THE CAFE-WALL ILLUSION involves a checkered arrangement of black and white tiles, rectangular or square, separated by thin lines of mortar. What is surprising is that the horizontal lines appear to converge toward the left or the right. The direction of convergence alternates: in one row the tiles seem to be wider on the left side and in the next row they seem to be wider on the right.

The illusion came to the attention of vision scientists in the early 1970's, when it was discovered on the wall of a cafe in Bristol, England. In 1979 Richard L Gregory and Priscilla Heard of the University of Bristol reported the first detailed study of the illusion. They related it to a much older illusion, known as the Munsterberg figure for the psychologist Hugo Munsterberg, who wrote about it in 1897. In the Munsterberg version too the top and bottom edges of individual tiles appear to tilt and the direction of tilt alternates from row to row, but the convergence is weaker. The white regions in particular are noticeable, seeming to flare vertically at one end. In both figures the tilt is an illusion: neither has any tilted elements. You can eliminate the illusion of tilt by sighting almost along the plane of the page. (You may see the accompanying illusions better if you slip a sheet of dark paper under the page to mask the printing on the other side.)

Gregory and Heard, and others after them, noticed that the cafe-wall illusion is pronounced when the black and white tiles contrast sharply in brightness and the layer of mortar is narrow and of intermediate brightness. When the mortar is just as bright as the white regions, the illusion is weaker or even missing; if it is even brighter, the illusion is certain not to appear. When the mortar is just as dark as the black regions, the arrangement produces the Munsterberg illusion, with its weaker convergence; if it is even darker, there is no convergence. The tiles can be colored instead of black and white, but unless the colors contrast in brightness, the illusion is lost. Identical tiles must be staggered in the array, but the illusion does not appear if they are offset so precisely that they form a chessboard.

Gregory and Heard likened the array to certain patterns invented by James Fraser in the early part of this century. Fraser showed how a narrow row of slightly tilted bright and dark lines gives the illusion of tilt to the row itself. The illusion is called the twisted-cord effect because each row of lines looks something like two cords spiraling around each other. The twisted-cord effect has never been satisfactorily explained. It probably has to do with the fact that the visual system's detectors responsible for determining small-scale (or "local") orientations may influence the perception of large-scale (or "global") orientations. The influence seems to be stronger when many identical, or only slightly different, locally tilted elements are viewed.

Is the tilt perceived in the cafe-wall illusion due to that kind of control of global orientation by local orientations? If it is, what are the locally tilted elements? The offset of the black and white tiles in adjacent rows might seem to serve the purpose, but the tiles are too large-and besides, such an explanation does not account for the requirement that the mortar supply a particular degree of contrast. For a long time investigators tried to identify some local tilt that could set up the global convergence of the rows.

Gregory and Heard suggested that the local tilt is generated when the visual system locates the borders of a mortar line. To counteract the incessant slight eye movements that shift borders over the retina, some mechanism must lock in the positions of the borders so that the pattern appears to be stationary. Where the mortar separates tiles of the same color (either white or black), the locking mechanism fixes the borders properly. But where the mortar separates contrasting tiles and when the mortar is intermediate in contrast, the locking mechanism may be less accurate, with the result that the borders are displaced slightly. Along the length of a mortar line the visual system then senses a periodic variation in just where the borders of the mortar are, and the line looks like a twisted-cord array.

In 1979 Bernard Moulden and Judy Renshaw of the University of Reading tackled the Munsterberg illusion with an idea from Hermann von Helmholtz, one of the 19th century's pioneers in vision research. When a bright white region adjoins a dull black one, their border is perceived as being shifted into the black region, an effect called irradiation. Such edge migration could account for the apparent vertical flaring of the end of a white region that is surrounded on three sides by black tiles. The opposite end, with white tiles above and below it, does not undergo this perceptual widening. The variation in the positions of the top and bottom edges of the white tiles thus creates local tilt.

Still another approach was taken in 198 3 by Mark E. McCourt of the University of California at Santa Barbara. He considered an effect called brightness induction, in which the horizontal variation of bright and dark tiles in the cafe-wall array subtly alters the apparent brightness along the horizontal mortar lines. The mortar between dark sections of tile seems to brighten slightly and the mortar between bright sections seems to darken. The apparently darkened mortar connects two dark tiles along a slant, and the apparently brightened mortar connects two bright tiles along a parallel slant. The region along a mortar line then resembles a twisted-cord array.

