Last modified: 2014-10-19 19:22:25 UTC
Created attachment 8693 [details] Comparison of four renderings of the Gradient Theorem, http://en.wikipedia.org/wiki/Gradient_theorem Web images are invariably stored in a gamma-compressed format. If the wrong gamma compression is applied to antialiased text, then in addition to the text appearing too light/dark, other distortions may be apparent. The dvipng command line in render.ml specifies --gamma 1.5. This causes an *extreme* darkening of the rendered equation, but also causes several other visual artifacts (enumerated below). The "ideal" gamma setting to use is 0.454545 (1/2.2), as referenced by the sRGB standard. Of course, that also generates far lighter text, and that too must be taken into account. (I suppose having an excessively dark gamma may aid readability on smartphones that resize everything.) The attached image contains four different renderings of the same equation, available at http://en.wikipedia.org/wiki/Gradient_theorem: 1) Straight-up copy of the png as downloaded from wikipedia. Ostensibly, this image came from texvc. 2) Attempted reproduction of 1) using "dvipng -D 142 -T tight --strict --gamma 1.5". This appears to be a fairly good reproduction. 3) "Ideal" rendered output: dvipng is run at 2400dpi (!), resized down to 142dpi in ImageMagick, and then gamma-compressed. Steps: a) dvipng -D 2400 -T tight --strict b) ImageMagick convert -depth 16 -define filter:filter=Box -resize 226x49 -gamma 2.2 -depth 8 (resize geometry chosen to shrink image size by 2400/142=16.9x) 4) Reproduction of 3) using dvipng -D 142 -T tight --strict --gamma 0.454545. This looks very close to 3). Comparing text samples 1 and 2 ("gamma 1.5") vs 3 and 4 ("gamma 0.45") on my LCD displays, I observe the following: * Obviously, gamma 1.5 output is darker. * The bold symbols q, p, r are of comparable weight at both gamma 1.5 and 0.45, while all the other symbols are much lighter at gamma 0.45. This makes it substantially easier to perceive the boldness of these symbols at gamma 0.45. * Notice in gamma 1.5, the integral sign is visibly jagged down its center, even when viewing it from a distance. Similarly, the parentheses appear "chunky". These appear much smoother at gamma 0.45. I would opine that, at the very least, developers make the gamma setting a configurable option. But beyond that... have developers given any thought towards lowering the gamma setting from 1.5?
Created attachment 8694 [details] 2400dpi equation image For reference, here is the high res (2400dpi) version of the equation, which was resized to create 3) in the four-sample image previously attached.
You're definitely right that the current rendering looks way too dark and the antialiasing looks pretty bad... but the 2.2 gamma seems much too light to me for on-screen reading, probably because many thin strokes are much thinner than one pixel at this size. I suspect the darker gamma got picked because darkening the antialiased thin strokes effectively makes them appear "wider", making the text overall more legible. Are there alternate font rendering settings or even alternate fonts that might be better for screen-oriented rendering? (Of course moving forward we may also want to be thinking about better in-client rendering to aid legibility on high-resolution displays and printing directly from the wiki. There are various MathML/SVG/scary HTML roads that can be taken there, all of which will be more work than tweaking the latex settings. :)
Created attachment 8696 [details] Comparison of four renderings of the Gradient Theorem, http://en.wikipedia.org/wiki/Gradient_theorem Includes original four samples referenced in original bug report, plus screenshot of same equation rendered in Adobe Acrobat.
Created attachment 8697 [details] Comparison of dvipng output, gammas 0.5-1.5 dvipng output at gamma settings 1.5, 1.4, 1.3, 1.2, 1.1, 1.0, 0.9, 0.8, 0.7, 0.6, 0.5, plus Acrobat screencap for comparison.
