Hermann Grid, curving
Above you see the widely known Hermann-grid illusion with a new twist.
What to observe
When the grid lines are straight, dark patches appear in the street crossings, except
the ones which you are directly looking at. When the streets are curving, the dark
patches vanish.
What to do
You can make modifications to the figure as obvious from the button labeling. The
automatic “run” is useful to compare the patches with and without the curves, but
can get annoying, so you can stop it. I personally am amazed that a very small amplitude
of the modulating sinusoid already kills the patches.
Comment
This demonstration is based on the ECVP2004 contribution by
János Geier et al. (abstract
below).
If you are acquainted with the “classical” explanation of the Hermann grid (previous
page), it will be obvious to you that this demonstration immediately invalidates
that explanation – the inhibitory patches should exert the same influence whether
the streets are curved or straight.
I never found the receptive field explanation sufficient, because the convolution
with the receptive field occurs with every retinal image and must be removed
by cortical deconvolution anyway. The special thing about the Herman grid is the
failure of this deconvolution, IMHO.
An extensive critique of the “old” Hermann grid
explanation can be perused at Peter Schiller's lab.
Sources
Schiller P et al. (Mar 2004, guessing from the file dates) web.mit.edu/bcs/schillerlab/research/A-Vision/A15-2.htm
Geier J, Sera L, Bernath (2004) Stopping the Hermann grid illusion by simple sine
distortion. ECVP 2004, abstract:
Almost the only explanation of the Hermann grid illusion
is the Baumgartner model: the effect is generated by the response of cells having
concentric ON–OFF or OFF–ON receptive fields (ie a Mexican-hat weighting function).
This model predicts that the illusion is independent from the relative directions
of the right-angled intersections. Some authors (Wolfe, 1984 Perception 13:33–40;
for a review see Ninio and Stevens, 2000 Perception 29:1209–1217) show that the
magnitude –not the existence– of the illusion depends on certain geometrical properties.
We made some simple distortions to the Hermann grid that make the illusion disappear
totally while the Hermann-grid character remains. The most effective of these was
to replace the straight lines with sine curves leaving the intersections right-angled.
The illusion is found to disappear at a surprisingly small sine amplitude (amplitude/period
<1/10). We supported these results with psychophysical measurements (n=29). Simple
geometrical consideration shows that the distortions produced here do not change
the weighted sum of the receptive field. We conclude that the Baumgartner model
is not an adequate explanation of the Hermann grid illusion, because its prediction
is contrary to the observations. The same distortions applied to the scintillating
grid made the scintillations disappear.
Lingelbach B, Ehrenstein W (2004) Neues vom Hermann-Gitter.
Optikum.
Geier J,
Bernáth L, Hudák M, Séra L (2008) Straightness as the main factor of the
Hermann grid illusion. Perception 37:651–665
Bach M (2008)
Die Hermann-Gitter-Täuschung: Lehrbucherklärung widerlegt. Der Ophthalmologe
Created: 2005-01-01
Last update: 2013-10-04