Hermann grid illusion

The Hermann grid illusion in its classical form is a grid of horizontal and vertical white bars on a black background. At the cross-section of the white bars, you can detect little grey spots, who disappear the moment you focus on them.

The illusion was first described by Ludimar Hermann (1838-1914) in 1870, who noticed it while  looking at some illustrations. You can view one of the original images in Lingelbach & Ehrenstein (2002). Sometimes the illusion is also called the Hering illusion (or combined Hermann-Hering illusion) because the illusion was first generally recognized by the public through the publication of Hering in 1920.

There are lots of variants in which the illusion sometimes increases or decreases or in some cases even disappears. You can see a few of them in the following Flash-animation.

• In variant 1, you can see grey smudges with white bars on a black background, as well as white smudges with black bars on a white background or with coloured smudges on a coloured background (see variant 2). The colour of the smudges is the same as the colour of the background.
• The illusion exists over a very large variation of width and number of bars. Variant 3 shows a grid with 9 (large), 36 en 100 (small) squares. According to Wolfe (1984), the illusion should be stronger with increasing number of bars with a maximum of 64 cross-sections (9 x 9 bars). Chaderjian (2002) finds no evidence for this.
• The illusion appears to be strongest with a ratio of 3:1 (black bars of width [3] against white bars [1]). In variant 4, you can manipulate this ratio for yourself and check if this is the case for you.
• The effect becomes more apparent by increasing the contrast between the vertical and horizontal bars but only if the vertical bars are placed in front of the horizontal ones and thus interrupting the white bars (see variant 5). The same effect appears with coloured bars but also here the coloured bars should be placed in front of the white ones (see variant 6).
• The illusion decreases but not vanishes if the grid is turned by 45° (see variant 7) or if you use curved bars (see variant 8).
• In variant 9 you see a succession of (only) horizontal white bars on a black background, followed by (only) vertical white bars. The quick succession integrates the image, causing gray spots to appear at the intersection of the virtual cross-sections.

Chaderjian, M., Price, J.M., & Parksa, T.E. A global factor in the Hermann grid illusion or an artifact? (2001) Psychonomic Bulletin & Review, 8, 70-72. [original text on the website Psychonomic Bulletin & Review (http://pbr.psychonomic-journals.org/content/8/1/70.full.pdf+html) on 08-04-2009]

The classical explanation (that you can find in virtual every handbook about perception) is based on the concept of receptive fields. Because many phenomena can’t be explained by this theory, an alternative explanation is given by Schiller & Carvey (2005).

The retina is organized in receptive fields; for more details: see a separate post. These are circular areas of light receptors (rods and cones) who control a neuron (ganglion cell). The receptive field of a neuron is thus that region of the retina in which light affects its activity. These ganglion cells are connected to cells in the brain for further analysis of their output. The receptive fields in the retina look like a donut with a centre and a surround. When light falls on the center, the ganglion cell will be excited (fires more). When light falls on the surround, the ganglion cell is inhibited (fires less). If light falls on both the center and the surround or outside the receptive field, nothing happens with the ganglion cell. The size of the receptive fields differ quite a lot. At the fovea, the central part of your vision, they are small. In the peripheral part of your vision , they are large.

So, why do you see grey spots at the section of the white bars in the grid? Look at figure 2. Let’s suppose that you focus at the cross at the right of the image. The receptive fields a t that location are quite small (you do focusing by bringing the projection of the object at the fovea). You can see them in the lower part of the image. It doesn’t make any difference if the receptive field falls at the intersection or at the non-intersecting parts of the image. Surround and centre are equally stimulated. At the left of the image, you will see some grey spots. At the bottom, you will find the receptive fields, which are much larger, because the projection of that part of the image falls in the periphery of your retina. Because the receptive fields are so big, there is a difference in output for a field that falls at the intersection of the vertical and horizontal white bars, compared to a field that falls in the street. The inhibition of the surround is much greater at the intersection because it is partly stimulated by the white bars. At the fovea, the receptive fields are small, so there is no difference between the one who falls at the intersection or in the street. Below, I have enlarged a little bit the image. centre of the image. The black squares on the left and the right of the figure are now in the peripheral part of your visual ; meaning the there are large receptive fields with lots of receptors. Suppose that there is a receptive field at the cross-section. Because this is a receptive field in the periphery, it is lare and it will cover the white cross-section but also parts of the black squares. The centre of the receptive filed will excite the ganglion cell. The surround will partly inhibit the ganglion cell because light falls on small parts of the black square. The net result of this combined excitation and inhibition is an impulse of the ganglion cell. This impuls is however smaller than in case of a receptive field at street because the surround is less stimulated than in case of the cross-section. In the fovea however, we have much smaller receptive fields (comparable in with C & D in figure). Because centre and surround are equally stimulated in the cross-sections in the street, there will be no contrast.

This explanation has several flaws and cannot explain certain phenomena (e.g. variant xx). You should for example expect that the width of the witte and black bar are determining for the illusion (very wide white bar will cover the entire receptive field in the central and peripheral part of the retina. Variant 3 and 4 show that this is not the case. Also colours are difficult to explain because that would imply the there exists receptive field with colour antagonism. It is also unclear why a rotation of 45° will decrease the illusion. It has no implication on a circular receptive field.