George,
probably you remember the time when we were
starting discussions about luminance and gray-
scale conversions, some years ago.
In this sense my post is not a correction but
an attempt to enlighten the background, to my
best knowledge at present.
Bill, thanks for your input as well.
Popular grayscale conversion formulas
are based entirely on CIE (1931) colorimetry,
measured for only 17 British observers by
Wright and Guild. The relevance of these
data was later confirmed and a little
corrected by Stiles.
Best introduction:
R.W.G.Hunt, Measuring Colour.
Using any set of primaries and a white
point WP, it is possible to express R,G,B
by unique CIE tristimulus values X,Y,Z,
where R,G,B and Y are normalized for the
range 0 to 1:
X = a11*R + a12*G + a13*B
Y = a21*R + a22*G + a23*B
Z = a31*R + a32*G + a33*B
Y is the eqivalent for luminance.
X and Z don’t contain any information
about luminance (a ‘dirty’ mathematical
trick).
Two sets of weights are common,
others can be calculated easily (e.g. for
AdobeRGB):
1. NTSC primaries and illuminant C WP 6774 K
Y = 0.299*R + 0.586*G + 0.114*B
2. Rec.709 primaries and D65 WP 6500K.
Together with a specific tone reproduction
curve this is sRGB
Y = 0.213*R + 0.715*G + 0.072*B
Aha, no.1 is the magic formula, but no.2
would be better for sRGB.
Each formula should be applied to linear RGB
values, whereas file data are gamma encoded.
In the past these weight factors were applied
to gamma encoded values without linearization.
For the practical application we encounter two
difficulties:
a) a formalistic grayscale conversion delivers
images with lacking contrast. How to deal
with this problem in advance to the conver-
sion(!) is nicely described by Dan Margulis,
Professional Photoshop.
b) Sorting colors by calculated luminance does
not create monotonously increasing percep-
tual luminance palettes.
This is known as Helmholtz-Kohlrausch-Effect:
Saturated colors appear brighter than
indicated by CIE luminance.
Results, including the H-K-Effect, are shown
here:
<
http://www.fho-emden.de/~hoffmann/gray10012001.pdf>
In either case, we are dealing here with photo-
metry, which contains besides physical inten-
sities the human sensitivity functions.
Best regards –Gernot Hoffmann