Varieties of higher-order symmetry

We challenge the conventional notion that symmetry perception requires positional correspondence between image elements by demonstrating that symmetry can be perceived solely through spatial variations in image statistics in the absence of direct element correspondence (i.e., second-order symmetry, in contrast to the traditional "first-order symmetry" concept characterized by explicit element matching). One example of the second-order symmetry patterns is constructed by modulating random dot carriers with low-pass symmetrical envelopes. Additional instances can be generated via symmetric modulation of dot density, orientation statistics, dot-pair statistics, binocular disparity, and motion flow. These patterns elicit robust symmetry percepts despite lacking local feature correspondence, challenging current models of symmetry detection. Instead, the implication is that the visual system infers a surface structure before symmetry assessment.