If you find anything [convincing] please let me know... :-/

hhp

If I'd raster a scanned page of text to b/w bitmap,
how could I now how many black pixels it has,
how many white pixels it has ?

AS

You mean like with Photoshop? Hmmm. Try this:
1) Make the canvas much bigger, with your original image centered and on a white background.
2) Apply a ridiculous amount of Gaussian Blur.
3) Measure the gray level = GL.
4) Calculate: (GL / 256) x X x Y , where X and Y are the original dimensions of your image block. The result will be the number of white pixels in the original, within ~4% accuracy.

hhp

Or ask this guy to help:
http://www.malgil.com/esl/aldus-fft/

hhp

Thank you, Hrant.
AS

http://www.malgil.com/esl/aldus-fft/

This looks very intriguing Hrant. Colour and rhythm[s] together on one page. Fascinating how role-architectural components (stems and bowls, for instance) and role-architecturally evoked material (counters and the space between letterforms) fall in and out of phase on the df1.jpg, df2.jpg and df3.jpg images but the overall pattern is strictly rhythmic. Fascinating too how gradations of colour fluctuate across FFT-L-masked.jpg

Alessandro and Hrant,

To get an exact pixel count in Photoshop got to Image>Historgram. The 'Pixels' information is the total and the 'Count' is the number of pixels of that level/colour*. It's probably best to have a greyscale or duotone image so you don't have to deal with the colour channels. (I've got PS7)

Have fun,

Ed

*(Edit) Hold the pointer over the graph, click and hold to select a range of levels.

Well, this stuff about the Fourier analysis seems to be a very interesting and unseful trick but as a simple graphic designer I would appreciate very much a plain language explanation of what does this analysis shows and how else can this information be used if someone could find the time and the patience to show me.

Very interesting. I also am interested in ways to measure typographic color and especially evenness. I've read the fourier-paper but didn't full understand. Maybe someone can give me some hints:

Is there any way to measure the evenness (and so to be able to compare between different designs) of a page?
Or at least make a graphic that clearly represents evenness of a page ?

ms

"Is there any way to measure the evenness (and so to be able to compare between different designs) of a page? (Or at least make a graphic that clearly represents evenness of a page?

Perhaps http://www.malgil.com/esl/aldus-fft/FFT-L-masked.jpg is as close as this kind of analysis can get.
You can gauge eveness by looking for darker and lighter sections across each horizontal line, and also by observing fluctuations on a whole-textblock scale. (But see William Berkson's caveat on http://www.typophile.com/forums/messages/30/69117.html?1113399795 (his 975 post)
It would be interesting to see how Fourier transforms of 'oldstyle', 'transitional', 'modern' and san serif pages compare. I'll link the author of the site to our discussion.

Peter,
thank you for the link. I have read the bouma of space craft thread before but didn't update reading since April, 10, or since Fourier came in.

Maybe that's a typical german science attitude but isn't there any possibility to express more or less evenness in numbers?

I ask, because for my research in bible editions with lots of text (http://www.typophile.com/forums/messages/30/68372.html?1112329656) it could be a good way to make different editions more comparable from an objective stance. This would also be fine to give an understandable standard for non-typographers.

ms

Michael, I'm no expert in Fourier analysis. Raph probably has a lot more depth than I. But as I understand the work on the Aldine site, you can extract numerical statistics. Probably the person to ask (or collaborate with) is the author of the Aldine transform page.

Michael: my guess is that Fourier analysis could give a numerical result that correlated strongly with perception of 'evenness'. If you would like me to try to cook something up, what would help is, using your German* scientific brain, to describe as precisely as possible what you'd like quantified.

* meine Mutti ist auf Deutschland

Raph,
that's very nice of you :-)
At the moment my brain is locked, due to my duty at work.
But I will describe tonight or tomorrow morning what exactly I'd like to be quantified.

first hints:
1) It would be fine if it could be quantified which quality justified columns have (that's one of the easy things, that also could be done by measuring the gaps, but Fournier may have broader based results).
2) The quality of the used fonts (outline, spacing and so on) and micro-typography regarding evenness of the page.
3) There are different editions in which verse numbers are set in bold or to big, thus making the text page very uneven and so distracting concentration from the text itself.
4) I think of course the space outside the column will have its influence on the perception of evenness too, but for a comparison should be omitted.
5) Not at least: The opacity of the paper and evenness of baselines between front and back also takes influence on legibility/readability or quality of typesetting.

