Radial Frequency Analysis of Contour Shapes in the Visual Cortex

Abstract

Cumulative psychophysical evidence suggests that the shape of closed contours is analysed by means of their radial frequency components (RFC). However, neurophysiological evidence for RFC-based representations is still missing. We investigated the representation of radial frequency in the human visual cortex with functional magnetic resonance imaging. We parametrically varied the radial frequency, amplitude and local curvature of contour shapes. The stimuli evoked clear responses across visual areas in the univariate analysis, but the response magnitude did not depend on radial frequency or local curvature. Searchlight-based, multivariate representational similarity analysis revealed RFC specific response patterns in areas V2d, V3d, V3AB, and IPS0. Interestingly, RFC-specific representations were not found in hV4 or LO, traditionally associated with visual shape analysis. The modulation amplitude of the shapes did not affect the responses in any visual area. Local curvature, SF-spectrum and contrast energy related representations were found across visual areas but without similar specificity for visual area that was found for RFC. The results suggest that the radial frequency of a closed contour is one of the cortical shape analysis dimensions, represented in the early and mid-level visual areas.

Fig 1. Stimuli.

A) Radial frequency patterns with different radial frequencies (3–6) and amplitudes (A1-4). B) All the different shapes were presented in four different orientations (polar phases 0, 90, 180 or 270 deg). In total, 65 different stimuli were used, circles and 64 modulated shapes (4 RFCs x 4 amplitudes x 4 orientations). C) RFC patterns are constructed by modulating a base circle with radial sine function. D) The concave and convex curvatures were calculated at the trough and peak, respectively, of the modulation function. Amplitude refers to the amount of modulation relative to the radius of base circle.

Fig 2. Activity across visual areas.

A) Within the searchlight, t-value for average activity across different modulated shapes was calculated for each voxel and for each participant. Median t-values across participants are shown on the flattened Freesurfer average surface. Left and right hemispheres are on the left and right sides, respectively. B) Signal changes for circles and modulated shapes in different visual areas. C) Signal changes as a function of local curvature. Value 0.35 depicts circle shape. D) Signal changes as a function of radial frequency in different visual areas.

Fig 3. Model and measured RDMs.

The RDMs describe the dissimilarity of the response patterns across different shapes. Five models were constructed based on the classification of the stimuli to four classes (Table 2) and one model was constructed by cross-correlating stimulus SF spectrum. Model RDMs for Radial Frequency, Amplitude, Convex Curvature, Contrast Energy, Spatial Frequency Spectrum, and Concave Curvature, and one example of the measured RDM from visual area V3AB. See S1 Fig for examples of measured RDMs in all areas.

Fig 4. Response profile maps.

Correlation maps for Radial Frequency (A), Amplitude (B), Convex Curvature (C), Concave Curvature (D), Spatial Frequency spectrum (E), and Contrast Energy (F). Within the searchlight, correlation with model RDMs was calculated for each voxel. Average correlations, larger than three standard deviations above the mean, across participants are shown on the flattened Freesurfer average surface. Left and right hemispheres on the left and right sides, respectively.

Fig 5. Visual area analysis.

A) Average correlations with Radial Frequency model for different visual areas in the left and right hemispheres. B) Average correlations with all models. Hemispheres have been averaged. Error bars depict standard error of mean across participants. C) Dorsal-Ventral difference. Average correlation difference between dorsal (V2d, V3d, V3AB, IPS0) and ventral (V2v, V3v, hV3, VO1) visual areas for model RDMs. *p < .05 (t-test).