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.     

Straightness as the main factor of the hErmann grid illusion

The generally accepted explanation of the Hermann grid illusion is Baumgartner's hypothesis that the illusory effect is generated by the response of retinal ganglion cells with concentric ON-OFF or OFF-ON receptive fields. To challenge this explanation, we have introduced some simple distortions to the grid lines which make the illusion disappear totally, while all preconditions of Baumgartner's hypothesis remain unchanged. To analyse the behaviour of the new versions of the grid, we carried out psychophysical experiments, in which we measured the distortion tolerance: the level of distortion at which the illusion disappears at a given type of distortion for a given subject. Statistical analysis has shown that the distortion tolerance is independent of grid-line width within a wide range, and of the type of distortion, except when one side of each line remains straight. We conclude that the main cause of the Hermann grid illusion is the straightness of the edges of the grid lines, and we propose a theory which explains why the illusory spots occur in the original Hermann grid and why they disappear in curved grids.     

A reversed Ebbinghaus–Titchener illusion in bantams (Gallus gallus domesticus)

A disk surrounded by smaller disks looks larger, and one surrounded by larger disks looks smaller than reality. This visual illusion, called the Ebbinghaus–Titchener illusion, remains one of the strongest and most robust illusions induced by contrast with the surrounding stimuli in humans. In the present study, we asked whether bantams would perceive this illusion. We trained three bantams to classify six diameters of target disks surrounded by inducer disks of a constant diameter into “small” or “large”. In the test that followed, the diameters of the inducer disks were systematically changed. The results showed that the Ebbinghaus–Titchener figures also induce a strong illusion in bantams, but in the other direction, that is, bantams perceive a target disk surrounded by smaller disks to be smaller than it really is and vice versa. Possible confounding factors, such as the gap between target disk and inducer disks and the weighted sum of surface of these figural elements, could not account for the subjects’ biased responses. Taken together with the pigeon study by Nakamura et al. (J Exp Psychol Anim Behav Process 34:375–387 2008), these results show that bantams as well as pigeons perceive an illusion induced by assimilation effects, not by contrast ones, for the Ebbinghaus–Titchener types of illusory figures. Perhaps perceptual processes underlying such illusory perception (i.e., lack of contrast effects) shown in bantams and pigeons may be partly shared among other avian species.     

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.     

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.     

Capturing lightness between contours

Homogeneously coloured bars may exhibit lightness differences at the intersections. A well-known example is the Hermann grid illusion, where crossing white bars on a black background show dark patches at the crossings. Jung (1973, Handbook of Sensory Physiology volume VII/3, pp 1-152) found that the dark patches persist when thin outlines are drawn at the intersections, and are even visible in foveal vision. Recently, it has been shown that making distortions to the contours of a Hermann grid-like configuration results in the disappearance of the illusory dark spots (Geier et al, 2008 Perception 37 651 665). We show that thin outlines at the crossings of the distorted Hermann grid induce lightness differences in the same direction as in the original Hermann grid illusion, even in foveal vision and in displays consisting of two crossing bars. Our experiments reveal that the induced lightness differences are independent of the luminance polarity and shape of the contours at the intersection. We suggest that the effect results from lateral inhibition and an additional spreading and capturing of these differences between luminance contours. A similar capturing between collinear contours may play a role in peripheral vision in the original Hermann grid.     

Scintillating lustre and brightness induced by radial lines

Gray disks inserted into the central gaps of an Ehrenstein pattern appear to lighten up and scintillate with each movement of the eye or stimulus pattern. We call this phenomenon scintillating lustre. Both phenomena-illusory brightness and scintillating lustre-depend on the presence of the radial inducing lines converging onto the gaps. Without the radii the gray disks appear matte. Using parametric stimulus variation, we show that the strength of scintillating lustre covaries with line-induced brightness enhancement when the length, width, number, and contrast of the radial lines, as well as the size of the gaps in the Ehrenstein figure, are varied. Following the proposal by Anstis (2000, Vision Research 40 2551-2556), we suggest that lustre results from a competition between the ON and OFF visual pathways. Whereas Helmholtz's binocular gloss is elicited by stereoscopically fused incremental and decremental stimuli, the present study demonstrates that lustre can also arise from the interaction between line-induced brightness (illusory increment) and a dark gray disk (physical decrement).     

