A graph that is made by perceiving it

The contrast sensitivity function shows how our sensitivity to contrasts is affected by spatial frequency. You can test it using gratings of alternating light and darker shade. Ian Goodfellow has this neat observation:

It’s a graph that makes itself! The image is the raw data, and by interacting with your visual system, you perceive a discontinuity which illustrates the limits of your perception.

Spatial frequency means how often things change in space. High spatial frequency changes means lots of small detail.  Spatial frequency is surprisingly important to our visual system – lots of basic features of the visual world, like orientation or motion, are processed first according to which spatial frequency the information is available at.

Spatial frequency is behind the Einstein-Marilyn illusion, whereby you see Albert Einstein if the image is large or close up, and Marilyn Monroe if the image is small / seen from a distance (try it! You’ll have to walk away from your screen to see it change).

The Einstein Monroe was created by Dr. Aude Oliva at MIT for the March 31st 2007 issue of New Scientist magazine

Depending on distance, different spatial frequencies are easier to see, and if those spatial frequencies encode different information then you can make a hybrid image which switches as you alter your distance from it.

Spatial frequency is also why, when you’re flying over the ocean, you can see waves which appear not to move. Although you vision is sensitive enough to see the wave, the motion sensitive part of your visual system isn’t as good at the fine spatial frequencies – which creates a natural illusion of static waves.

The contrast sensitivity image at the head of this post varies contrast top to bottom (low to high) and spatial frequency left to right (low to high). The point at which the bars stop looking distinct picks out a ridge which rises (to a maximum at about about 10 cycles per degrees of angle) and then drops off. Where this ridge is will vary depending on your particular visual system and what distance you view the image at. It is the ultimate individualised data visualisation – it picks out the particular sensitivity of your own visual system, in real time. It’s even interactive, instantly adjusting for momentary changes in parameters like brightness!

More on hybrid images (including some neat examples): Oliva, A., Torralba, A., & Schyns, P. G. (2006, July). Hybrid images. In ACM Transactions on Graphics (TOG) (Vol. 25, No. 3, pp. 527-532). ACM.

More on the visual system, including the contrast sensitivity function: Frisby, J. P., & Stone, J. V. (2010). Seeing: The computational approach to biological vision. The MIT Press.

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