creating an image like this from a font using fourier transforms

Ryan Maelhorn's picture

Reading Berkson's article on his Caslon Text over at ILT, I came across this fascinating image.

"Here the white bands show the frequency of the black running across the page, with the distance between the whites I believe being about the width of the n. (Thanks to Peter Enneson for the graphic.)"

Apparently this was generated from a font using Fourier transforms, but I can't seem to find much about exactly how this was done. I have been interested in images that convey information about type faces in an abstract and non-text way for some time now.

Ryan Maelhorn's picture

Still very interested in finding out more about this. In the meantime, here is an image that uses Futura in a 'abstract and non text' setting. What appeals to me is that it still exudes all the personality of a setting of Futura, without using words and individual letters.

The image is from "FUTURA by AG4," well worth watching in its own right.

enne_son's picture

Ryan, the graphic is just a slice. I actually did quite a few of these.
To give some background, see:
I'll give an overview of my work with fourier transforms and describe the photoshop plugins and filters I used in subsequent posts.


Ryan Maelhorn's picture

Looking forward to this, thanks Peter!

Ultimately I'd like to figure out some way of using this analysis method to provide qualitative feedback to a font designer while they are working on their font. I wonder if it could be used to identify "poorer" type design, and "better" type design?

Here are 2 images made from the same text. I attempted to make them as square as possible. The first uses a typeface I think most of us find "better" -- Gill Sans Medium. The second uses a typeface I think most of us find "poorer" -- Comic Sans.

I wonder how the resulting FFT derived and posterized images would be different between the two?

Note: In an attempt to make the 2 images as close as possible, I had to adjust the scale of the Comic Sans version both in width and height, as well as its' letter and word spacing.

hrant's picture

The further the two things you compare, the harder it is to draw practical conclusions. Ergo: start with something as basic as comparing well and poorly spaced versions of the same font.


enne_son's picture

[Ryan] “Ultimately I’d like to figure out some way of using this analysis method to provide qualitative feedback to a font designer while they are working on their font. I wonder if it could be used to identify ”poorer” type design, and “better” type design?”

I think this is possible, but we need to establish what the benchmarks are. This might require a large comparative database, good theories about cortical integrational mechanics, and some sensitive tests for readability that go beyond basic reading speed. I think I have a decent handle on extracting spacing benchmarks from fourier transforms.

I discussed fourier transforms in a presentation I did some years ago. See:
starting on page 20
starting on page 6

The incentive for doing these was a discussion on typophile initiated by Raph Levien I believe, about typographical spacing systems currently in use based on different spacing algorithms implemented in page makeup software like InDesign and QuarkXPress. I believe this was in 2005 or earlier and led to:
What I was looking at was the amount of “phase alignment” of the vertical parts of strokes, as signaled by the structure of the brightest sections on the x-axis of the transforms. White means ‘lots.’ Phase alignment has to do with proportionality in the width-of-letters dimension and spacing combined. Well-set type by typographic standards typically results in a narrow phase alignment without strong competing harmonics (such as one should find in grating patterns, where auto-correlation is ubiquitous and the phase-alignment is absolute). If the phase-alignment is so narrow it causes competing harmonics, there is a picket-fence effect.

Phase alignment differs from type to type, but in all well-set type (by typographic standards), follows the same pattern:

It's characteristics also vary with weight (or boldness) and polarity:
I haven't isolated the issue of serifs / sans serifs or contrast (traditional, eg. garamond versus modern, eg. bodoni)

Here are more that relate to spacing:
Changing spacing causes a horizontal shift in phase, and effects how diffuse or sharp the phase alignment is. Presumably these values can be quantified. This is explored further here:
The choice of Mendoza in these test is somewhat arbitrary — I was using the face in one of my projects.

I concentrated on the information in the horizontal axis. Luciano Perondi (Italy) did some work with fourier transforms surrounding the question of even colour and irregularities in fonts for ATypI Helsinki in 2005. These factors would probably relate to other parts of the transforms than just the horizontal or vertical axis.

The black in the transforms is noise. I couldn't find a more sophisticated way to highlight the aspect I was looking for.

The work I did was in the frequency domain. Fourier transforms also put amplitude results in a separate channel. I tried to look at amplitude results for letters, words and extended text, but couldn't determine how amplitude results could be of use.

I hope these are of use.

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