Spatial-scale contribution to the detection of mirror symmetry in fractal noise

We investigated how the detection of mirror symmetry depends on the distribution of contrast energy across spatial scales. Stimuli consisted of vertically symmetric noise patterns with fractal power spectra defined by 1/f beta slopes (-2 < or = beta < or = 5). While overall rms contrast remained fixed at 25%, symmetry-detection thresholds were obtained by corrupting the signal with variable amounts of noise with identical spectral characteristics. A first experiment measured thresholds as a function of spectral slope, and performance was found to be substantially facilitated in images with power spectra that characterize natural scenes (1.2 < or = beta < or = 3.2). In a second experiment, symmetry was removed from randomly chosen octave bands and replaced by noise with the same spectral profile. Results revealed that only in images with 1/f2 spectra does performance decrease by constant amounts across all frequency bands. Together, the results imply that symmetry mechanisms extract equal amounts of information from constant-octave frequency bands but lack the ability to whiten stimuli whose spectral slopes differ from those of natural scenes. Results are qualitatively well predicted by a multichannel model that (1) relies on spatial filters with equal-volume point-spread functions and constant-octave frequency bandwidths and (2) restricts the computation of symmetry to spatial regions whose dimensions are proportional to the filters' spatial scale. These findings are also consistent with the notion that mechanisms that mediate the perception of form exploit the ability of early vision to reduce second-order redundancy in natural scenes.