Hermann Grid

Grid Illusions

hermannGrid


The widely known Hermann-grid illusion (Hermann 1870).

Dark patches appear in the street crossings, except the ones which you are directly looking at.

Rather weak, but in every textbook…

See below for the classical explanation. HOWEVER: see the next page for a convincing rejection of this explanation.

 

[This page is also available in Czech language.]

HermExplanation Baumgartner The classical explanation

1. Why do we see the dark patches?

Look at the left part of the left diagram and assume an on-center retinal ganglion cell. Its receptive field is indicated by the reddish disk. When the ganglion cell is, by chance, looking at the grating so that its centre ('+') is positioned at a crossing (left-top), there are 4 bright patches in the inhibitory surround. A ganglion cell looking at a street (left-bottom) however only gets 2 inhibitory patches, so it will have a higher spike rate then the one at the crossings. This was measured by Baumgartner (1960) in Freiburg, see picture on the right.

2. Why don't we see the patches when we look right at them?

Because then we direct the fovea at the crossings, and in the fovea the receptive fields are much smaller (see the small reddish disks on the right of the left figure). With such small receptive fields it obviously does not matter whether they are at the crossings or not.

3. Why is this explanation, so plausible it sounds –and it is in every textbook– not the full story?

See the next page for a simple refutation.

Sources

Hermann L (1870) Eine Erscheinung simultanen Contrastes. Pflügers Archiv für die gesamte Physiologie 3:13–15

Hartline HK, Wagner HG, Ratliff F (1956) Inhibition in the Eye of Limulus. J Gen Physiol 39:651–673

Baumgartner G (1960) Indirekte Größenbestimmung der rezeptiven Felder der Retina beim Menschen mittels der Hermannschen Gittertäuschung. Pflügers Arch ges Physiol 272:21–22

Spillmann L (1994) The Hermann Grid Illusion: a Tool for Studying Human Perceptive Field Organization. Perception 23:691–708

Lingelbach, B & Ehrenstein, WH Jr (2002) Das Hermann-Gitter und die Folgen. DOZ 5:13–20, www.leinroden.de/304herfold.htm

Corney D, Lotto RB (2007) What Are Lightness Illusions and Why Do We See Them? PLoS Comput Biol 3:e180
This interesting paper shows that the Herman grid illusion “automatically” occurs as a by-product when an artificial neural network is trained for brightness constancy.

Bach M (2008) Die Hermann-Gitter-Täuschung: Lehrbucherklärung widerlegt. Der Ophthalmologe


Advice by Bernd Lingelbach gratefully acknowledged.   

Created: 1999-Jul-18


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Last update 2014-06-15 by Michael Bach (G+)