Re: Usable Tones in Different Gammas
Re: Usable Tones in Different Gammas
- Subject: Re: Usable Tones in Different Gammas
- From: "Bruce J. Lindbloom" <email@hidden>
- Date: Tue, 12 Dec 2000 10:15:23 -0600
In a recent message, Robin Myers shared his analysis of usable gray levels
for different gammas. His results are shown here (I edited out the
non-printing characters from his original message):
>
Available Grayscale Values
>
Gamma 0-63 64-127 128-191 192-255 Total Values
>
1.8 22 52 64 64 202
>
2.2 13 43 64 64 184
Robin's calculations are correct, but I for one missed his basic premise and
maybe others missed it as well. Robin's calculations start with 256 (i.e.
8-bit) levels representing linear intensity (read gamma = 1.0). So he has
taken a gamma = 1.0 scale, and then quantized it to 8-bits. This forms the
starting point for his following calculations. The bottom line of his study
is that the farther you deviate from gamma = 1.0, (with the already
quantized 8-bit data) the fewer levels you end up with. Although Robin did
not explicitly state it, the gamma that produces the most levels is of
course the original gamma, namely 1.0, which maintains all 256 levels.
Be careful in drawing conclusions from this study and applying them to
situations whose original premise is different (i.e. cases where you are not
starting with 8-bit, gamma 1.0 data). For example, a 36-bit scanner has
12-bits of gamma 1.0 data per channel, at least inside the scanner hardware.
Typically (although not always), a LUT is utilized to reduce 12-bits down to
8-bits. The content of such a LUT will usually have a non-linear function,
such as gamma = 2.2. Device profiles are even more sophisticated non-linear
functions which in normal use will produce 8-bit non-linear (i.e. non-gamma
1.0) data.
If you are quantizing color from higher-bit down to 8-bit, you should choose
a gamma value that is more representative of the human visual system (CIE
L*), such as 2.2. I have posted to this list before that an analysis of the
"best" gamma depends on your definition of "best." Two candidates are a)
minimizing the RMS error and b) minimizing the largest error between a gamma
function and the CIE L* function:
Gamma = 2.3243 Minimizes RMS Error
Gamma = 2.1723 Minimizes Largest Error
So gamma = 2.2 seems like a good choice. A better choice than 1.8 and a
MUCH better choice than 1.0.
--
Bruce J. Lindbloom, Pictographics Intl. Corp.