The Hermann grid illusion revisited

The Hermann grid illusion consists of smudges perceived at the intersections of a white grid presented on a black background. In 1960 the effect was first explained by a theory advanced by Baumgartner suggesting the illusory effect is due to differences in the discharge characteristics of retinal ganglion cells when their receptive fields fall along the intersections versus when they fall along non-intersecting regions of the grid. Since then, others have claimed that this theory might not be adequate, suggesting that a model based on cortical mechanisms is necessary [Lingelbach et al, 1985 Perception 14(1) A7; Spillmann, 1994 Perception 23 691 708; Geier et al, 2004 Perception 33 Supplement, 53; Westheimer, 2004 Vision Research 44 2457 2465]. We present in this paper the following evidence to show that the retinal ganglion cell theory is untenable: (i) varying the makeup of the grid in a manner that does not materially affect the putative differential responses of the ganglion cells can reduce or eliminate the illusory effect; (ii) varying the grid such as to affect the putative differential responses of the ganglion cells does not eliminate the illusory effect; and (iii) the actual spatial layout of the retinal ganglion cell receptive fields is other than that assumed by the theory. To account for the Hermann grid illusion we propose an alternative theory according to which the illusory effect is brought about by the manner in which S1 type simple cells (as defined by Schiller et al, 1976 Journal of Neurophysiology 39 1320-1333) in primary visual cortex respond to the grid. This theory adequately handles many of the facts delineated in this paper.     

Dark adaptation and the Hermann grid illusion

The latency of the perception of the dark spot at the intersection of a Hermann grid was measured before and after dark adaptation. It was found that dark adaptation significantly increased the latency of perception of the spot while light adaptation had no effect. This finding was predicted from the Jung and Spillman account of the Hermann grid illusion and from the Kuffler et al. finding that inhibitory receptive fields of the cat’s retinal ganglion ceils are reduced in size and responsiveness after dark adaptation. The significance of this finding in relation to other simultaneous contrast phenomena is discussed.     

Global factors in the Hermann grid illusion

Most explanations of the Hermann grid illusion are local in nature. For example, in Baumgartner's model the effect is generated by the response of cells having concentric on-off or off-on receptive fields. Such models predict that the magnitude of the illusion at a given intersection should be the same whether that intersection is viewed in isolation or in conjunction with other intersections in a grid. Two experiments are reported. The first demonstrates that illusion magnitude grows with the number of intersections. The second shows that this growth is seen when the intersections are arranged in an orderly grid but not when they are placed irregularly. These results suggest that a purely local model for the Hermann grid illusion is not a complete explanation. Global factors must be involved.     

Chromatic induction effects in the Hermann grid illusion.

The chromatic Hermann grid illusion was investigated in sixteen subjects, with variation of the lightness contrast between the chromatic inducing squares and the background, and the saturation and hue of the inducing squares. Subjects made magnitude estimates of the sharpness and clarity of perceived dots at the intersections of the grid, and matched the appearances of the dots with Munsell chips. A chromatic induction effect was found to occur in the absence of lightness contrast, but the sharpness of the illusory dots increased with increasing lightness contrast (p less than 0.001). The saturation of the perceived dots increased with increases in the saturation of the inducing squares (p less than 0.05), and was higher for the longer wavelengths than for the shorter wavelengths (p less than 0.005). Neural units with center-surround arrangements responding differentially to light of the same color in the center and the surround, e.g. red off-centers and red on-surrounds, could account for the chromatic induction effect.     

Variations on the Hermann grid: an extinction illusion

When the white disks in a scintillating grid are reduced in size, and outlined in black, they tend to disappear. One sees only a few of them at a time, in clusters which move erratically on the page. Where they are not seen, the grey alleys seem to be continuous, generating grey crossings that are not actually present. Some black sparkling can be seen at those crossings where no disk is seen. The illusion also works in reverse contrast.     

Healin' groovy: movement affects the appearance of the healing grid illusion

Vection alters the perception of a visual illusion. It enhances the illusory completion of the healing grid (Kanai, 2005, Best Illusion of the Year Contest, Vision Sciences Society). When we perceive our self-motion, the mode of vision is different from that of when we are stationary.     

