Hermann Grid Research Articles

Illusions as neuro-signs

One of the reasons visual scientists find illusions fascinating is that their pictorial simplicity belies the complexity of visual processing. Illusions can direct us towards neurophysiological interpretations at many levels, which I have called ‘neuro-signs’. The most useful visual illusions are those that point to the simplest neural level possible, that is, those that provide signs of neural processing at early stages of the visual system, such as in the retina itself. The region of the retina that can change the activity of nerve cells throughout the visual system when light falls on it is called the ‘receptive field’ of those nerve cells. Primate retinal ganglion cells have receptive fields that are concentric and antagonistic — if the centre of a receptive field is excited by light the surround is inhibited (called ‘surround inhibition’), or vice versa. Are there any visual signs of such neural antagonism? There could be. In the black and white grid pattern shown below, a variety of illusory dots can be seen at the intersections of the black and white grid. In the upper half, dark grey dots appear at the white intersections between the black rectangles, although a light meter would not register such effects. This is called a Hermann grid; its reverse in the lower half, where illusory light grey dots are seen in the black intersections, is called a Hering grid. In both cases, the dots at an intersection disappear as soon as it is fixated, but they remain at those nearby. The dots are more difficult to see at the smallest intersections in both grids. Because of this effect, it is thought the illusory dots might be related to the distance from the centre of the retina (or ‘retinal eccentricity’); receptive fields have been found to be much smaller around the centre of the retina than more peripherally. Indeed, the optimal separation for producing the illusory dots increases with retinal eccentricity in a similar manner to the increase in receptive field size. But why do the illusory dots appear at all? One suggestion is that concentric receptive fields of the same dimensions will be stimulated differently when they fall at an intersection between four rectangles than when flanked by two rectangles — there would be more surround inhibition at an intersection than elsewhere. This would make a light intersection darker than its neighbours and a dark intersection lighter. Such an interpretation does not account for the dots that are visible between rectangles that are simply outlines, although these dots are not as compelling. When coloured rectangles are placed on a grey background (see above), the illusory dots at the intersections take on the colour of the rectangles: they appear to be light green in the grey intersections of the upper half, and reddish in the grey intersections of the lower half. This is because some receptive fields at the retinal ganglion cell level display colour opponency — the centre can be excited by, say, red and the surround inhibited by green; others operate on blue–yellow opponency. Hermann–Hering grids provide signs of a link between visual perception and neurophysiology. The link is made at an early stage of visual processing — the differences in the activity of the retinal ganglion cells — with the assumption that the neural signals for these differences are preserved in their transmission to the visual cortex of the brain. N Wade, Department of Psychology, University of Dundee, Dundee DD1 4HN, UK. This is the second in a short series of articles by Nicholas Wade, describing some common visual illusions.

Similar mechanisms underlie simultaneous brightness contrast and grating induction

The experiments explore whether the mechanism(s) underlying grating induction (GI) can also account for simultaneous brightness contrast (SBC). At each of three test field heights (1, 3 and 6 deg), point-by-point brightness matches were obtained from two subjects for test field widths of 32 deg (GI condition), 14, 12, 8, 6, 3 and 1 deg. The point-by-point brightness matches were quantitatively compared, using GI condition matches as a standard, to assess systematic alterations in the structure and average magnitude of brightness and darkness induction within the test fields as a function of changing test field height and width. In the wider test fields induction structure was present and was generally well-accounted for by the GI condition sinewave predictions. As test field width decreased the sinewave amplitude of the induced structure in the test field decreased (i.e., flattened), and eventually became negative (i.e., showed a reverse cusping) at the narrower test field widths. As expected, both subjects showed a decrease in overall levels of brightness and darkness induction with increasing test field height. For any particular test field height, however, relative brightness increased with decreasing test field width. This brightness increase began at larger test field widths as test field height increased. The results are parsimoniously accounted for by the output of a weighted, octave-interval array of seven difference-of-gaussian filters. This array of filters differs from those previously employed to model various aspects of spatial vision in that it includes filters tuned to much lower spatial frequencies. The two-dimensional output of this same array of filters also accounts for the GI demonstrations of Zaidi [(1989) Vision Research, 29, 691–697], Shapley and Reid's [(1985) Proceedings of the National Academy of Sciences USA, 82, 5983–5986] contrast and assimilation demonstration, and the induced spots seen at the street intersections of the Hermann Grid. The physiological plausibility of the filter array explanation of brightness induction is discussed, along with a consideration of its relationship to other models of brightness perception.