There are a few knobs that could be tweaked on the TeX side of things, in decreasing order of potential magnitude: * Computer Modern is known to be a really light font on the screen, and there are a few potentially darker alternatives. A really good overview of the math font selections available for TeX is at http://mirrors.med.harvard.edu/ctan/info/Free_Math_Font_Survey/survey.pdf. There's also the LaTeX Font Catalogue at http://www.tug.dk/FontCatalogue/mathfonts.html. * The weight of Computer Modern does not scale proportionally with increasing point side -- strokes are relatively thicker at smaller point sizes. In principle, this means that you might be able to get a weightier font, looking better at gamma 2.2, by reducing the point size and increasing the DPI setting. But I don't know how big of an effect this has. * Various outline versions of Computer Modern are tweaked slightly differently, and some versions are considered darker than others. See for instance this discussion: http://arxiv.org/help/pscm. The only other particularly useful rendering alternative I'm aware of is dvips+convert, which of course already appears to be implemented. I haven't yet studied if that would generate any better of an output than dvipng does. (dvipng also appears to be applying the inverse gamma setting from what it should be, insofar as gamma 0.454545 *darkens* the image in any image editor.) Besides that, yeah, something like MathJax would also solve this issue by offloading the actual text rendering to the client. Certainly the darker gamma setting can be justified in terms of maximum compatibility, even if perhaps it wasn't necessarily chosen for that reason. And while gamma 2.2 might be "the best" in terms of lowest distortion -- ie, the closest representation of a high-resolution printout of the same equation -- given that we're talking about web pages and not printed pages, using a gamma significantly lower than 2.2 may be quite reasonable. There are always tradeoffs of course. --- On the subject of possibly selecting a better dvipng gamma setting, I have some new images: * I've replaced the original comparison image with a new one, with a 5th sample -- a screen cap of the equation PDF drawn in Adobe Acrobat. It looks great of course (it's kinda their job to look great hehe), but it also looks both much lighter than the Wikipedia rendering (#1) but much darker than my resized rendering (#3). * I've also uploaded a comparison of dvipng gamma settings from 0.5-1.5, along with the Acrobat rendering, to perhaps help select a new default dvipng gamma setting. Pay close attention to the integral sign between the Acrobat rendering and *any* of the dvipng renders for gamma >0.5 -- very interesting.
Great examples! :) On my screens I'm reasonably happy with the overall visible weight of the chars around the 0.8-1.0 range but the antialiasing still looks a bit nasty on those (while definitely not as bad as at 1.5). If we don't end up doing anything else I'd probably be inclined to go with changing the value into that range (but should try a few other renderings to make sure it doesn't get unreasonably light on other chars or smaller bits of text). This does though remind me of bug 16719 -- right now there's not a great system in place to manage updating old renderings other than changing the hashing such that all the old files get rebuilt on next parse (which can cause a CPU spike in production; not sure if that's still a concern for deployment at present).
Created attachment 8701 [details] Rudimentary specimen LaTeX document, using most of what is allowed to be used with the Math extension.
I tend to agree that the 0.8-1.0 range looks the best. I'd probably choose gamma 1.0, for the simple fact that.... it's 1. I've attached a rudimentary specimen LaTeX doc that covers most of the math symbols documented on Wikipedia, plus a few sample formulas. From there, I played with adjusting math fonts and sizes, to see if I could find anything significantly better than cm at gamma 1.0. Lemme know if you want these PNGs uploaded (they're big). I particularly focused on sans- serifs under the hopes of killing two birds with one stone -- I suppose that, while we're on the topic of esoteric typesetting issues, we probably shouldn't be pairing Computer Modern with whatever default sans-serif font is used for the rest of Wikipedia :) The Arev font looks *particularly* nice; even at gamma 0.5, it's quite weighty, yet has clearly distinguishable boldfaces. But it seems to have three or four significant rendering issues (specifically: capital "I", vertical var "|", and over/underbraces) and I'm not a big fan of the parentheses. If you can tolerate more blurriness, and 10-100x worse performance, you can make convert upsample the equation by 2-4x, resample with a Gaussian filter, then apply some ridiculously dark gamma setting. The filter's blurriness gives the gamma compression a lot of room to work in, and unsurprisingly, all of the rendering artifacts I originally mentioned vanish.
Created attachment 13502 [details] Right: Chrome showing SVG Left: Firefox showing MathML rendering
I would be happy about comments concerning the new rendering mode using svg and MathML demonstrated on http://math-test2.instance-proxy.wmflabs.org/wiki/Fourier_series
It seems that this is no problem in MathML rendering mode anymore.