A supporting experiment revealed that if you darken and brighten the mortar lines so that they actually vary periodically in brightness, as in the bottom illustration at the right, the cafe-wall illusion is stronger than normal. Also, if the mortar is replaced with bright and dark lines that actually slant between tiles of equal brightness, the illusion is stronger still.

M. J. Morgan of University College London and Moulden may have hit on the best explanation of the cafe-wall illusion in 1986. They relied on a vision model that has been gradually crafted in the past 25 years. Particularly influential in the development was the late David Marr, who worked at the Massachusetts Institute of Technology. I shall first outline a simple version of the model, concentrating on the retinal processing and leaving out the mathematical details, and then return to the illusion.

Marr argued that the early stages in the visual pathway construct a "raw primal sketch" of the reality being viewed. The sketch lacks the richness of the actual scene but has blobs, bars, terminations and segments of edges that roughly map real objects. To construct the sketch, the early visual processing by the retina and the brain identifies the sharp changes in brightness that correspond to edges.

The processing begins in the retina when photoreceptors absorb photons and then send signals through bipolar cells to ganglion cells [left]. Each ganglion cell responds to a particular set of photoreceptors that are spread over a small circle, the cell's receptive field.

(The illustration shows only a few of the photoreceptors.) The field is partitioned into a center and a surround that respond antagonistically to determine the net response of the cell when the field is illuminated.

The strength of a signal from a ganglion cell is the rate at which it fires impulses deeper into the visual system. An unilluminated cell fires slowly, at its "resting rate." Suppose only the center photoreceptors are illuminated. One type of cell, called an on-center cell, increases its firing rate while other type, called an off-center cell, turns off. If only the surround is illuminated, the changes are just the opposite: an on-center cell turns off while an off-center cell fires faster than its resting rate. If both the center and the surround of either type of cell are illuminated equally, the cell may fire just a little more frequently than its resting rate.

Suppose an edge separating bright and dark regions falls across the retina [see illustration right]. In the even illumination on the bright side, both on-center and off-center cells fire either at their resting rate or somewhat faster. On the dark side, both types of cells fire at only their resting rate. The cells that straddle the edge are more active. Any on-center cell whose center is in brighter light than one side of its surround fires vigorously; so does any off-center cell whose center is in dimmer light than one side of its surround. The signals from the two types of cells are sent separately along the visual pathway but are eventually brought together when oriented edges are added to the raw primal sketch. If the on-center cells are active in one place on the retina and the off-center cells are active nearby, there must be an edge between the two sets-and so an edge is added to the sketch.

Marr contended that the output of a ganglion cell is a measure of how rapidly the variation in brightness changes across the receptive field. If the illumination is uniformly bright or dark or changes gradually, the cells fire at their resting rate or only slightly faster. But if the variation in illumination changes abruptly, as it does at an edge, certain cells are much more active, namely the on-center cells on the bright side of the edge and the off-center cells on the dark side. When you see a narrow dark line, two edges are detected and the interior of the line activates off-center cells, whereas just outside the line on-center cells are activated. When you see a narrow bright line, the distribution of activity is the opposite.

Morgan and Moulden applied the Marr model to the cafe-wall and Munsterberg illusions. Consider the cafewall illusion when the mortar has intermediate brightness. The uniformly bright or dark interiors of the tiles generate weak ganglion signals. These regions are gray in the illustration at the left. Stronger signals come from the edges of the tiles and the mortar. Where the mortar separates bright sections of tile, the relative darkness of the mortar activates off-center cells. The line of off-center activity connects with the edges of images of dark tiles, where there are also strong off-center signals. These regions are black in the illustration. Where the mortar separates dark sections of tile, the relative brightness of the mortar activates on-center cells. The line of activity connects with the edges of images of bright tiles, which also generate strong on-center signals. These regions are white in the illustration. (Do not take the gray, black and white of the illustration literally. The shading is meant to represent signal strengths; the true shading that you perceive is probably added at a later stage of the visual system.)

