Studies in Visual Perception, III
An Analysis of the Cafe Wall Illusion.

by Jack Schwartz

Courant Institute of Mathematical Sciences. New York University

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The famous and much-studied Cafe Wall illusion, introduced in the paper "Border locking and the Cafe Wall illusion" by Richard L. Gregory and Priscilla Heard, Perception, 1979, v 8, pp 365-380,available on line at [get paper] seems never to have been fully understood. In the cited paper Gregory and Heard try to explain the illusion using a notion of 'perceptual locking', and make the enigmatic observation
"When the tiles are displaced by half a tile width in alternate rows, the locking across the mortar only occurs where half a light tile faces half a dark tile (b in the figure). Where the light halves face, and where the dark halves face, the locking will not be across the mortar, but only on their own tileŅmortar borders (a and c in the figure). There are therefore different locking signals along the length of each bright and dark tile, producing wedge-like distortion of the tiles."

However one interprets this suggestion it is hard to see how it can account for the illusion's most central feature, the direction in which the mortar lines are perceived to slope, as seen in the following figure, and (in another variant) on Figure 4. In this paper and its accompanying figure we will offer another account of the illusion, attempt to buttress this account with convincing demonstrations,and offer some observations on the potential utility of this illusion and others derived from it as a tool for elucidating an important issue in visual psychophysics, the behavior of the visual system's direction (slope) detecting mechanisms.

The basic form of the illusion is shown in Figure 1.

Figure 1. The basic Cafe Wall Illusion.

An important and revealing property of the illusion, reported by Gregory and Heard, is that it is seen only if the 'mortar' lines between the 'bricks' in the figure are intermediate in luminance between the 'dark bricks' and the 'light bricks, disappearing if the mortar is either darker than the dark bricks or lighter than the light bricks. This is shown in the following animation.

Figure 1b. Luminance dependencies in the Cafe Wall Illusion.

As noted by Haig (see Haig, N. (1989) "A new visual illusion, and its mechanism," Perception, v. 18, 333-345) a closely related illusion can be given a 'gradient' form seen in our next figure.

Figure 1c. A 'gradient' variant of the Cafe Wall Illusion.

Why, and from what, does this curious perception arise? Is it a global property of the image seen, or does it arise, in a manner not immediately apparent, from particular image micro-elements? To begin answering this question, let us first ask whether the illusion is orientation sensitive. Is it affected by a 90 degree rotation? Figures 2 and 3 show that it is not affected either by such a rotation or by a rotation through a randomly chosen angle. Thus the illusion is rotationally invariant.

Figure 2. Cafe Wall Illusion turned vertically.

Figure 3. Cafe Wall Illusion tilted.

Figure 4 shows that the illusion is basically one of slope, so that the remark of Gregory and Heard on 'wedge-like distortion' is beside the point.The 'wedges' in figure 1 are formed simply because alternating horizontal lines are perceived to slope in opposite illusory directions. Figure 5 confirms the fact that the illusion is rotationally invariant in this version also.

Figure 4. The 'Progressive' Cafe Wall Illusion.

Figure 5. 'Progressive' Cafe Wall Illusion turned vertically.

Given the rotational invariance of the basic Cafe Wall effect, it should be clear that the 'Progressive' Cafe Wall Illusion can be developed circularly, as in the following figure. When this is done, it becomes quite impossible to see without mechanical aid that the apparently spiral lines in the figure are actually perfect circles. The slope illusion is strong enough to falsify the topology of the image.

Figure 6. A circular version of the Cafe Wall Illusion.

In light of the above, suspicion concerning the source of the Cafe Wall illusion turns to the image micro-elements which break symmetry most drastically, the T-shaped junctions seen in all the preceding figures. The animation we give next would seem to confirm this guess. When the junctions are seen the illusion is present, when they are hidden it is absent.

Figure 7. Blotting out some of the critical elements of the Cafe Wall Illusion.

To confirm the account of the Cafe Wall illusion that Figure 7 suggests, we should blot out all elements of the illusion except the immediate vicinity of the suspect T-junctions, and see if the illusion persists. This is done in our next figure, which sows quite plainly that the illusion does not survive this manipulation. Even though the upper part of the figure shows some definite instability of slant, the characteristic Cafe Wall 'wedges' are barely, or not at all, present. Thus some feature of the figure other than the obviously important T-junctions must play a role.

