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.     

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.     

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.     

The effects of curvature on the grid illusions

Grid illusions, including the Hermann grid and scintillating grid (in which light disks are superimposed upon the grid intersections), are diminished by curving the alleys that limn the repeating pattern. Curvature might either disrupt the processes that induce the illusion, or simply make the illusory effects harder to see. To determine which mechanism might be invoked, we examined the effects of curving the alleys upon the vanishing-disk illusion, a phenomenon in which a single disk in a grid intersection is rendered less detectable. This illusion is of reduced visibility, rather than generating an illusory apparition as in the Hermann grid or scintillating grid. Thus, inhibition of illusory influence would enhance disk visibility, while a general reduction of visibility would render disks even harder to detect. We find that thresholds for both scintillation and the disk itself increase in a graded manner with increased curvature. Measuring the effect of curvature upon the vanishing disk with traditional forced-choice staircase methods demonstrates that the effect of curvature is upon detection, not subjective criterion. Furthermore, disks that are easy to detect within a rectilinear grid are more difficult to detect when the alleys are curved. Thus, curvature of the alleys induces a general tendency to inhibit the visibility of features, and is not specifically a repression of illusory effects.     

Luminance gradient can break background-independent lightness constancy

A display with a luminance gradient was shown to induce a strong lightness illusion (Logvinenko, 1999 Perception 28 803-816). However, a 3-D cardboard model of this display was found to produce a much weaker illusion (less than half that in the pictorial version) despite the fact that its retinal image is practically the same. This is in line with the hypothesis that simultaneous lightness contrast is solely a phenomenon of pictorial perception (Logvinenko et al, 2002 Perception 31 73-82). The residual lightness illusion in the 3-D model can be accounted for by the fact that this model is a hybrid display. Specifically, while it is a real object, a pictorial representation (of the illumination gradient) is superimposed on it. Thus, lightness in the 3-D display is a compromise between two opposite tendencies: the background-independent lightness constancy and the lightness illusory shift induced by the luminance gradient.     

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.     

Reply to “Reconsidering evidence for the suppression model of the octave illusion,” by C. D. Chambers,J. B. Mattingley,and S. A. Moss

Chambers, Mattingley, and Moss (2004) present a review of research and theory concerning the octave illusion, a phenomenon that was originally reported by Deutsch (1974). The authors argue against the two-channel model proposed by Deutsch (1975a) to explain the illusory percept that was most commonly obtained and propose, instead, that the illusion results from binaural fusion and diplacusis. This article replies to the arguments raised by Chambers et al. (2004) and argues that the octave illusion and the two-channel model proposed to explain it are in accordance with growing evidence for what-where dissociations in the auditory system and for illusory conjunctions in hearing.     

Flank transparency: the effects of gaps,line spacing,and apparent motion

We analyze the properties of a dynamic color-spreading display created by adding narrow colored flanks to rigidly moving black lines where these lines fall in the interior of a stationary virtual disk. This recently introduced display (Wollschl?ger et al, 2001 Perception 30 1423-1426) induces the perception of a colored transparent disk bounded by strong illusory contours. It provides a link between the classical neon-color-spreading effect and edge-induced color spreading as discussed by Pinna et al (2001 Vision Research 41 2669-2676). We performed three experiments to quantitatively study (i) the enhancing influence of apparent motion; (ii) the degrading effect of small spatial discontinuities (gaps) between lines and flanks; and (iii) the spatial extent of the color spreading. We interpret the results as due to varying degrees of objecthood of the dynamically specified disk: increased objecthood leads to increased surface visibility in both contour and color.     

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.     

Orientation misperceptions induced by contrast polarity: comment on "Contrast polarities determine the direction of Café Wall tilts" by Akiyoshi Kitaoka, Baingio Pinna, and Gavin Brelstaff (2004)

According to Kitaoka et al (2004, Perception 33 11-20), the Café Wall illusion can be reduced to misalignment effects produced locally by a large shape on a line passing nearby. I demonstrate here that the interacting units are edges and not whole shapes, and that the source of the illusion does not consist in a local tilt but in a tendency of the edges to join when they have the same contrast polarity.     

The riddle of the Rotating-Tilted-Lines illusion

Gori and Hamburger (2006, Perception 35 853-857) devised a new visual illusion of relative motion elicited by the observer's motion. We propose that the systematic error of direction discrimination found by Lorenceau et al (1993, Vision Research 33 1207 - 1217) can explain this illusion. The neural correlate of such a systematic error with respect to the two types of neurons in the primary visual cortex, namely end-stopped and contour cells, is discussed.     

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.     

