conversion/notlinear.html

<html><head><title>High-speed Conversion of Floating Point Images to
8-bit</title></head><body bgcolor=black text=#c0c0c0 link=#80c0c0 vlink=#ffc0c0>

<h1>When not to use linear floating point</h1>

There are a few places where you expect linear floating point to work
better and it comes out worse. The reason for this is that many
algorithims are designed to produce an perceptually-uniform output and
linear floating point is <i>not</i> perceptually uniform.

<p>For instance a straight gray ramp looks quite non-centered when drawn
in linear floating point:

<p><img src=pics/ramplinear.gif>

<p>The same ramp drawn directly in sRGB output pixels produces what
most people expect:

<p><img src=pics/rampsrgb.gif>

<p>Fortunately you can easily get quite close to the sRGB output by
simply squaring the values before using in a linear
representation. This makes it relatively easy to modify an existing
algorithms to produce similar output in linear floating point without
changing their speed much. Here is the ramp squared (so the .5 in the
middle turned into .25) in linear floating point:

<p><img src=pics/rampsrgb.gif>

<p>A problem I have not solved is when both the true linear and the
perceptual data is needed. This seems to be a problem with line art
graphics. The left column is some text and and graphics drawn in
linear floating point, and the right is the same graphics drawn in
sRGB. The bottom row is exaclty the inverse of the top row:

<p><img src=pics/textasrgb.png><img src=pics/textalinear.png>
<br><img src=pics/textbsrgb.png><img src=pics/textblinear.png>

<p>The linear image produces better antialiasing. But it looks like
the sRGB version produces the correct inverted image. In fact
mathematically the linear inverted image is correct, but your mind
apparently inverts things in perceptually-uniform space, making the
sRGB look like the correct inverse. I am not sure if there is a way to
get both nice antialiasing and get the expected inverted image.