## Sunday, February 15, 2015

# A Filter Darkly

Last week, this was making the rounds: I Am Sitting In
Stagram, an art
piece based on iterated Instagramming of
an image. With a nod to Alvin Lucier's sound piece *I Am Sitting In A
Room*, the idea
of reposting successive images to Instagram and using the resultant
degradation to aesthetic effect was inspirational.

For whatever reason, I Am Sitting In Stagram didn't appear to use the filters, which are the most dramatic and characteristic image modifications available in Instagram.

So I was inspired to iteratively apply the Instagram filters to see what would happen. For each image iteration, I only stopped when an additional filter application resulted in little or no difference You can see all the intermediate images in the fixed_points Instagram feed (modulo some weirdnesses when images didn't post, possibly because I hit invisible rate limits). In pretty much all cases this converged quite rapidly: within ten or twenty iterations. The results are "eigenimages" of the filters, and are pretty dramatic:

The original image (at top left) is "house" from the SIPI Volume 3 image test corpus. Clockwise, eigenimages of the Kelvin, Perpetua, and Sutro filters are shown. These exaggerate the more subtle effects of the filters: for example the Kelvin filter lightens and shifts the hues toward yellows and reds; the Perpetua has a high-pass filter that emphasizes edges, and the Sutro has a strong vignetting combined with a high pass, darkening, and hue flattening.

My favorite eigenimages are from filters that both mess with the color and blow out the center, such as the Rise, Sierra, and Hudson images below.

Mathematically, these resultant images are termed *fixed
points*
of the filter process; that is given a filter function F on an image
x, F(x) = x when x is a fixed point. Also F(x) = F(F(x)) = F(F(F(x)))
and so on. As a more concrete example, to find the fixed point of the
cosine function, start with any number and repeatedly take the cosine:
it will converge to a fixed point of cos(x) = x = 0.739085133. This
kind of invariance is an interesting and deep part of mathematics
(q.v. the Banach Theorem, and eigenvectors of a matrix transformation)
which I urge interested readers to pursue.

Above is an original B&W photo and three steps toward an eigenimage of
the "lo-fi* filter; it's intriguing how the filter manages to shift
the hue of a colorless image so that Tricky Dick ends up with a
glorious scarlet jacket. Finally I leave you with the following
eigenimage of the (appropriately enough) "77" filter. I was originally
going to use the *Lenna* image
beloved of image processors, but having been guilty of inadvertent
sexism
in past publications, I decided to change the status quo with:

Interested readers might note the title alludes to not only 1 Corinthians but Philip K. Dick's (the Immortal Bard?) *A Scanner Darkly*