Note that in the illustration the regions of strong on-center and off-center signals form a repeated pattern that resembles two or three steps. The steps climb to either the left or the right, forming a slightly tilted composite. The tilt means that when edges are added to the raw primal sketch, they will be slightly tilted along the mortar line. The repetition means that the local tilt generates a global tilt, as in the case of the twisted-cord array. The illusion works not because there is local tilt in the array but because the processed signals make the raw primal sketch of the mortar line look as if it came from tilted elements.

You may find the explanation to be a long reach, but it accounts quite neatly for the illusion's dependence on the brightness of the mortar. If the mortar is just as bright as the bright tiles, the off-center signal from where the mortar separates bright tiles is missing, and the resemblance between the ganglion-processed patterns of the array and a twisted-cord array is weaker. If the mortar is even brighter, those regions have strong on-center signals, and no illusion appears.

If the mortar is as dark as the dark tiles, the illusion of convergence is weaker and perhaps even absent, because there are no on-center signals from where the mortar separates dark tiles. If the mortar is darker still, off-center signals are generated at the line of separation and the illusion is certain not to appear.

The irradiation seen in the Munsterberg illusion may also incorporate another artifact resulting from edge location. In 1984 Morgan, Moulden, G. Mather of University College London and R J. Watt of Reading suggested that irradiation is due to a nonlinear response to light in the early part of the visual system. Although the site was not specified, presumably it is at the photoreceptors, the bipolar cells or their myriad interconnections. The term "nonlinear" means that if the brightness of the light is changed by a small increment, the corresponding change in the visual system's response is different depending on whether the light is bright or dim. The nonlinear response alters the ganglion cell's "measurement" of the rate at which the brightness varies across its receptive field, and as a result the edge seems to be shifted slightly into the dark region.

There are several variations of the Munsterberg illusion; two, published in 1978 by R H. Day of Monash University in Australia, are shown at the left above. The first one is a stripped-down version of the illusion, in which the middle line appears to tilt with respect to the top and bottom lines, which are actually parallel to it. In the second version the offset of the tiles varies | from row to row.

Day also published an older array, seen at the right above, that produces what is called the kindergarten illusion. He added a note about an unpublished observation made by Gregory, who pointed out that although the kindergarten array resembles the Munsterberg array, when the two are constructed with equally bright colored tiles the kindergarten array retains some sense of convergence, whereas the Munsterberg array does not. Perhaps some other mechanism plays a role in the powerful kindergarten illusion.

Another illusion of convergence was published in 1980 by Steve P. Taylor and J. Margaret Woodhouse of Cardiff, Wales [see illustration below]. When the same line serves as the border of two adjacent square outlines, no illusion appears (left), but when adjacent borders are formed by two distinct lines, there is a sense of convergence (middle). A stripped-down version is also shown (right); the array resembles a twisted-cord array even though there are no explicitly tilted elements. I find that these bare-bones designs exhibit tilt (with respect to long, freestanding parallel lines) even if they are arranged in a column or placed on a page at random. In 1985 Paola Bressan of the University of Padua demonstrated that the illusion of convergence disappears if the lines in the stripped-down version are made too thin or too thick.

I think the illusion must have to do with how the lines are mapped in the visual system's raw primal sketch. If they are too thin, they are represented by horizontal lines. If they are too thick, their details are more faithfully mapped with edges that retain their horizontal structure. But if they are of intermediate size, they are mapped with tilted bars that approximate their shape without the details. Later the details are added, so that you finally perceive the stacked lines, but the impression of tilt lingers.

You might search for the various illusions on tiled walls or in graphic designs and modern art. I wonder, incidentally, how many times a graphic design has had to be drawn wrong-or a tiled wall redesigned-in order to look right!

Bibliography

BORDER LOCKING AND THE CAFE WALL ILLUSION. Richard L Gregory and Priscilla Heard in Perception, Vol. 8, pages 365-380; 1979.

VISION: A COMPUTATIONAL INVESTIGATION INTO THE HUMAN REPRESENTATION AND PROCESSING OF VISUAL INFORMATION. David Marr. W. H. Freeman and Company, 1982.

THE MÜNSTERBERG FIGURE AND TWISTED CORDS. M. J. Morgan and B. Moulden in Vision Research, Vol. 26, No.11, pages 1793-1800, 1986.

FURTHER STUDIES OF THE CAFE WALL AND HOLLOW SQUARES ILLUSIONS. J. Margaret Woodhouse and Steve Taylor in Perception, Vol. 16, pages 467-471; 1987.

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