMS"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1068\/p040239","article-title":"Violations of symmetry and repetition in visual patterns","volume":"4","author":"Bruce","year":"1975","journal-title":"Perception"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1037\/0096-1523.4.4.691","article-title":"Orientation and symmetry: Effects of multiple, rotational and near symmetries","volume":"4","author":"Palmer","year":"1978","journal-title":"J. Exp. Psychol. Hum. Percept. Perform."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1037\/0033-295X.103.3.429","article-title":"Goodness of visual regularities: A nontransformational approach","volume":"103","author":"Leeuwenberg","year":"1996","journal-title":"Psychol. Rev."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1510","DOI":"10.3390\/sym2031510","article-title":"Behind the looking-glass: A review on human symmetry perception","volume":"1","author":"Treder","year":"2010","journal-title":"Symmetry"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1727","DOI":"10.1098\/rspb.2003.2434","article-title":"A feature-based model of symmetry detection","volume":"270","author":"Scognamillo","year":"2003","journal-title":"Proc. Biol. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.actpsy.2007.10.001","article-title":"Using relational structure to detect symmetry: A Voronoi tessellation based model of symmetry perception","volume":"128","author":"Dry","year":"2007","journal-title":"Acta Psychol."},{"key":"ref_12","first-page":"1","article-title":"A biologically plausible model of human shape symmetry perception","volume":"10","author":"Poirier","year":"2010","journal-title":"J. Vis."},{"key":"ref_13","unstructured":"Fairchild, M.D. (2005). Color Appearance Models, Wiley-IS&T. [2nd ed.]."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1649","DOI":"10.1016\/0042-6989(95)00202-2","article-title":"Towards a texture naming system: Identifying relevant dimensions of texture","volume":"36","author":"Rao","year":"1996","journal-title":"Vis. Res."},{"key":"ref_15","first-page":"299","article-title":"Similarity and features of natural textures","volume":"25","author":"Heaps","year":"1999","journal-title":"J. Exp. Psychol: Hum. Percept. Perform."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1791","DOI":"10.1016\/j.visres.2008.05.015","article-title":"Perceived roughness of 1\/f\u03b2 surfaces","volume":"48","author":"Padilla","year":"2008","journal-title":"Vis. Res."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1232","DOI":"10.1364\/JOSAA.27.001232","article-title":"Measuring perceived differences in surface texture due to changes in higher order statistics","volume":"27","author":"Emrith","year":"2010","journal-title":"J. Opt. Soc. Am. A Opt. Image Sci. Vis."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"289","DOI":"10.3758\/CABN.3.4.289","article-title":"Descriptive and evaluative judgment processes: Behavioral and electrophysiological indices of processing symmetry and aesthetics","volume":"3","author":"Jacobsen","year":"2003","journal-title":"Cogn. Affect. Behav. Neurosci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/j.actpsy.2003.06.001","article-title":"Perceived complexity and the grouping effect in band patterns","volume":"114","author":"Strother","year":"2003","journal-title":"Acta Psychol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"354","DOI":"10.1109\/TPAMI.2004.1262332","article-title":"A computational model for periodic pattern perception based on frieze and wallpaper groups","volume":"26","author":"Liu","year":"2004","journal-title":"IEEE Trans. Pattern Anal. Mach. Int."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1007\/3-540-60268-2_300","article-title":"Pattern orientation and texture symmetry","volume":"970","author":"Chetverikov","year":"1995","journal-title":"Lect. Notes Comput. Sci."},{"key":"ref_22","unstructured":"Park, H., Martin, G.R., and Bhalerao, A.H. (October, January 16). Structural Texture Segmentation using Affine Symmetry. Proceedings of the International Conference on Image Processing, San Antonio, TX, USA."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Zwillinger, D. (2002). CRC Standard Mathematical Tables and Formulae, Chapman and Hall, CRC. [31st ed.].","DOI":"10.1201\/9781420035346"},{"key":"ref_24","unstructured":"We can also recommend the wikipedia page (http:\/\/en.wikipedia.org\/wiki\/Wallpaper_group) as an excellent resource for examples and an accessible introduction as to why there are only 17 unique wallpaper groups."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1080\/00029890.1978.11994612","article-title":"The plane symmetry groups: Their recognition and notation","volume":"85","author":"Schattschneider","year":"1978","journal-title":"Am. Math. Mon."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1068\/p270965","article-title":"Effects of pattern orientation and number of symmetry axes on the detection of mirror symmetry in dot and solid patterns","volume":"27","author":"Wenderoth","year":"1998","journal-title":"Perception"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/3\/2\/246\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:56:12Z","timestamp":1760219772000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/3\/2\/246"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,5,25]]},"references-count":26,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2011,6]]}},"alternative-id":["sym3020246"],"URL":"https:\/\/doi.org\/10.3390\/sym3020246","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2011,5,25]]}}}