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.     

The tactual horizontal-vertical illusion depends on radial motion of the entire arm

Wesought to clarify the causes of the tactual horizontal-vertical illusion, where vertical lines are overestimated as compared with horizontals in Land inverted-T figures. Experiment 1 did not use L or inverted-T figures, but examined continuous or bisected horizontal and vertical lines. It was expected that bisected lines would be perceived as shorter than continuous lines, as in the inverted-T figure in the horizontal-vertical illusion. Experiment 1 showed that the illusion could not be explained solely by bisection, since illusory effects were similar for continuous and bisected vertical and horizontal lines. Experiments 2 and 3 showed that the illusory effects were dependent upon stimulus size and scanning strategy. Overestimation of the vertical was minimal or absent for the smallest patterns, where it was proposed that stimuli were explored by finger movement, with flexion at the wrist. Larger stimuli induce whole-arm motions, and illusory effects were found in conditions requiring radial arm motion. The illusion was weakened or eliminated in Experiment 4 when subjects were forced to examine stimuli with finger-and-hand motion alone, that is, their elbows were kept down on the table surface, and they were prevented from making radial arm motions. Whole-arm motion damaged performance and induced perceptual error. The experiments support the hypothesis that overestimation of the vertical in the tactual horizontal-vertical illusion derives from radial scanning by the entire arm.     

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.     

Properties of long-range illusory contours produced by offset-arcs

Researchers have used several different types of illusory contours to investigate properties of human perception. One rarely used illusory contour is a combination of the abutting grating and Kanizsa illusions. We call this the offset-arcs illusion and provide an empirical investigation of the illusion. Through a series of four experiments, using different methods of measurement, we show that changes to the phase of the abutting-grating part of the inducing stimulus can dramatically change the perceived strength and clarity of the long-range illusory contour. The easy manipulation of illusion strength should make the offset-arcs illusion applicable to a wide range of studies that utilize long-range illusory contours. The lack of a brightness component to the illusion should allow the offset-arcs illusion to help separate perceptual grouping from surface brightness effects that are often confounded in other illusory contours.     

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.     

A global factor in the Hermann grid illusion or an artifact?

In the first of the present experiments, subjects were required to estimate the strength of the Hermann grid illusion in grids containing various numbers of intersectionseven though those grids were not actually presented. The positive relationship found by Wolfe (1984) for real grids was, nevertheless, replicated. It is argued that this suggests that a response bias might have been the source of his effect (although other possibilities are also noted). In addition, in a second experiment, subjects who were not aware of the fact that grid size was being manipulated (i.e., between subjects) showed no consistent effect of that factor, thus supporting the same suggestion.     

Interaction of Perception and Action in Discrete and Continuous Rapid Aiming Tasks

Previously, we have shown that discrete and continuous rapid aiming tasks are governed by distinct visuomotor control mechanisms by assessing the combined visual illusion effects on the perceived and effective index of difficulty (ID). All participants were perceptually biased by the combined visual illusion before they performed the rapid aiming tasks. In the current study, the authors manipulated the order of performing perceptual and motor tasks to examine whether perceptual or motor experience with the illusory visual target would influence the subsequent perceived and effective ID in discrete and continuous tapping tasks. The results supported our hypothesis showing that perceptual experience with the illusory visual target in the discrete condition reduced the effective ID in the subsequent discrete tapping task, and motor experience with the illusory visual target in the continuous condition reduced the illusion effects on the perceived ID in the subsequent perceptual judgment task. The study demonstrates the coinfluence of perception and action, and suggests that perception and action influence one another with different magnitude depending on the spatial frame of reference used to perform the perceptuomotor task.     

Illusory displacement of a moving trace with respect to the grid during oscilloscope motion

Observers report that a trace streak, which follows a sinusoidal path, moves vertically with respect to the oscilloscope’s grid when an oscilloscope is oscillated in the vertical plane. The vertical component of the trace streak motion with respect to the grid is illusory. This illusion is stable across a limited range of illumination and physical motion conditions. We hypothesize that this illusion is based on the manner in which the visual system calculates the vertical location of the grid and the trace: the trace location is determined on a moment-to-moment basis, whereas the grid tends to be seen in its average vertical position. The results of two experiments indicate that this hypothesis can account, at least partially, for the illusion. The illusion may have practical implications for pilots or navigators who track target blips on radar screens in moving aircraft.     