Spatial Parameters Affecting the Hermann Grid and the Scintillating-Grid Illusions

The Hermann grid and the scintillating grid are examples of brightness-contrast illusions. The scintillating grid consists of a Hermann grid with bright disks about 1.4 times the diameter of the grid elements superimposed upon the intersections. The resulting scintillation effect can be described as striking illusory spots, darker than the background, perceived as flashing within the bright disks with each flick of the eye. Although the scintillation effect is different from the classical Hermann grid illusion, one prerequisite for its occurrence is the presence of a grid eliciting the Hermann grid illusion (Schrauf et al, Vision Research in press). At the 12th ECVP we showed that the Hermann grid illusion can be reduced by bright diagonals within the squares of the grid which have the effect of suppressing the 45°/135° components of the Fourier spectrum (Lingelbach et al, 1989 Perception18 536 – 537). In a pilot study we successively reduced the length of the diagonals, and found that this suppression works well even if the diagonals are reduced to small tips near the grid intersections. According to Baumgartner's receptive-field account (Baumgartner, 1960 Pflügers Archiv272 21 – 22), such elements should cause additional inhibition, thus decreasing the neuronal discharge rate and corresponding illusory percept. This is not the case: if any illusion is perceived, it is considerably weaker. The strength of the scintillation effect is similarly reduced by this manipulation. Thus the present results cannot easily be accounted for by Baumgartner's model.

From Elements to Perceptions

Gestalt psychologists in the early part of the century challenged psychophysical notions that perceptual phenomena can be understood from a punctate (‘atomistic’) analysis of the elements present in the stimulus. Their ideas also inhibited later attempts to explain vision in terms of single-unit recordings from individual neurons. A rapprochement between Gestalt phenomenology and physiology seemed unlikely when the first ECVP was held in Marburg, Germany, in 1978. Since that time, response properties of neurons have been discovered that invite an interpretation of visual phenomena (including ‘illusions’) in terms of neuronal processing. Indeed, it is now possible to understand some Gestalt phenomena on the basis of known neurophysiological mechanisms. I begin by outlining the great strides that have been made since the advent of microelectrode recording from single neurons. Initially, cells (‘detectors’) selectively responding to the contrast, spatial frequency, wavelength, orientation, movement, and disparity of a stimulus placed in their receptive fields were used to interpret simple perceptual phenomena (eg, Mach bands, Hermann grids, tilt aftereffect, MAE). In recent years, cells at higher levels of the visual system have been discovered that might explain a number of more complex phenomena: the perception of illusory (occluded) contours by end-stopped cells in area V2, the filling-in of artificial scotomata by neurons in V3, colour constancy by ‘perceptive’ neurons in V4, and the perception of coherent motion in dynamic noise patterns by cells in MT. Studies of flow fields and biological motion in area MST have recently been added to account for our perceptions as we move through our environment. Prompted by these findings, a shift from local to global interactions ‘beyond the classical receptive field’ has taken place in our search for the neural substrates of perception. Current research has focused on three kinds of mechanisms: (i) converging feed-forward projections as the basis for new response properties emerging at higher levels, (ii) recruitment of lateral connections to explain filling-in, and (iii) backward propagation from higher to lower levels to account for binding and figure - ground segregation. How such mechanisms compute large-scale surface properties such as brightness, colour, and depth from local features—indeed how they construct the surfaces themselves from complex natural scenes—is only one of the many questions that are under scrutiny today. Future research will have to tackle the all-important question: How does the analysed information come together again? Furthermore, the contributions of eye movements, attention, learning, other sense modalities, and motor actions will have to be taken into consideration before we arrive at a more complete understanding of visual perception.

