Cortical Shape Adaptation Transforms a Circle Into a Hexagon

Method

The author and 82 university students, including graduate students, participated in Experiment 1. All students were naive to the purpose of the experiment and provided written consent.

All stimuli were generated and presented on a computer (Sony VGN-Z91JS) with an LCD screen. Stimuli were displayed within an area of 1,200 × 900 pixels (20.5° × 15.5° of visual angle). Observers fixated on a center cross while their head was held steady by a chin rest. The viewing distance was 60 cm. Each adaptation display consisted of 16 yellow circles (55.0 cd/m²) with a diameter of 2.86° of visual angle or 16 yellow hexagons with the same area subtended by the circles. These circles and hexagons were either filled or unfilled, depending on the condition, and were distributed on a gray background (26.1 cd/m²; Fig. 1). Thus, there were four conditions, defined by the adaptation stimuli that were presented: unfilled circles, filled circles, unfilled hexagons, and filled hexagons. The outlines of the unfilled shapes had a thickness of 11.4 min of arc.

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Fig. 1.

Illustration of a sample trial in Experiment 1. Observers viewed a blank gray screen with a fixation cross for 3 s; then the adaptation stimuli (unfilled circles in the example shown here) appeared for 10 s. The screen then went blank for 3 s, during which most observers saw afterimages, such as the hexagonal shapes shown here. After the blank screen had been displayed for 1 s, a click sound prompted observers to attend to the shape of the afterimages. A 1-s mask consisting of a Mondrianesque pattern was then presented. Finally, observers selected the shape that most closely resembled the afterimage they saw, making their selection from seven possibilities printed on a sheet of paper.

At the start of each trial, participants saw a blank gray screen with a fixation cross. Then, the adaptation stimuli were presented for 10 s, after which participants saw a blank gray field for 3 s. A click sound followed 1 s after the stimuli vanished, to prompt observers to attend to the shape of the afterimage. The gray field was then replaced by a 1-s mask consisting of a Mondrianesque pattern with various colors and shapes. Observers then chose one of seven shapes that was most similar to the shape of the afterimage they had seen. The seven choices, all with the same area, were triangle, square, pentagon, hexagon, octagon, dodecagon, and circle. These shapes were printed on a sheet of paper that was placed in front of the observer. The participants individually performed the task twice per condition. The observers were told not to pay attention to the orientation of the shapes in the afterimage in judging their similarity to the stimuli shapes. This direction was given because the perceived orientations of the polygon afterimages were ambiguous and followed no fixed pattern.

Results and discussion

As Figure 2 shows, both filled and unfilled circles typically produced afterimages of hexagons or octagons rather than circles. The filling-in hypothesis cannot explain why outlined corners were clearly perceived in the afterimages of unfilled shapes.

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Fig. 2.

Results from Experiment 1 (top row) and Experiment 2 (bottom row). Each graph shows the percentage distribution of the seven response options when the adaptation stimuli were filled and when they were unfilled. Adaptation stimuli consisted of either circles (left panels) or hexagons (right panels); the shapes in Experiment 1 were static, and the shapes in Experiment 2 were dynamic (see insets). After viewing each adaptation stimulus, observers selected which one of seven shapes most closely resembled the shape in the afterimage they saw.

The notable difference between the distributions of the afterimage shapes seen after viewing hexagonal stimuli and those seen after viewing circular stimuli is that two peaks (i.e., for hexagons and circles) exist in the distribution resulting from adaptation to hexagonal stimuli, as compared with just one peak (for hexagons) resulting from adaptation to circular stimuli. In addition, when the adapted shape was a hexagon, circular afterimages were reported more frequently (especially for the unfilled hexagonal stimuli) than when the adapted shape was a circle. This perceived change of an adapted hexagon into a circular afterimage is a counterpart of the perceived change of an adapted circle into a hexagonal afterimage. The line-approximation hypothesis cannot explain this effect.

Pinna (1991) reported that radially arranged rectangles induced a circular subjective contour, but a physically drawn circle that replaced the subjective contour was seen as a polygon (Pinna termed this phenomenon the “illusion of angularity”). This phenomenon is consistent with the illusion seen here in showing perceptual ambiguity between corners and curvatures of shapes. However, the illusion of angularity originates from a difference in shape processing between real and subjective contours. In addition, the illusion of angularity in a real circle is produced by external inducers. However, the present illusion is caused by adaptation to the circular contour itself.

The present results demonstrate the possibility that afterimage formation is determined by cortical shape adaptation and not by simple retinal bleaching. To examine the importance of the shape of the adaptation stimulus independently of the shape of retinal bleaching, I used a dynamic adaptation stimulus in Experiment 2.

Method

Four conditions were used in Experiment 2, one for each type of adaptation stimulus: unfilled rotating circles, filled rotating circles, unfilled rotating hexagons, and filled rotating hexagons. Circles rotated at 1.0 revolutions per second, and hexagons rotated at 0.2 revolutions per second. The center of rotation of the circles was 14.0 min of arc apart from the center of the circle. The dynamic hexagon and circle stimuli produced similar circular retinal paintings (i.e., circular retinal bleaching). The method was the same as in Experiment 1. The author and 92 observers (including all observers in Experiment 1) completed one trial for each condition. All observers except the author were naive to the purpose of the experiment and provided written consent.

Results and discussion

As Figure 2 shows, adaptation to circle stimuli typically produced hexagonal afterimages. Few observers selected a circle shape, despite the circular retinal painting generated by the stimulus. However, the circular retinal paintings produced by rotating hexagons yielded circular afterimages for the majority of observers. The two distributions of afterimages produced by rotating circles and rotating hexagons were almost completely dissociated. This tendency was equivalent for filled and unfilled shapes.