Directional harmonic theory: a computational Gestalt model to account for illusory contour and vertex formation

Visual illusions and perceptual grouping phenomena offer an invaluable tool for probing the computational mechanism of low-level visual processing. Some illusions, like the Kanizsa figure, reveal illusory contours that form edges collinear with the inducing stimulus. This kind of illusory contour has been modeled by neural network models by way of cells equipped with elongated spatial receptive fields designed to detect and complete the collinear alignment. There are, however, other illusory groupings which are not so easy to account for in neural network terms. The Ehrenstein illusion exhibits an illusory contour that forms a contour orthogonal to the stimulus instead of collinear with it. Other perceptual grouping effects reveal illusory contours that exhibit a sharp corner or vertex, and still others take the form of vertices defined by the intersection of three, four, or more illusory contours that meet at a point. A direct extension of the collinear completion models to account for these phenomena tends towards a combinatorial explosion, because it would suggest cells with specialized receptive fields configured to perform each of those completion types, each of which would have to be replicated at every location and every orientation across the visual field. These phenomena therefore challenge the adequacy of the neural network approach to account for these diverse perceptual phenomena. I have proposed elsewhere an alternative paradigm of neurocomputation in the harmonic resonance theory (Lehar 1999, see website), whereby pattern recognition and completion are performed by spatial standing waves across the neural substrate. The standing waves perform a computational function analogous to that of the spatial receptive fields of the neural network approach, except that, unlike that paradigm, a single resonance mechanism performs a function equivalent to a whole array of spatial receptive fields of different spatial configurations and of different orientations, and thereby avoids the combinatorial explosion inherent in the older paradigm. The present paper presents the directional harmonic model, a more specific development of the harmonic resonance theory, designed to account for specific perceptual grouping phenomena. Computer simulations of the directional harmonic model show that it can account for collinear contours as observed in the Kanizsa figure, orthogonal contours as seen in the Ehrenstein illusion, and a number of illusory vertex percepts composed of two, three, or more illusory contours that meet in a variety of configurations.     

Lightness effects in Delboeuf and Ebbinghaus size-contrast illusions

We examined lightness effects observed in Delboeuf and Ebbinghaus size-contrast illusions. Results of four experiments are reported. Experiment 1 was conducted with Delboeuf-like stimuli and shows that the disk that appears bigger appears either lighter or darker than the disk that appears smaller, depending on the contrast polarity between disks and background. Experiment 2 shows that the direction of these lightness effects is not influenced by the luminance of the size-contrast inducers. Experiment 3 shows that a similar lightness effect is also observed in modified Ebbinghaus size-contrast displays. Experiment 4 tested the presence of the size-contrast illusion in the stimuli used in experiments 2 and 3.     

Controlling the uncontrollable: effects of stress on illusory perceptions of controllability.

Individuals' failure to exercise actual control over an event might be compensated for by trying to bolster a generalized, subjective sense of control. Control might then be sought by undertaking acts the effect of which on the environment is illusory. This observation led to the hypothesis that stress, which undermines persons' sense of control, would engender illusory perceptions of controllability. The hypothesis was tested in 3 experiments that required Ss to choose between 2 gambling forms. Although the 2 forms were essentially identical, 1 was designed to instill an illusion of control. The results showed that highly stressed Ss, compared with those who experienced low stress, preferred gambling forms that heightened perceptions of controllability.     

Are illusory contours a cause or a consequence of apparent differences in brightness and depth in the Kanizsa square?

The causal flows between the processes responsible for illusory contour clarity, brightness, and apparent depth in the Kanizsa square were examined. The sixty-four stimuli used consisted of all possible combinations of eight disk luminances and eight centre-to-centre separations between nearest disks. Ten subjects were instructed to rate the clarity of the illusory contour and the brightness and apparent depth differences between the Kanizsa square and its surround in each stimulus. On the basis of results obtained with the causal inference method, using partial correlations and path analysis, it is suggested that clarity of illusory contour can be influenced directly by disk separation, and that the output from the process responsible for illusory contour clarity has some effect on the processes responsible for the apparent depth and brightness differences.     

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.