Influence of Scanning Eye Movements on the Scintillating-Grid Illusion

The scintillating grid is an example of a brightness contrast illusion in which bright disks are superimposed on a Hermann grid. Dark spots are perceived within the bright disks as flashing with each flick of the eye (Schrauf et al Vision Research in press). With steady fixation, stimulation must be brief for the illusion to occur. Varying exposure duration with steady fixation, we found the maximum illusion at durations between 210–350 ms (Schrauf et al, 1996 Perception25 Supplement, 78). In the present study voluntary saccadic eye movements were used to produce brief exposures during fixations. The task of 5 trained subjects was to scan scintillation grids of five different spacings (0.5 – 2.0 deg separation of grid elements, observation time 60 s) in a manner yielding a maximum scintillating effect. Eye movements were recorded binocularly at 100 Hz with the Demel Debic 90 infrared corneal reflection tracker (resolution: 6 min arc). For each fixation we calculated latency and position. Durations and amplitudes of the saccades increased with decreasing angular separation of grid elements. When the illusion was maximal, roughly 60% of fixation durations were between 250 and 550 ms. These durations overlap with those obtained with steady fixation combined with variable exposure durations. Unlike the Hermann grid illusion, where illusory dark spots can be perceived at very brief exposure durations, the scintillating grid illusion takes much more time to develop. The long optimal durations found here are discussed in relation to mechanisms of scanning eye movements.

The Scintillating Grid Illusion

Disk-shaped luminance increments were added to the intersections of a Hermann grid consisting of medium grey bars on a black background. Illusory spots, darker than the background, were perceived as flashing within the white disks with each flick of the eye. This striking phenomenon may be referred to as the scintillating grid illusion. We determined the conditions necessary for cancelling the Hermann grid illusion, as well as the luminance requirements and the size ratio between disks and bars that elicits the scintillation effect. The fact that scanning eye movements are necessary to produce the scintillation effect sets it apart from the Hermann grid illusion.

2502 The pincushion grid illusion: a kind of the neon spreading illusion?

The flowering responses of Brunonia australis (blue pincushion) and Calandrinia sp. to vernalization, photoperiod, temperature and plant age were investigated to provide a foundation for manipulating flowering in these potential potted plants. Plants were vernalized at 4.8 °C for 0, 3 or 6 weeks at the plant age of 1–4 or 8–14 leaves. Following vernalization, plants were grown at 25/10 or 35/20 °C (day/night) under short days (11 h, ambient daylight averaged 380 ± 44 μmol m−2 s−1) or long days (16 h) provided by an additional 5 h night break (21:00–2:00 h at <4.5 μmol m−2 s−1 from incandescent lamps), for 85 days. This is the first work to investigate flowering of these ornamental species. Both species showed enhanced flowering following vernalization and a quantitative requirement for long days. The reduction of the time until the first visible inflorescence (Brunonia) or flower (Calandrinia) buds by 8–13 days was affected by vernalization for 3 or 6 weeks, respectively. Long days were effective for reducing the time to first visible floral bud and increasing the number of inflorescence or flowers per plant for both species. For Brunonia, LDs replaced vernalization when applied to plants with 1–4 leaves. Raising temperature from 25/10 to 35/20 °C increased the number of flowers per plant of Calandrinia by 2–2.5-fold for plants with 1–4 or 8–14 leaves respectively.

The pincushion grid illusion: a kind of the neon spreading illusion?