These results demonstrate that the shape of the adaptation stimulus is critical for afterimage formation, independently of the shape of the retinal paintings they create. The results cannot be considered an artifact from employing an LCD screen. If the observers had viewed some traces of the moving figures remaining on the screen, they would have seen circular shapes after viewing all four types of stimuli.

Unlike the results of Experiment 1, the findings of Experiment 2 indicate that although the shape of the retinal painting produced by a rotating hexagon was circular, it did not yield a hexagonal afterimage. The corners of the rotating hexagons were exhibited equally along the circular path, so adaptation to a corner occurred equally along the circle, resulting in an afterimage of a perfect circle. However, responses to rotating circles were essentially the same as to stationary circles; that is, the shape adaptation arose only to a curvature along the circular path, typically resulting in a hexagonal afterimage. Thus, curves and corners could have a competing relationship in cortical shape processing. When one shape produces fatigue through adaptation, the other shape possibility dominantly appears.

Method

Forty-four observers participated in Experiment 3. All participants were naive to the purpose of the experiment and provided written consent. Using a mirror stereoscope and an LCD screen (Mitsubishi RDT204WM) with a resolution of 1,376 × 768 pixels, I presented different adaptation stimuli to participants’ left and right eyes using the left and right halves of the screen (see Fig. S1 in the Supplemental Material). All stimuli were presented against a pair of gray backgrounds (27.1 cd/m² each), one of which appeared above and one of which appeared below a central fixation cross. The cross and the backgrounds were embedded within a dotted texture.

There were five conditions, which were defined by the stimulus presented to the left eye. In each condition, the right eye viewed six static yellow circles (108 cd/m²). In four of the conditions, the left eye viewed six blue shapes (13.1 cd/m²), which varied per condition: static circles, slowly rotating circles (1.0 revolutions per second), rotating stars (0.2 revolutions per second), and rotating hexagons (0.2 revolutions per second). In an additional condition, no stimuli were presented to the left eye (which saw the gray background only). The rotating stars consisted of eight lines of equal length (122% of the circle diameter). Images were presented to both eyes in corresponding retinal positions. Yellow and blue figures are difficult to fuse binocularly because their luminance polarities against a gray background are opposite.

To ensure that observers viewed stimuli binocularly, I embedded two random-dot stereograms in the dotted texture on both the left and right sides of the central fixation cross. These two stereograms instantiated two small rectangles. Before testing, subjects acknowledged that they could perceive the rectangles floating in front of the dotted texture, which confirmed that they were viewing the stimulus display binocularly.

After a 10-s adaptation period, a blank field was presented to each eye for 2 s. The blank field for the left eye was colored black (0.45 cd/m²) to diminish the left-eye afterimage, and the blank field for the right eye was colored white (112 cd/m²) to suppress visibility of the left-eye afterimage. All observers confirmed that they saw only a blue or purple afterimage in the bright test field, which suggests that the origin of the afterimage was in the right eye. After the blank fields were presented for 2 s (with a click sound at 1 s to prompt observers to attend to the afterimages), observers saw a 1-s mask, as in the previous two experiments. All observers were then asked to rate the roundness of the right-eye afterimages four times for each condition. Twenty-two of the observers also rated the plain-background condition (in which only the right eye saw a stimulus; see Fig. 3). Ratings were made on a scale ranging from 0 (perfectly angular; i.e., a polygon) to 10 (perfectly round; i.e., a circle).

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Fig. 3.

Results from Experiment 3: mean rating of the roundness of right-eye afterimages as a function of condition. Conditions were defined by the stimulus presented to the left eye; the right eye viewed static yellow circles in all conditions. Error bars show ±1 SE.

Results and discussion

As Figure 3 shows, despite the right eye being always adapted to circles, the perceived afterimage shapes changed depending on the adaptation stimulus presented to the left eye. A one-way analysis of variance revealed a significant difference between conditions, F(3, 129) = 167.38, p = 2.73 × 10⁻⁴⁴. Multiple comparisons using Ryan’s (1959) method revealed significant differences between all conditions (p < .001), except for the plain-background and static-circle conditions, t(21) = 0.31, p = .76, two-tailed.

The right-eye afterimage exhibited the most angular shapes when the left eye was adapted to rotating circles. This result was expected because each eye image should produce a polygon afterimage, as was the case in Experiments 1 and 2. However, after the left eye viewed rotating hexagons, the shapes perceived in the right-eye afterimage were almost circular. This demonstrates that adaptation to a polygon in the left eye suppressed adaption to a circle in the right eye to produce a polygonal afterimage (i.e., adaptation to circles should have produced a polygonal afterimage, as in Experiment 1). In the rotating-star condition, the ratings were in the middle of the scale. This may be because the image presented to the left eye was neither round nor angular. The right-eye afterimage was affected by left-eye adaptation, although the right eye adapted to circles in all cases. Thus, the adaptation process that forms afterimages appears to exist in the cortex, where it collects shape information from input from both eyes.

These results could be interpreted as reflecting the amount of exposure to curves and corners after binocular rivalry. In the static- and rotating-circle conditions, both eyes viewed a circle, even though there was binocular rivalry. In the rotating-star and rotating-hexagon conditions, only the right eye input was a circle. In addition, in the rotating-hexagon condition, the left-eye input included corners. The rated roundness seems to reflect these differences in exposure to curves and corners. Although whether or not binocular rivalry actually precedes shape processing in adaptation remains to be investigated, it appears that the shape-processing mechanisms collect information from both eyes.