Figure 8. Removal of all Cafe Wall elements other than the T-junction neighborhoods.

We can attempt to identify this 'second influence' by blotting out features of the original Cafe Wall figure a bit more cautiously, as seen in our next figure. (Oval blots are used to avoid the strong direction cues that rectangular blots might carry.) It will be seen that after this degree of surgery the illusion of slant is weakened,but definitely not absent. Thus it must be the edges of the bright and dark rectangles near the horizontal 'mortar' lines, and not either the center of these rectangles or the vicinity of the vertical mortar line, that carries the visual feature that we are trying to track down.

Figure 9. Removal of other Cafe Wall elements seen to be non-critical.

To progress further,we turn to examine a related but easier case, that of the so-called Fraser or 'twisted cord' illusion, seen in the following figure.

Figure 10. The basic 'twisted cord' illusion.

Note that, like the Cafe Wall illusion, the twisted cord figure has a 'progressive' version, shown in our next Figure.

Figure 10b. 'Progressive' version of the 'twisted cord' figure.

An obvious theory can be offered for the illusion of slope that appears in these figures. The horizontal lines seen contain obvious sloping elements. In the theory being explored in the present series of papers, these will cause a strong reaction in the visual map which detects slope at the angle of these elements, and so will appear as 'bright spots' in this 'slope image'. When this map is combined, in preparation for the integration of internal visual system lines, with the simultaneously present intensity image, in which the horizontal lines in the Fraser image appears without breaks, it will be found that this second image is in register with a slant mage not too far distant from it in overall slope. Since this is standard evidence for the presence of a slanted line, a slanted line percept will be generated.

To refine this account of the twisted cord illusion we need to note another of its properties, which is revealed on comparison of Figure 10 to the two following figures. The comparison shows that the illusion of global slope disappears, or at any rate is very greatly weakened, if the background is either lighter than or darker than both of the elements of the cord. Although this is the exact opposite of a property of Glass figures noted in an earlier paper of this series, we can account for it in much the same way. When the background is intermediate in intensity between the light and the dark cord elements, these elements are, in our theory, processed independently and in parallel, one by an assumed dark-dots channel and the other in a matching but separate light-dots channel.

Figure 11. The twisted cord figure against a white background.

Figure 12. The basic 'twisted cord' figure against a black background.

We can imagine the neural image formed in the dark-dots channel as that obtained by taking the minimum of the intensity of each pixel with the average intensity of the nearby background. Thus, when the background is intermediate between the two cord elements, the dark-dots image is something like that shown in Figure 13, and the light-dots image something like that shown in Figure 14. Thus, precisely because these two channels are separated, clear and compatible slant percepts can be generated in both of them. If the background is either lighter than or darker than both cord elements, a horizontal line will be seen in one of the dark-dot and light-dot images, and the other image will be empty. Thus no clear slant image will be formed in either. This reasoning shows us that because the twisted cord illusion is only visible when its light and dark elements are separated, while Glass swirl is only visible when its light and dark elements are not separated,they will respond in exactly opposite ways to changes in background intensity.

Figure 13. Putative dark-dots image when the twisted cord figure against an intermediate gray background.

Figure 14. Putative light-dots image when the twisted cord figure against an intermediate gray background.

The foregoing discussion suggests that for the Cafe Wall illusion to develop, it is necessary both that micro-perceptions of slant be generated at the T-junctions (which are the only elements that break the left-right symmetry of the figure), and that the horizontal lines be broken up in the dark-dots and light-dots images whose 'early' processing precedes the assembly of full edges, to prevent a countervailing signal representing horizontal orientation from becoming too strong. When the mortar lines are intermediate in luminosity between the dark and the white squares, this cannot happen between two dark squares, since there the mortar line is seen as light; nor, ipso facto, between two light lines. Hence the crucial areas for mortar-line breakage in the light and dark areas must be where it lies between a dark and a light square. This consideration leads us to expect that if we obliterate this contrast the Cafe Wall slant will disappear, even if the T-junctions remain visible. The following figure tests this expectation.

Figure 15. Masking of horizontal mortar sections between light and dark rectangles

Its well to check the conclusions emerging from the preceding discussion by verifying that the Cafe slant is not strongly affected if we blot out all but the figure elements which the preceding discussion has identified as essential. Our next figure does this.

Figure 16. Masking of all inessential elements of the Cafe Wall image.

