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> * What gamma curve yields the perception of equal width of black-on-white and white-on-black thin lines (also relevant for text)? (Hint: likely not linear lum

> * What gamma curve yields the perception of equal width of black-on-white and white-on-black thin lines (also relevant for text)? (Hint: likely not linear luminance) Gamma curves do not affect black and white themselves, only intermediate grays. It’s true that grays are usually used to draw antialiased black and white lines, but we can also think about “ideal” (axis-aligned, pixel-centered, non-antialiased) black and white lines. By framing this as a question about gamma, you’ve implicitly assumed that “ideal” black lines on white would have equal perceived thickness to “ideal” white lines on black. This is not the case, as typographers have known for decades. The right way to draw perceptually equal-thickness black-on-white and white-on-black lines is to vary the line width (perhaps even by more than a full pixel if the lines are thick enough!). Gamma only comes in afterwards, to help us reproduce the varied widths accurately, and the accurate way to do that is in a linear color space.

raphlinus 7y ago
I should have clarified that I meant lines with subpixel phase and possibly widths that are not integral numbers of pixels, ie the antialiased case. Also I totally agree that we need to take into account the perceptual differences between black-on-white and white-on-black even assuming the display technology is perfect. That's one reason doing these studies is not trivial!
- anderskaseorg 7y ago
  The non-antialiased “case” is one spot among the continuum of antialiased “cases”; it doesn’t satisfy totally different perceptual rules. What gamma curve would you propose to correct for the perceptual equality of a 9.3px white-on-black line with a 11.6px black-on-white line? What I’m saying is that you’re presupposing the wrong layer to make the correction (antialiasing or no).
  - raphlinus 7y ago
    You are correct. Change my third question to, "after applying a correct gamma curve to achieve perceptually uniform line widths in the unipolar case, what is the correspondence of line widths when inverting the polarity to preserve the perception of width matching?" Then you want to break that down into the contribution assuming a perfect display and the effect from lower dpi. This question is less important than the other two, and plausibly the best place to address the effect is in design, rather than rendering.
    - glowcoil 7y ago
      As a simple demonstration, here's an image of a 1px white-on-black line and a 1px black-on-white line: https://imgur.com/a/9d9Tu3x https://imgur.com/a/9d9Tu3x It's axis-aligned and box-filtered so there are no shades of gray, which means gamma is irrelevant. The white-on-black line appears to have a greater thickness than the black-on-white line. There's a lot of empirical research showing that reading performance is better with positive-polarity (black-on-white) text than with negative-polarity text [1, 2], probably because the higher overall luminance results in a smaller pupil size and thus a sharper retinal image [3]. So, white-on-black lines appear thicker than black-on-white lines because the eye doesn't focus as sharply on them. This is true regardless of which color space blending is performed in. Given this fact, if one wants to achieve uniform perceptual line thickness for black-on-white and white-on-black text, a more principled approach than messing with color blending would be to vary line width or the footprint of the antialiasing filter based on the luminance of the text (and possibly the background). This is the approach Apple and Adobe have taken for years with stem darkening/font dilation. [1]: http://jdobr.es/pdf/Dobres-etal-2016-Displays.pdf http://jdobr.es/pdf/Dobres-etal-2016-Displays.pdf [2]: https://www.uni-duesseldorf.de/home/fileadmin/redaktion/Oeffentliche_Medien/Fakultaeten/Mathematisch-Naturwissenschaftliche_Fakultaet/Psychologie/AAP/Publikationen/2009/Buchner_Mayr_Brandt__2009_.pdf https://www.uni-duesseldorf.de/home/fileadmin/redaktion/Oeff... [3]: http://www.psychologie.hhu.de/fileadmin/redaktion/Oeffentliche_Medien/Fakultaeten/Mathematisch-Naturwissenschaftliche_Fakultaet/Psychologie/AAP/Publikationen/in_press/Piepenbrock-in_press-Smaller_pupil_size_and_better.pdf http://www.psychologie.hhu.de/fileadmin/redaktion/Oeffentlic...
      - raphlinus 7y ago
        One caveat, if viewing this image on a high-dpi display there will be blurring from image upsampling by the browser. My eyes have the same result as yours: the white line appears thicker than the black one. Here's the interesting thing about your observation: doing alpha compositing of text in a perceptual space (as opposed to a linear space) results in a thickening of black-on-white and a thinning of white-on-black. So doing gamma "wrong" actually results in better perceptual matching. Do you have evidence that either Apple or Adobe varies the amount of stem darkening based on text luminance? I've tested Apple (macOS 10.12 most carefully) and have not seen this.

