Similar symmetries: The role of wallpaper groups in perceptual texture similarity

Symmetry

Volumn 3, Issue 2, 2011, Pages 246-264

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

^a HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

Pattern recognition; Texture classification; Texture similarity; Wallpaper groups

Indexed keywords

EID: 84860599810     PISSN: None     EISSN: 20738994     Source Type: Journal    
DOI: 10.3390/sym3020246     Document Type: Article

References (26)

1. Abas, S.J.; Salman, A.S. Symmetries of Islamic Geometrical Patterns; World Scientific Publishing Company: Toh Tuck Link, Singapore, 1994.
2. Rønning, F. Geometry and Islamic Patterns. Available online: http://people.exeter.ac.uk/PErnest/pome24/index.htm (accessed on 23 May 2011).
3. Tyler, C.W. The human expression of symmetry: Art and neuroscience. Available online: http://www.ski.org/CWTyler_lab/CWTyler/Art%20Investigations/Symmetry/Symmetry.html (accessed on 23 May 2011).
4. Grünbaum, B.; Grünbaum, Z.; Shephard, G.C. Symmetry in moorish and other ornaments. Comput. Math. Appl. 1986, 12, 641-653.
5. Grünbaum, B. What symmetry groups are present in the Alhambra? Not. AMS 2010, 53, 670-673.
6. Bruce, V.; Morgan, M. Violations of symmetry and repetition in visual patterns. Perception 1975, 4, 239-249.
7. Palmer, S.; Hemenway, K. Orientation and symmetry: Effects of multiple, rotational and near symmetries. J. Exp. Psychol. Hum. Percept. Perform. 1978, 4, 691-702.
8. van der Helm, P.; Leeuwenberg, E. Goodness of visual regularities: A nontransformational approach. Psychol. Rev. 1996, 103, 429-456.
9. Treder, M.S. Behind the looking-glass: A review on human symmetry perception. Symmetry 2010, 1, 1510-1543.
10. Scognamillo, R.; Rhodes, G.; Morrone, C.; Burr, D. A feature-based model of symmetry detection. Proc. Biol. Sci. 2003, 270, 1727-1733.
11. Dry, M.J. Using relational structure to detect symmetry: A Voronoi tessellation based model of symmetry perception. Acta Psychol. 2007, 128, 75-90.
12. Poirier, F.J.A.M.; Wilson, H.R. A biologically plausible model of human shape symmetry perception. J. Vis. 2010, 10, 1-16.
13. Fairchild, M.D. Color Appearance Models, 2nd ed.; Wiley-IS&T: Chichester, UK, 2005.
14. Rao, A.; Lohse, G. Towards a texture naming system: Identifying relevant dimensions of texture. Vis. Res. 1996, 36, 1649-1669.
15. Heaps, C.; Handel, S. Similarity and features of natural textures. J. Exp. Psychol: Hum. Percept. Perform. 1999, 25, 299-320.
16. β surfaces. Vis. Res. 2008, 48, 1791-1797.
17. Emrith, K.; Chantler, M.; Green, P.; Maloney, L.; Clarke, A. Measuring perceived differences in surface texture due to changes in higher order statistics. J. Opt. Soc. Am. A Opt. Image Sci. Vis. 2010, 27, 1232-1244.
18. Jacobsen, T.; Höfel, L. Descriptive and evaluative judgment processes: Behavioral and electrophysiological indices of processing symmetry and aesthetics. Cogn. Affect. Behav. Neurosci. 2003, 3, 289-299.
19. Strother, L.; M.Kubovy. Perceived complexity and the grouping effect in band patterns. Acta Psychol. 2003, 114, 229-244.
20. Liu, Y.; Collins, R.T.; Tsin, Y. A computational model for periodic pattern perception based on frieze and wallpaper groups. IEEE Trans. Pattern Anal. Mach. Int. 2004, 26, 354-371.
21. Chetverikov, D. Pattern orientation and texture symmetry. Lect. Notes Comput. Sci. 1995, 970, 222-229.
22. Park, H.; Martin, G.R.; Bhalerao, A.H. Structural Texture Segmentation using Affine Symmetry. In Proceedings of International Conference on Image Processing, San Antonio, TX, USA, September 16.October 19, 2011; pp. II-49-II-52.
23. Zwillinger, D. CRC Standard Mathematical Tables and Formulae, 31st ed.; Chapman and Hall, CRC: Boca Raton, FL, USA, 2002.
24. 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.
25. Schattschneider, D. The plane symmetry groups: Their recognition and notation. Am. Math. Mon. 1978, 85, 439-450.
26. Wenderoth, P.; Welsh, S. Effects of pattern orientation and number of symmetry axes on the detection of mirror symmetry in dot and solid patterns. Perception 1998, 27, 965-976.