The tilted Hermann grid illusion: 'illusory spots' versus 'phantom bands'

The Hermann grid illusion became a cause célèbre, when it was reported that small figural changes from straight to curved bars abolish the dark illusory spots. We demonstrate that this is not an all-or-none effect; rather, the visual system tolerates some tilt/curviness. We transformed straight and curved Hermann grids to rhombic Motokawa grids by gradually tilting the horizontal bars. Initially, we observed only dark illusory spots, then dark spots combined with phantom bands traversing the rhomb along the minor axis, and finally dark phantom bands only. This shows that two kinds of illusions can coexist in the same grid pattern.     

Straightness as a cue for luminance edge interpretation

In order to determine the reflectance of a surface, it is necessary to discount luminance changes produced by illumination variation, a process that requires the visual system to respond differently to luminance changes that are due to illumination and reflectance. It is known that various cues can be used in this process. By measuring the strength of lightness illusions, we find evidence that straightness is, used as a cue: When a boundary is straight rather than curved, it has a greater tendency to be discounted, as if it were an illumination edge. The strongest illusions occur when a boundary has high contrast and has multiple X-junctions that preserve a consistent contrast ratio.     

Pigeons perceive the Ebbinghaus-Titchener circles as an assimilation illusion

A target circle surrounded by larger "inducer" circles looks smaller, and one surrounded by smaller circles looks larger than they really are. This is the Ebbinghaus-Titchener illusion, which remains one of the strongest and most robust of contrast illusions. Although there have been many studies on this illusion in humans, virtually none have addressed how nonhuman animals perceive the same figures. Here the authors show that the Ebbinghaus-Titchener figures also induce a strong illusion in pigeons but, surprisingly, in the other direction; that is, all five successfully trained pigeons judged the target circle surrounded by larger circles to be larger than it really is and vice versa. Further analyses proved that neither the gaps between target and inducer circles nor the cumulative weighted surface of these figural elements could account for the birds' responses. Pigeons are known to show similarities to humans on various cognitive and perceptual tasks including concept formation, short-term memory, and some visual illusions. Our results, taken together with pigeons' previously demonstrated failure at visual completion, provide strong evidence that pigeons may actually experience a visual world too different for us to imagine.     

An illusion of movement complementary to the horizontal-vertical illusion

Blindfolded subjects moved a stylus held in the hand over a standard distance of 4.5 ins. in a given direction. They then attempted to move the same distance in a direction at right angles to the first. Eight combinations of movements were investigated. The results reveal an illusion such that the extent of movements to left or right across the body is underestimated, while the extent of movements towards or away from the body in the mid-line is overestimated. The illusion applies to speed as well as extent of movement. Movement up or down in a vertical plane is equivalent to movement towards or away from the body in a horizontal plane.

The interaction of this illusion with the well-known horizontal-vertical illusion of visual perception explains a failure to find any net illusory effect where lines visually displayed in different orientations were matched for length by unseen movements in similar orientations.

Whether the visual and movement illusions simply co-exist or whether they are functionally related is not yet clear.     

Causal illusion as a cognitive basis of pseudoscientific beliefs

Causal illusion has been proposed as a cognitive mediator of pseudoscientific beliefs. However, previous studies have only tested the association between this cognitive bias and a closely related but different type of unwarranted beliefs, those related to superstition and paranormal phenomena. Participants (n = 225) responded to a novel questionnaire of pseudoscientific beliefs designed for this study. They also completed a contingency learning task in which a possible cause, infusion intake, and a desired effect, headache remission, were actually non-contingent. Volunteers with higher scores on the questionnaire also presented stronger causal illusion effects. These results support the hypothesis that causal illusions might play a fundamental role in the endorsement of pseudoscientific beliefs.     

