Calculating "k" (grayscale) from RGB?
AJW
Does anyone know how Photoshop 6 calculates the value "K" in the Grayscale
color info palette given values for RGB?
In a similar but somewhat inverse question, I'm trying to think through how
I could generate a table of RGB values that would take some "hue" (say, pure
Red) from K=0% to K=100%, stepping by 5%. For instance, pure Red (255,0,0)
has K of 41%. What calculations would I do to keep the same basic "hue" of
red, but take it from K=0 through K=41 to K=100?
At first I thought I could use the HSB colorspace rather than RGB and just
increase brightness B, but that's not the same as the grayscale K (which is,
I think, an approximation for "value", as in Munsell value).
Any suggestions appreciated... Thanks.
-ajwe
RossF
Gray value percentages are dependent on your "Gray" setting in
Edit>Color Settings (gamma or dot gain, depending on whether you are
designing for screen or print, respectively). It's also dependent on
the RGB color space that the image is in. For instance, pure red is
K=41 in one space (gray gamma 2.2, Adobe RGB ???), but will be some
other K value using another gamma or dot gain setting and/or another
color space.
The gray values you get from colors also depend on how the conversion
is made. Grayscale conversion values are based on perceptual
brightness or lightness--the L in L*a*b, but there are other ways to
convert--Desaturation, Luminosity blend, Channel Mixer....
One way you could get a range of colors that approximately follow K
values by steps would be to create the gray steps, then with
Hue/Saturation, use "Colorize", and set the Hue and Saturation you
want. After the adjustment, Edit>Fade Hue/Saturation and select Color
as the blending mode. Maybe not mathematically precise, but should be
completely functional.
Ross
AJWE
> Gray value percentages are dependent on your "Gray" setting in
> Edit>Color Settings (gamma or dot gain, depending on whether you are
> designing for screen or print, respectively). It's also dependent on
> the RGB color space that the image is in. For instance, pure red is
> K=41 in one space (gray gamma 2.2, Adobe RGB ???), but will be some
Right. Gamma 2.2 and Adobe RGB.
> The gray values you get from colors also depend on how the conversion
> is made. Grayscale conversion values are based on perceptual
> brightness or lightness--the L in L*a*b, but there are other ways to
> convert--Desaturation, Luminosity blend, Channel Mixer....
I've been experimenting with various formulas from the Poynton Color FAQ but
can't seem to come up with a formula that gets me reliably close to the
value of "K" that PhotoShop uses in the grayscale color "info" palette. FYI
(to other readers): The grayscale "K" value seems to correspond to what
happens when you change mode from RGB to Grayscale; i.e., if I create an
image with various colors, all of which have the same K, converting it to
Grayscale by switching mode produces a completely even-toned picture. The
other methods convert differently and you get areas with different levels of
gray. (BTW, when you monitor both K and L*a*b, the L* moves similarly to K,
but it's not linearly proportional...)
> One way you could get a range of colors that approximately follow K
> values by steps would be to create the gray steps, then with
> Hue/Saturation, use "Colorize", and set the Hue and Saturation you
> want.
This works very well for producing the scale -- thanks. I was hoping to use
a little program I wrote that can generate Photoshop Palette Files to
automatically create a palette for me using a set of colors I choose; the
palette would consist of colors of varying "value" (similar to Munsell
Value) ranging from K=0 to K=100. But I can't quite get the equations to
work out right. In any case, the method you describe makes it easy enough
for me to pick a hue and then manually grab colors at any level of K that I
choose.
Thanks,
-AJWE
RossF
I think you'd need to understand Lab conversions. I don't know the
math, but basically, every color has an "L" value. An "L" value always
converts to the same K value (unless you change your Gray work space)
no matter what the color component ("a" and "b"). For instance, I just
checked a gamma 2.2 gray space, and these are the values:
K L
10 91
20 82
30 73
40 64
50 54
60 44
70 32
80 20
90 6
For a dot gain of 20%, the same L values result in K values of 13, 25,
37, 48, 58, 68, 78, 87, and 94.
Any palette of RGB colors you create based on K values would be
dependent on the gray work space in use--the same palette would
produce different K values. Also, if an image is in another RGB color
space than when the palette was created, those same RGB numbers in the
palette are now different colors, and hence, produce different K
values.
Here's another idea that you may find useful:
You could create an Action that builds a bunch of "swatches" with
varying Lightness. Pick a color that has a 50% associated K value.
Start the Action by creating a swatch (filled rectangular selection)
with the foreground color. Record, as a series of steps:
1. Copy original 50% swatch
2. Move copy (Transform relative)
3. Adjust>Hue/Saturation Lightness value on the copy (each +-10
adjustment on Lightness creates a +-5% change in K value if the before
value is 50%).
4. Select original 50% swatch layer
5. Repeat steps 1-4 using different transform and Lightness
adjustments for each copy.
The Action will create a bunch of swatches based on the current
foreground color. After the Action runs, you can either manually
create a color table with the Eyedropper and Swatches palette, or
convert to Indexed Color mode and save the Color Table
(Image>Mode>Color Table).
Ross