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

Abstract

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.

Behind the Looking-Glass: A Review on Human Symmetry Perception

“…Based on these results, they proposed that similar mechanisms might underlie the encoding of orientation and the encoding of symmetry. This accords with studies that demonstrate the simultaneous processing of symmetry at different spatial scales and for different orientation content, suggesting that simple cortical filters such as those found in V1 could subserve symmetry detection [71,86,87,[107][108][109].…”

Subordinate-level categorization relies on high spatial frequencies to a greater degree than basic-level categorization

“…This is because structural information at the object level becomes finer in spatial terms as the object moves farther away, gradually slipping below the acuity limit of the observer. Also, in natural images, low spatial frequencies have much higher contrast levels, with the energy dropping off as a 1/f n function, where f is frequency and n is an exponent between about 1.1 and 2.2 (see, e.g., Field & Brady, 1997;Rainville & Kingdom, 1999). This means that obscuration that reduces contrast-such as glare or fog-will tend to affect the higher frequencies more.…”

“…Therefore, there will almost certainly be some variability in the difficulty of recognizing different object classes when their images are filtered at any given cutoff. However, there do exist striking statistical regularities in the distribution of energy and information across spatial frequency in natural images overall (see, e.g., Field & Brady, 1997; Rainville & Kingdom, 1999), so it is unlikely that object recognition performance, relative to spatial filtering, will be completely idiosyncratic. That is, it seems likely that our results have some degree of generalizability to other object classes.…”

Interactions between constituent single symmetries in multiple symmetry

“…The priming effect was defined by Δd', calculated by subtracting d' on random primes from d' on one-fold symmetrical primes. The priming effects were not significant, negative, and positive when the symmetry axes in the prime and target had the same orientation, nonorthogonal orientations, and orthogonal orientations, respectively (similar filtering techniques had been employed by, e.g., Dakin & Herbert, 1998;Julesz & Chang, 1979;Rainville & Kingdom, 1999. Each image was generated starting from randomly distributed Gaussian luminance (μ = 0, σ = 0.125).…”