The line-motion illusion can be reversed by motion signals after the line disappears

In the line-motion illusion, a briefly flashed line appears to propagate from the locus of attention, despite being physically presented on the screen all at once. It has been proposed that the illusion reflects low-level visual information processing that occurs faster at the locus of attention (Hikosaka et al 1993 Vision Research 33 1219-1240; Perception 22 517-526). Such an explanation implicitly embeds the assumption that speeding or slowing of neural signals will map directly onto perceptual timing. This 'online' hypothesis presupposes that signals which arrive first are perceived first. However, other evidence suggests that events in a window of time after the disappearance of a visual stimulus can influence the brain's interpretation of that stimulus (Eagleman and Sejnowski 2000 Science 287 2036-2038; 289 1107a; 290 1051a; 2002 Trends in Neuroscience 25 293). If the online hypothesis were true, we should expect that events occurring after the flashing of the line would not change the illusion. Consistent with our hypothesis that awareness is an a posteriori reconstruction, we demonstrate that the perceived direction of illusory line-motion can be reversed by manipulating stimuli after the line has disappeared.     

Eye position affects audio-visual fusion in darkness

We investigated the frame of reference involved in audio-visual (AV) fusion over space. This multisensory phenomenon refers to the perception of unity resulting from visual and auditory stimuli despite their potential spatial disparity. The extent of this illusion depends on the eccentricity in azimuth of the bimodal stimulus (Godfroy et al, 2003 Perception 32 1233-1245). In a previous study, conducted in a luminous environment, Roumes et al 2004 (Perception 33 Supplement, 142) have shown that variation of AV fusion is gaze-dependent. Here we examine the contribution of ego- or allocentric visual cues by conducting the experiment in total darkness. Auditory and visual stimuli were displayed in synchrony with various spatial disparities. Subjects had to judge their unity ('fusion' or 'no fusion'). Results showed that AV fusion in darkness remains gaze-dependent despite the lack of any allocentric cues and confirmed the hypothesis that the reference frame of the bimodal space is neither head-centred nor eye-centred.     

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.     

Perceptual continuation and depth in visual phantoms can be explained by perceptual transparency

We try to explain perceptual continuation and depth in the visual-phantom illusion in terms of perceptual transparency. Perceptual continuation of inducing gratings across the occluder in stationary phantoms could be explained with unique transparency, a notion proposed by Anderson (1997 Perception 26 419-453). This view is consistent with a number of previous reports including that of McCourt (1994 Vision Research 34 1609-1617) who criticized the stationary phantom illusion from the viewpoint of his counterphase lightness induction or grating induction, which might involve invalid transparency. Here we confirm that the photopic phantom illusion (Kitaoka et al, 1999 Perception 28 825-834) really gives in-phase lightness induction and involves bistable transparency. It is thus suggested that perceptual continuation and depth in the visual-phantom illusion depend on perceptual transparency.     

New twists for an old turning illusion

A Vernier-offset illusion induced by rotating lines, introduced by Matin et al (1976 Perception & psychophysics 20 138-142) was re-examined using onset, offset, and reverse trajectories inspired by flash-lag illusion research, with both Vernier and alignment-with-vertical judgments being recorded. The pattern of illusions found was generally in agreement with a differential latency of stimulus ends account described by those authors, although certain variants of modern spatial projection theories, and a differential latency of attribute account, could also accommodate much of the data.     

Illusory conjunctions die hard: a reply to Prinzmetal, Diedrichsen, and Ivry (2001).

M. Donk (1999) showed that various data patterns that have been considered as evidence for the existence of illusory conjunctions may be due to errors of target-nontarget confusion, an account that challenges the mere existence of illusory conjunction. In a reply, W. Prinzmetal, J. Diedrichsen, and R. B. Ivry (2001) argued against this conclusion, claiming that some earlier findings can be explained only when one assumes that illusory conjunctions exist. The current article shows that Prinzmetal et al.'s claims cannot refute any of Donk's earlier conclusions, suggesting indeed that one can only conclude that "illusory conjunctions are an illusion."     

What is the appropriate control for the tilt illusion?

Recently it has been suggested that when tilt illusions are measured by parallel matching to the test arm of an acute angle, the usual control condition involving a match to the test arm in the absence of the inducing arm is inappropriate. According to Hotopf et al this is so because the pretest contains a second, depth-based illusory effect which is not contained in the test conditions. Whereas Hotopf et al gave indirect evidence for this claim, direct evidence is presented here for their assertion. The results suggest that there is no single stimulus configuration which could serve as a pretest control for all tilt illusion stimuli. Rather, the condition in which the test and inducing lines intersect at 90 degrees probably is the appropriate control for all other inducing-test-line angle displays.