I'm looking for a mathematical definition of this scale.
http://docs.gimp.org/en/gimp-tool-levels.html says 0 is black and 255 is
white. What's in between? Is 7 double the brightness of 6?
What is the luminance / brightness of each of the levels?
Is it a logarithmic scale?
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Life is
The answer appears to be: sRGB, the color space to which gimp defaults
(unless you've specified another color space?).
The formula for converting sRGB levels to relative luminance is in the sRGB
spec. A table of the Levels and their corresponding relative luminance
is here: