Date Published: March 28, 2019
Publisher: Public Library of Science
Author(s): Susana Martinez-Conde, Michael B. McCamy, Xoana G. Troncoso, Jorge Otero-Millan, Stephen L. Macknik, Manabu Sakakibara.
Vasarely’s nested squares illusion shows that the corners of concentric squares, arranged in a gradient of increasing or decreasing luminance, generate illusory “corner-folds,” which appear more salient (either brighter or darker) than the adjacent flat (non- corner) regions of each individual square. The Alternating Brightness Star (ABS) illusion, based on Vasarely’s classic nested squares, further shows that the strength of these corner-folds depends on corner angle. Previous psychophysical studies showed the relationship between corner angle and perceived contrast in the ABS illusion to be linear, with sharp angles looking higher in contrast, and shallow angles lower in contrast. Center-surround difference-of-Gaussians (DOG) modeling did not replicate this linear relationship, however, suggesting that a full neural explanation of the nested squares and ABS illusions might be found in the visual cortex, rather than at subcortical stages. Here we recorded the responses from single area V1 neurons in the awake primate, during the presentation of visual stimuli containing illusory corner-folds of various angles. Our results showed stronger neural responses for illusory corner-folds made from sharper than from shallower corners, consistent with predictions from the previous psychophysical work. The relationship between corner angle and strength of the neuronal responses, albeit parametric, was apparently non-linear. This finding was in line with the previous DOG data, but not with the psychophysical data. Our combined results suggest that, whereas corner-fold illusions likely originate from center-surround retinogeniculate processes, their complete neural explanation may be found in extrastriate visual cortical areas.
Vasarely’s ‘nested squares’ illusion shows that the corners of concentric squares, arranged in a gradient of increasing or decreasing luminance, generate illusory diagonals, or “folds,” which appear more salient (i.e. brighter or darker) than the adjacent flat (non-corner) regions of each individual square (Fig 1A and 1B) . The Alternating Brightness Star (ABS) illusion, which we developed based on Vasarely’s classic nested squares , further shows that the strength of the illusion depends on the corner angle, with sharp angles generating “corner-folds” that look higher in contrast, and shallow angles generating “corner-folds” that look lower in contrast (Fig 1C and 1D) (see http://smc.neuralcorrelate.com/demos/ABS-illusion.html for an interactive demonstration of the ABS illusion). Previous work attributed the nested squares and ABS illusions to changes in local contrast, and moreover found that applying a DOG (difference-of-Gaussians) filter to nested corners of varying angles resulted in outputs that qualitatively matched one’s subjective perception of the corresponding illusory folds . Yet, psychophysical quantification of illusory strength revealed not just a parametric, but a linear relationship between corner angle and perceived contrast, which was not apparent in the DOG model’s output [3,4]. The mismatch between the DOG simulations and the psychophysical data suggested that a subcortical (i.e. center-surround) explanation of the nested squares and ABS illusions may be an incomplete one. However, no research to date has recorded the responses of visual system neurons—cortical or subcortical—during the presentation of these illusions.
We recorded the responses from 118 single V1 neurons from two rhesus macaques (102 neurons from monkey J and 16 neurons from monkey A), during the presentation of brightness illusions based on Vasarely’s ‘nested squares,’ but discarded 60 neurons before analyzing the data because of technical problems (i.e. noise in the eye coil signal, instability of the recording throughout the session, or poor fixation performance). Thus, we present data from 58 neurons total. Though we started each recording session with the intent to present all three experimental conditions (details below) to each individual neuron, it was challenging to hold the neuronal recordings stable for more than 60–90 minutes at a time. Because data collection usually entailed 30–60 minutes per experimental condition (in addition to the 20–30 minutes necessary to characterize the size, location and orientation of each RF), we were able to test all three conditions in 7 neurons, two conditions in 11 neurons, and a single condition in 40 neurons out of the 58.
In 1961, Barlow proposed that the brain transmits visual data “so that their redundancy is reduced but comparatively little information is lost” [30,31]. This “redundancy-reducing hypothesis” has been used as an explanation of why neurons at the early levels of the visual system (retina/LGN) are suited to perform edge-detection, or contour-extraction. However, redundancy reduction should not be constrained to edges, but should theoretically apply to any feature in the visual scene. Just as edges are a less redundant feature than diffuse light, Attneave proposed in the 1950s that “points of maximum curvature” (i.e. discontinuities in edges, such as curves, angles, and corners—any point at which straight lines are deflected) are also highly informative . If points of high curvature are less redundant than points of low curvature, then sharp corners should also be less redundant than shallow corners. This led to our previous predictions that neural responses to sharp corners should be enhanced compared to those of shallow corners, and thus that sharp corners should be perceptually more salient than shallow corners.