The flowering responses of Brunonia australis (blue pincushion) and Calandrinia sp. to vernalization, photoperiod, temperature and plant age were investigated to provide a foundation for manipulating flowering in these potential potted plants. Plants were vernalized at 4.8 °C for 0, 3 or 6 weeks at the plant age of 1–4 or 8–14 leaves. Following vernalization, plants were grown at 25/10 or 35/20 °C (day/night) under short days (11 h, ambient daylight averaged 380 ± 44 μmol m−2 s−1) or long days (16 h) provided by an additional 5 h night break (21:00–2:00 h at <4.5 μmol m−2 s−1 from incandescent lamps), for 85 days. This is the first work to investigate flowering of these ornamental species. Both species showed enhanced flowering following vernalization and a quantitative requirement for long days. The reduction of the time until the first visible inflorescence (Brunonia) or flower (Calandrinia) buds by 8–13 days was affected by vernalization for 3 or 6 weeks, respectively. Long days were effective for reducing the time to first visible floral bud and increasing the number of inflorescence or flowers per plant for both species. For Brunonia, LDs replaced vernalization when applied to plants with 1–4 leaves. Raising temperature from 25/10 to 35/20 °C increased the number of flowers per plant of Calandrinia by 2–2.5-fold for plants with 1–4 or 8–14 leaves respectively.

Perception Laboratory: A Computer Program to Demonstrate Perceptual Phenomena

I developed an interactive computer program that allows one to demonstrate and experiment with various phenomena in visual perception using IBM-compatible computers. The program contains modules for demonstrating the color afterimage, the cafe illusion, additive color mixing and the opponent-process theory of color vision, the glowing axes illusion, the Hermann grid, the McCollough effect, the motion aftereffect, the neon illusion, and simultaneous contrast. The user has considerable control over the stimuli making up the image and can manipulate the variables that contribute to the perception of the effect. The program can be used far classroom demonstrations and student laboratory projects.

"The analogy between stereo depth and brightness": a reexamination.

A forced-choice experiment is reported, the results of which demonstrate that the cyclopean analogues of the Hermann grid, the embedded squares, and Mach bands can be readily observed. It is concluded that the earlier failure by Brookes and Stevens to observe these cyclopean analogues does not prove that spatial filtering of horizontal disparity is fundamentally different from the spatial filtering of the luminance image.

The Hermann grid illusion: a tool for studying human perspective field organization.

Psychophysical research on the Hermann grid illusion is reviewed and possible neurophysiological mechanisms are discussed. The illusion is most plausibly explained by lateral inhibition within the concentric receptive fields of retinal and/or geniculate ganglion cells, with contributions by the binocular orientation-specific cortical cells. Results may be summarized as follows: (a) For a strong Hermann grid illusion to be seen bar width must be matched to the mean size of receptive-field centers at any given retinal eccentricity. (b) With the use of this rationale, the diameter of foveal perceptive-field centers (the psychophysical correlate of receptive-field centers) has been found to be in the order of 4-5 min arc and that of total fields (centers plus surrounds) 18 min arc. These small diameters explain why the illusion tends to be absent in foveal vision. (c) With increasing distance from the fovea, perceptive-field centers increase to 1.7 deg at 15 deg eccentricity and then to 3.4 deg at 60 deg eccentricity. This doubling in diameter agrees with the change in size of retinal receptive-field centers in the monkey. (d) The Hermann grid illusion is diminished with dark adaptation. This finding is consistent with the reduction of the center-surround antagonism in retinal receptive fields. (e) The illusion is also weakened when the grid is presented diagonally, which suggests a contribution by the orientation-sensitive cells in the lateral geniculate nucleus and visual cortex. (f) Strong induction effects, similar to the bright and dark spots in the Hermann grid illusion, may be elicited by grids made of various shades of grey; and by grids varying only in chroma or hue. Not accounted for are: the illusory spots occurring in an outline grid ie with hollow squares, and the absence of an illusion when extra bars are added to the grid. Alternative explanations are discussed for the spurious lines connecting the illusory spots along the diagonals and the fuzzy dark bands traversing the rhombi in modified Hermann grids.

