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Bart Farell; The perception of symmetry in depth. Journal of Vision 2005;5(8):519. doi: 10.1167/5.8.519.
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© ARVO (1962-2015); The Authors (2016-present)
The visual system is sensitive to symmetries in spatial position, and bilateral symmetry about a vertical axis has a particular salience. However, symmetries about an axis or point within the frontoparallel plane form only a subset of the symmetries realizable in 3-D space. Which among this larger set of symmetries are humans sensitive to?
To determine the existence of a specific sensitivity to symmetry in depth, I presented stereo displays of items (disks or Gabor patches) that were distributed symmetrically or asymmetrically in depth. The projection of the cyclopean array onto the frontoparallel plane was always symmetrical about a particular axis (vertical, horizontal, left oblique or right oblique). Disparity values were assigned symmetrically on either side of this axis. Asymmetrical arrays were generated by perturbing the disparity of a single one of these items.
Disparity thresholds were lowest for discriminating symmetrical and asymmetrical depths on either side of the vertical axis. Thresholds did not differ significantly between the horizontal and oblique axes of symmetry. To determine whether the results were due to differences in sensitivity to disparity across retinal locations, I also collected data for discriminating repetitions and non-repetitions of depth values; here translation rather than reflection determined correspondence. The items' frontoparallel positions (and retinal locations) were the same as in the symmetry-asymmetry discrimination task. However, thresholds as a function of the axis of symmetry were not the same in the two tasks. In the repetition task threshold did not differ across the four axes. Hence, humans do evince a specific sensitivity to the symmetry of patterns in depth, particularly patterns whose corresponding points have the same coordinates when projected onto the sagittal plane. These depth-symmetric patterns are 3-D analogs of the traditional focus of symmetry research—2-D patterns with symmetry about the vertical axis.
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