The discursive form of human understanding as the source of the transcendental illusion

Kant famously claims that pure reason is subject to a transcendental illusion in which the subjective validity and the regulative use of a principle of reason are conflated with its objective validity and constitutive use. His doctrine of transcendental illusion is puzzling for he insists that this illusion is natural as well as necessary. The two dominant interpretation strategies cannot make sense of this puzzle because they turn out to be either too strong or too weak: they either struggle to account for the legitimate, regulative use of the transcendental principle of reason or fall short of explaining the necessity of the transcendental illusion. In contrast, I shall argue that it is possible to account for the fact that the transcendental illusion is natural and necessary because it has its source in the discursive form of our human understanding, and that this illusion can nevertheless be known to be illusory because our discursive nature can be recognised as a merely particular form of understanding by comparing it with a possible, intuitive form of understanding in an act of critical self-reflection.     

A static geometrical illusion contributes largely to the footsteps illusion

When a black and a white rectangle drifts across a stationary striped background with constant velocity, the rectangles appear to alternately speed up and slow down. Anstis (2001, Perception 30 785-794; 2004, Vision Research 44 2171-2178) suggested that this 'footsteps' illusion is due to confusion between contrast and velocity signaling in the motion detectors of the human visual system. To test this explanation, three experiments were carried out. In experiment 1, the magnitudes of the footsteps illusion in dynamic and static conditions was compared. If motion detectors play an important role in causing the illusion, it should be reduced in the static condition. Remarkably, however, we found that the illusory misalignment between the black and the white rectangle was even more prominent in the static condition than in the dynamic condition. In experiment 2, we measured the temporal-frequency properties of the footsteps illusion. The results showed that the footsteps illusion was tuned to low temporal frequencies. This suggests that the static illusory misalignment can contribute sufficiently to the dynamic illusory misalignment. In experiment 3, the magnitude of the illusion was measured with the rectangles drifting on a temporally modulated background instead of a spatially modulated background. If contrast affects the apparent velocity of the rectangles, temporal modulation of a uniform background should also cause the footsteps illusion. However, the results showed that the magnitude of the illusion was much reduced in this condition. Taken together, the results indicate that the footsteps illusion can be regarded as a static geometrical illusion induced by the striped background and that motion detectors play a minor role at best.     

Thresholds for the perception of angular acceleration as indicated by the oculogyral illusion

A motorized chair (with precise servo controls) accelerated the observer in a clockwise (CW) or counterclockwise (CCW) direction at rates that ranged in logarithmic progression from 0.02 to 6.00 deg/sec². The target, a narrow collimated Line of light, was contained within a goggle device worn by the observer and therefore fixed in relative position to him. The illusion, appearing as rightward or leftward movement of the visual target in the direction of acceleration, was determined by a double staircase procedure among 300 normal and 4 labyrinthine-defective observers. None of the latter perceived the illusion. The majority of normal observers revealed no substantial directional difference (CW vs. CCW threshold). Threshold frequency distributions ranged in rate (deg/sec²) from 0.020 to 0.950; the threshold of response in more than half the normal observers was less than 0.10, in over three-fourths was less than 0.20, in over 90% less than 0.30, and 100% less than 1.00.     

Induced motion considered as a visually induced oculogyral illusion

The possibility that nystagmus suppression contributes to illusory motion was investigated by measuring perceived motion of a stationary stimulus following the removal of an optokinetic stimulus. This was done because optokinetic nystagmus typically outlasts cessation of an optokinetic stimulus. Therefore, it would be expected that a stationary fixated stimulus should appear to move after removal of an optokinetic stimulus if illusory motion results from nystagmus suppression. Illusory motion was reported for a stationary fixation target following optokinetic stimulation. This motion was reported first in the same direction as the preceding induced motion, then in the opposite direction. The two directions of illusory motion following optokinetic stimulation are interpreted as resulting from the use of smooth ocular pursuit to suppress first one phase of optokinetic after nystagmus and then the reverse phase. Implications for the origins of induced motion are discussed.     

The solitaire illusion: An illusion of numerosity

A new illusion in which the apparent number of elements of two kinds is determined by their spatial arrangement is described. The illusion is such that one large cluster appears to contain more elements than several small clusters, clustering being determined by Gestalt principles. The illusion was found both in adults and in children of 8 years.