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Matthias Treder, Peter van der Helm; There is no symmetry like orthogonal symmetry. Journal of Vision 2007;7(9):764. doi: 10.1167/7.9.764.
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Where does the saliency advantage of two-fold symmetry over one-fold symmetry stem from? Is it only the presence of an extra symmetry axis, or is it also the fact that the symmetry axes are orthogonal? So far, empirical studies identifying the superiority of two-fold symmetry considered exclusively orthogonal symmetry axes. To shed more light on the role of orthogonality in two-fold symmetry, we used stimuli consisting of two non-overlapping spatial frequency bands. Each band contained either a perfect one-fold symmetry or a random noise pattern. This allowed for the construction of orthogonal and non-orthogonal two-fold symmetries. The resulting stimulus comprised either an orthogonal or a non-orthogonal two-fold symmetry, a one-fold symmetry or a random pattern. While each symmetry was perfect within its own spatial frequency band, the combination of the bands yielded noisy symmetries at a pixel level. Non-cardinal axes, tilted ±22.5 degrees relative to the vertical or horizontal, were used to prevent confounding effects of differentially salient axis orientations (e.g., vertical and horizontal). The task of the observer was to discriminate between symmetric and random stimuli. Results show that two-fold symmetries with orthogonal axes are significantly more salient than two-fold symmetries with non-orthogonal axes. We currently explore whether this difference is due to the mutual enhancement of orthogonal symmetry axes, or, vice versa, the mutual interference of non-orthogonal axes.
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