I have scans (not all yet) of about 40 to 50 different german editions of the bible (find a list of used fonts in the above mentioned thread "Paul Saenger").
And would, if possible, try, if there could be a measured objective confirmation (as an addition) of typographical observations. Also I would find it interesting if there could be something like a quality scale in which those quantification could be enclosed - and from which you could compare different editions.

Because I also want to try to bring awareness of skilled sophisticated typography to people, who don't know anything about typography, than "take Arial for your letters, it looks modern" - and those people often look at typographical questions as "that's a matter of taste " - a quantifiable look on evenness could help.

So it would be very interesting if you could cook something up.

ms

Ah, and of course:
I want to compare entire pages (as much as possible of the same part of the text).
And maybe additionally show, how different sorts of text take their influence on the appearance (and so should be taken in account in typographical decisions).

Where does your Mutti come from?

ms

Raph, sorry,

I have a lot of work at the moment, so it took a while to get back to my paper/thesis.

If Fourier analysis is capable of giving a numerical judgement on evenness of spacing it should as well be possible to measure the evenness of a whole column.
Of course then you have a mix of all: good spacing could be overrun by poor justification, as well as good justification by bad type spacing. And both by the use of bold verse-numbering within the text.
And of course fonts themselves have different values of evenness (it would be a very interesting thing to me to measure if Rotis is objectively mor uneven than other fonts - and how much).
But at least there should be a result for the complete perception of evenness.
Maybe in another step you could take out one factor by the other (maybe by filling white spaces with sample text or neutral color from the page itself and so measuring the evenness of type only).
I really don't know if results will be significant, and if Fournier analysis would lead to usable results, but I would like to try.

So maybe you can show me how to make Fourier analysis of a text column or cook something that can help.

Sprechen Sie auch deutsch?

Michael:

I think that Fourier analysis can give some numbers related to perception of 'evenness', but I doubt that any such mechanically derived number can replace or even come close to a panel of human experts. What Fourier analysis can do is to give you some spatial characteristics you can compare with your own evenness ranking; you'll be the judge of correlation.

Also, Fourier works best on stems, lines, and spacing; it is less usable for analysis of closed areas and round features - if you want numbers, you will need some other basis for those.

Sergei,

of course, I never thought mathematical analysis could replace human experts. I also much more rely on skilled human experts.
And I think a judgement of significance has to be done - and maybe at the end of testing the result will be that Fourier analysis or any other mathematical approach won't show anything.

I'm not keen for numbers - I only followed some trace that may lead to another confirmation of old human skills - and maybe my German scientific brain (-half) demanded food ;-)

There is/maybe one point I am setting some expectations on:

Human experts in typography are not regarded highly in our time. Especially by the millions of people who think with a computer they now can do the same things as learned typographers before.

I'm working with half of my time in the church. And though church has been a custodian of the word and long time also of the written form of the word, nowadays there is almost nothing left of skill and care.
Asking experts when setting printed matter is a rare exception. Often their judgement is taken as personal taste. If I tell sometimes "this or that layout is uneven" people don't believe because the edges of the column are mathematical straight. They look for things that can be measured. They don't see inner unevenness. It takes some time to open eyes (of course that's a job I like very much: open eyes for aesthetical decisions, care and skill for words and script).
And it would help, if there were a mathematical way to show: "Here you can see in an objective number, what experts already have said about that layout."
Maybe it would help to raise typographical awareness.

>Can anyone point me towards some reading on the topic of typographic color and how to design for optimal color when creating a text face?

Maths and theory are not the answer, Paul.
If you want to understand text color, I would suggest finding a sample of letterpress printing which you think is immaculate, and attempting to mimic it by recreating the typeface digitally, by eye, from scratch. That means looking at the printed type through a magnifying glass, rather than scanning it and tracing it.