ヘルマン格子上の錯視斜線の方位

ヘルマン格子上の錯視斜線の方位

A Mathematical Model of Perception with Reference to Peripheral Vision and its Application to the Hermann Grid Illusion

Central vision and peripheral vision are two of main components of visual perception. The functional differences between the two visions are considered with two points of view: the physiological receptive field and the psychological perceptive field.

Neural dynamics of 1-D and 2-D brightness perception: a unified model of classical and recent phenomena.

Computer simulations of a neural network model of 1-D and 2-D brightness phenomena are presented. The simulations indicate how configural image properties trigger interactions among spatially organized contrastive, boundary segmentation, and filling-in processes to generate emergent percepts. They provide the first unified mechanistic explanation of this set of phenomena, a number of which have received no previous mechanistic explanation. Network interactions between a Boundary Contour (BC) System and a Feature Contour (FC) System comprise the model. The BC System consists of a hierarchy of contrast-sensitive and orientationally tuned interactions, leading to a boundary segmentation. On and off geniculate cells and simple and complex cortical cells are modeled. Output signals from the BC System segmentation generate compartmental boundaries within the FC System. Contrast-sensitive inputs to the FC System generate a lateral filling-in of activation within FC System compartments. The filling-in process is defined by a nonlinear diffusion mechanism. Simulated phenomena include network responses to stimulus distributions that involve combinations of luminance steps, gradients, cusps, and corners of various sizes. These images include impossible staircases, bull’s-eyes, nested combinations of luminance profiles, and images viewed under nonuniform illumination conditions. Simulated phenomena include variants of brightness constancy, brightness contrast, brightness assimilation, the Craik-O’Brien-Cornsweet effect, the Koffka-Benussi ring, the Kanizsa-Minguzzi anomalous brightness differentiation, the Hermann grid, and a Land Mondrian viewed under constant and gradient illumination that cannot be explained by retinex theory.

ヘルマン格子上のグレー・スポット及び対角線錯視

ヘルマン格子上のグレー・スポット及び対角線錯視

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.

A stereoscopic presentation of the hermann grid

A stereoscopic presentation of the hermann grid

A given visual field location has a wide range of perceptive field sizes

Increment thresholds were measured at the intersections of a modified Hermann Grid at several retinal locations and at photopic, mesopic and scotopic adaptation levels. On a concentric perceptive field explanation of the illusion, these results suggest that a broad distribution of perceptive field sizes exists at each visual field location. The peak of this distribution lies close to the previously reported perceptive field size at that location. As the adaptation level decreases, the distribution shifts upwards in size. At scotopic levels lateral inhibition only occurs for large stimuli. The size distribution can be used to account for the spatial extent of some contrast phenomena.

Perceptive field sizes and a new version of the Hermann grid.

The Hermann grid has been explained in terms of concentric receptive fields and also used to determine the size of centers and surrounds in perceptive fields in humans. A new figure, which is simply the outlines of the squares of the Hermann grid, shows that receptive fields having a range of excitatory and inhibitory sizes may be responsible for the Hermann illusion.

Illusory colour changes in Hermann grids varying only in hue

Illusory changes at the intersections of Hermann grids differing only in hue were studied in normal and colour-deficient observers. The response patterns indicate that colours ranging either from red-purple to yellow ( Red group), or from green to purple-blue ( Blue-Green group) can be substituted for each other without greatly changing the strength of the illusion. The same holds for green-yellow, purple and grey ( Neutral group). For a strong illusion, the overlying stripe and the background must belong to one colour group and the underlying stripe to the other. The illusory patches are characterized by an increase of chroma and/or a hue shift, usually away from the colour of the underlying stripe. The observed illusions may be mediated by R- and G-cones only.