Abstract
By definition, a visual stimulus is symmetric if one part of this stimulus is a reflection of another part about an axis. Here, we show that observers can perceive symmetry in stimuli without such correspondence. The stimuli were created by multiplying a carrier pattern with an envelope. The carriers were either white noise patterns with the luminance of its pixels drawn from a uniform distribution or random dot patterns with dot density ranged from 0.01 to 0.1. A proportion of dots (coherence) had their corresponding across the centered vertical axis of the image. The envelopes were low-pass filtered (cut-off frequency 6 cycles per image) white noise patterns. We used a 2AFC paradigm, in which one interval contained a non-zero coherent target while the other zero-coherence pattern, and PSI adaptive staircase method to measure symmetry detection threshold. The task of the five observers was to determine which interval contained the symmetry stimulus. In Experiment 1, we measured the envelope modulation depth threshold for symmetry detection. Even with 0% coherence carrier, the observers were able to detect symmetry with only 7%-15% modulation depth in a symmetric envelope, suggesting that symmetry perception can be achieved through a spatial variation of contrast-contrast even though there is no point-to-point correspondence in the image. In Experiment 2, We measured the carrier coherence threshold for random dot patterns with various combinations of carrier and envelope coherence. At 1% dot density, the carrier coherence threshold was invariant at around 45-54% regardless of the envelope coherence. At 5% and 10% dot density, the carrier coherence threshold decreased when the envelope coherence was greater than 50%. Such a dot density effect implies that it is necessary to interpolate a surface for symmetry detection. Overall, we demonstrated that a human observer can perceive symmetry without any point-to-point correspondence in the image.