raphlinus 7y ago

I should have clarified that I meant lines with subpixel phase and possibly widths that are not integral numbers of pixels, ie the antialiased case. Also I totally agree that we need to take into account the perceptual differences between black-on-white and white-on-black even assuming the display technology is perfect. That's one reason doing these studies is not trivial!

anderskaseorg 7y ago
The non-antialiased “case” is one spot among the continuum of antialiased “cases”; it doesn’t satisfy totally different perceptual rules. What gamma curve would you propose to correct for the perceptual equality of a 9.3px white-on-black line with a 11.6px black-on-white line? What I’m saying is that you’re presupposing the wrong layer to make the correction (antialiasing or no).
- raphlinus 7y ago
  You are correct. Change my third question to, "after applying a correct gamma curve to achieve perceptually uniform line widths in the unipolar case, what is the correspondence of line widths when inverting the polarity to preserve the perception of width matching?" Then you want to break that down into the contribution assuming a perfect display and the effect from lower dpi. This question is less important than the other two, and plausibly the best place to address the effect is in design, rather than rendering.
  - glowcoil 7y ago
    As a simple demonstration, here's an image of a 1px white-on-black line and a 1px black-on-white line: https://imgur.com/a/9d9Tu3x https://imgur.com/a/9d9Tu3x It's axis-aligned and box-filtered so there are no shades of gray, which means gamma is irrelevant. The white-on-black line appears to have a greater thickness than the black-on-white line. There's a lot of empirical research showing that reading performance is better with positive-polarity (black-on-white) text than with negative-polarity text [1, 2], probably because the higher overall luminance results in a smaller pupil size and thus a sharper retinal image [3]. So, white-on-black lines appear thicker than black-on-white lines because the eye doesn't focus as sharply on them. This is true regardless of which color space blending is performed in. Given this fact, if one wants to achieve uniform perceptual line thickness for black-on-white and white-on-black text, a more principled approach than messing with color blending would be to vary line width or the footprint of the antialiasing filter based on the luminance of the text (and possibly the background). This is the approach Apple and Adobe have taken for years with stem darkening/font dilation. [1]: http://jdobr.es/pdf/Dobres-etal-2016-Displays.pdf http://jdobr.es/pdf/Dobres-etal-2016-Displays.pdf [2]: https://www.uni-duesseldorf.de/home/fileadmin/redaktion/Oeffentliche_Medien/Fakultaeten/Mathematisch-Naturwissenschaftliche_Fakultaet/Psychologie/AAP/Publikationen/2009/Buchner_Mayr_Brandt__2009_.pdf https://www.uni-duesseldorf.de/home/fileadmin/redaktion/Oeff... [3]: http://www.psychologie.hhu.de/fileadmin/redaktion/Oeffentliche_Medien/Fakultaeten/Mathematisch-Naturwissenschaftliche_Fakultaet/Psychologie/AAP/Publikationen/in_press/Piepenbrock-in_press-Smaller_pupil_size_and_better.pdf http://www.psychologie.hhu.de/fileadmin/redaktion/Oeffentlic...
    - raphlinus 7y ago
      One caveat, if viewing this image on a high-dpi display there will be blurring from image upsampling by the browser. My eyes have the same result as yours: the white line appears thicker than the black one. Here's the interesting thing about your observation: doing alpha compositing of text in a perceptual space (as opposed to a linear space) results in a thickening of black-on-white and a thinning of white-on-black. So doing gamma "wrong" actually results in better perceptual matching. Do you have evidence that either Apple or Adobe varies the amount of stem darkening based on text luminance? I've tested Apple (macOS 10.12 most carefully) and have not seen this.