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Shivam Vedak, Rick Gilmore, Peter Kohler, Yanxi Liu, Anthony Norcia; The Salience of Lower-Order Features in Highly Self-Similar Wallpaper Groups. Journal of Vision 2015;15(12):839. doi: 10.1167/15.12.839.
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© ARVO (1962-2015); The Authors (2016-present)
Symmetric visual patterns arise frequently in natural images and human cultural artifacts. All 2-D symmetric patterns that tile the plane represent one of 17 “wallpapers” -- combinations of the fundamental symmetries of rotation, translation, glide reflection and reflection. Most research on human perception has focused on two-fold reflection. Here we examine how human observers classify patterns with varying combinations of the fundamental symmetries. Clarke et al. (2011) found that five of the seventeen wallpaper groups (P1, P3M1, P31M, P6, and P6M) had a high degree of self-similarity. We presented adult participants (n=11) with twenty spatial-frequency-normalized exemplars from each of the five highly self-similar wallpaper groups. Each exemplar was generated from a seed region containing random grayscale noise, which was then replicated, rotated, reflected, and translated according to the pattern of regularity reflected in each wallpaper group. Observers were instructed to sort the exemplars into as many subsets as they wished based on any criteria they saw appropriate. We used the Jaccard index to measure the degree to which observers sorted exemplars from the wallpaper patterns into consistent categories. Observers found consistent patterns of self-similarity between the wallpaper groups, p< .001. P1 exemplars were judged to be more self-similar than than the other groups, p< .001, and P6M exemplars were judged to be more self-similar than P6, p< .001. The findings suggest that mirror and translational symmetry influence unconstrained observer judgments about pattern regularity. Visual inspection of the subsets generated by observers suggested that the presence of salient secondary features (i.e. emergent global geometric structures such as striations, grid patterns, and characteristic shapes) influences the detection of self-similarity in wallpaper patterns. The results contribute to an emerging understanding of how group theory may shed light on human and machine pattern detection.
Meeting abstract presented at VSS 2015
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