Different symmetries, different mechanisms

Abstract

Three common symmetries exist in the natural visual world: (i) mirror symmetry, i.e., reflections around a vertical axis, (ii) radial symmetry, i.e., rotations around a point, and (iii) translational symmetry, i.e., shifted repetitions. Are these processed by a common class of visual mechanism? Using stimuli comprising arrays of Gaussian blobs we examined this question using a visual search protocol in which observers located a single symmetric target patch among varying numbers of random-blob distractor patches. The testing protocol used a blocked present/absent task and both search times and accuracy were recorded. Search times for mirror and radial symmetry increased significantly with the number of distractors, as did translational-symmetry patterns containing few repetitions. However translational-symmetry patterns with four repeating sectors produced search slopes close to zero. Fourier analysis revealed that, as with images of natural scenes, the structural information in both mirror- and radial-symmetric patterns is carried by the phase spectrum. However, for translational patterns with four repeating sectors, the amplitude spectrum appears to capture the structure, consistent with previous analyses of texture regularity. Modeling revealed that while the mirror and radial patterns produced an approximately Gaussian-shaped energy response profile as a function of spatial frequency, the translational pattern profiles contained a distinctive spike, the magnitude of which increased with the number of repeating sectors. We propose distinct mechanisms for the detection of different symmetry types: a mechanism that encodes local positional information to detect mirror- and radial-symmetric patterns and a mechanism that computes energy in narrowband filters for the detection of translational symmetry containing many sectors.

Keywords: Mirror; Radial; Spatial vision; Symmetry; Translational; Visual search.

Fig. 1

Examples of mirror (left), radial (middle) and translational (right) symmetry. Although the objects themselves are three-dimensional, their two-dimensional projections onto the fronto-parallel plane (and hence also retinal image) are representative of the three types of symmetry studied here psychophysically

Fig. 2

Examples of symmetric target patterns composed of luminance defined Gaussian blobs. Mirror symmetry containing two and four sectors are shown in a and b, respectively. Radial symmetry containing two and four sectors are shown in c and d, respectively. Translational symmetry containing two, three and four sectors are shown in e, f and g, respectively

Fig. 3

Example search arrays with set sizes of (a) 4 and (b) 16. Both examples contain a mirror symmetric target highlighted with a red circle (not present during testing)

Fig. 4

Mirror symmetry with 2 (blue) and 4 (magenta) sectors (left), radial symmetry with 2 (blue) and 4 (magenta) sectors (middle) and translational symmetry with 2 (blue), 3 (green) and 4 (magenta) sectors (right). Error bars are ± 2 SE

Fig. 5

Each row shows the following for a different symmetric pattern: Column 1: the symmetric pattern under consideration. Column 2: a noise pattern. Column 3: the result of combining the phase information from the noise with the amplitude information from the symmetric pattern. Column 4: the result of combining the amplitude information from the noise with the phase information from the symmetric pattern. Column 5: the output of the filter-rectify-filter (FRF) model, the blue plots the model output for the noise patterns, while the red plots the output for the symmetric patterns

Fig. 6

Search times as a function of set-size for the regular patterns, the target present and absent conditions are plotted in red and blue, respectively. SEs have been omitted as they are approximately the size of the data points