Note that the preceding figure would seem to agree poorly with any 'bandpass' account of the origin of the Cafe Wall illusion.

Finally, to verify the controlling influence of the T-junctions, and the fact that they fully determine the perceived direction of slant, we show a kind of 'image graft' in which the T-junctions of the ordinary Cafe Wall illusion are superposed on the checkerboard pattern that ordinarily would produce the 'progressive' form of the illusion.

Figure 17. Superposition of the T-junctions of the ordinary Cafe Wall illusion on the checkerboard taken from the 'progressive' form of the illusion.

Before concluding we must comment on one essential aspect of the situation which the preceding discussion has been glossed over. We have noted that the T-junctions of the Cafe Wall illusion determine its local tendency to give rise to a sensation of slope, but not explain why, or what rules apply to determine he direction of this slope. The empirical rule can be stated simply. At each T-junction, three regions will meet. Two, therefore the majority, will be of one luminance level relative to the horizontal mortar line; the third, therefore the minority, will be of the opposite polarity relative to this line. The illusory slope always seems to turn the nominally horizontal mortar line a bit into the minority area. The preceding analysis suggests that the luminosity of the vertical mortar lines is irrelevant to the slant effect, a conclusion which our next figure confirms.

Figure 18. Effect on the slant illusion of varying the luminosity of the vertical mortar lines.

This observation,and the preceding discussion, suggest the following explanation for the tendency of the T-junctions to create a local slant percept. Consider the light-dots image, which is obtained by representing the average background luminance as grey, and brightening every pixel darker than this until it becomes this background grey. In this transformed image, the black-to yellow T-junction seen at the left of the following figure will appear in the light-dots (resp. dark-dots) image in the transformed version shown in the middle (resp.on the right) of the following figure. Note that the light-dots image contains a 'step' from which an appropriate slant micro-percept could develop. The same is true, mutis mutandis, at junctions where two bright and one dark rectangles meet.

Figure 19. Putative 'light-dots' and 'dark-dots' versions of the T-junction image shown on the left.

In their influential discussion of the Cafe Wall illusion (which they refer to as the 'Munsterberg figure'), Morgan and Moulden (see Morgan, M. J. and B. Moulden, (1986) "The Munsterberg figure and twisted cords," Vision Research, 26, no. 11, 1793-1800) remark that 'The critical part of the mortar line is where it divides regions of the same color... Removing the mortar line between same color squares, and replacing it with the color of the squares, abolishes the Munsterberg entirely, whereas removing it between opposite color squares, and replacing it with either color, has very little effect." The analysis and demonstrations given above contradicts this very directly.They attempt to explain the Cafe Wall illusion by holding that early stages of visual processing, perhaps directly retinal contrast processing using the imagined 'difference of Gaussians' image differentiator proposed by Marr and Poggio as an edge finder, convert it into a hidden version of the twisted cord figure. In support of this, they exhibit various interesting images derived from the Cafe Wall figure by filtering. However, their most significant figure (their Figure 3) shows the claimed twisted cord elements only somewhat indistinctly in the 'mortar' regions of the filtered image lying between bricks of opposite color. It is not clear that this account can carry much conviction.


Since the Cafe Wall illusion is intensity, not color, dependent, we can assign random colors to its bricks, as long as the resulting brick luminance does not bring the brick to the other side of the general mortar luminance. This allows disruption of the visual cues which give the standard form of the illusion a certain sense of geometric regularity. This makes it much easier to misperceive the figure's topology, and to develop a perception in which the horizontal lines seem to be crossing somewhere just out of one's field of view. The following figure shows such a 'motley' wall.

Figure 20. The Cafe Wall Illusion made more incoherent by the use of colors.

Gregory and Heard note various interesting scale dependencies of the Cafe Wall illusion. These deserve additional investigation. Some of them are illustrated in the following figure.

Figure 21. Various rescalings of the Cafe Wall Illusion.

If the cord elements in the twisted cord illusion are shown in a two-frame animation loop, directly in the first frame and intensity-reversed in the second, a curious tristable illusion calling for explanation develops. The cord elements can be seen either within a chaotically changing field, or moving smoothly, either to the right or to the left, but neither for long. When the smooth motion percept appears the chaotic noisiness of the motion field often seems to drop substantially. The following animation shows this effect.

Figure 22. A motion illusion developed from the twisted cord figure. (See comments above)