what is the mathmatical formula of Gradient map

Thanks all you guys!

I recently learn a lot about color model, and get to know that Photoshop use HCY(hue, chroma, luminance) color model in many cases.

For the gradient map, I have known the approximate formula.

let luminance Y = (R/255)*0.30 + (G/255)*0.59 + (B/255)*0.11, then just use Y to choose the color in map.

R(converted) = (1-Y)*R(leftside of map) + Y*R(right side of map)

G(converted) = (1-Y)*G(leftside of map) + Y*G(right side of map)

B(converted) = (1-Y)*B(leftside of map) + Y*B(right side of map)

For Y=50%, the above formula is accurate;

For Y<50%, the calculated result is a little smaller than actual value;

For Y>50%, the calculated result is a little greater than actual value.

Also, I wrote a CEP extension to show HCY color value:

GitHub - XiaoXiaoLui/photoshop_hsl_plugin: CEP extension for showing HCY or HSL color in photoshop

Interestingly if you have three areas of pure primary RGB values (255 for each) and then run DeSaturate on them. You'll get the same appearance as you do with a Black to White Gradient Map. EXCEPT for Adobe RGB (1998). That gives a very different result in the reds especially.

I suspect it has something to do with the mean averaging of the hue value relative to the size of the gamut you're calculating the average for. a 50% mean average in one gamut will not be the same, relative to coordinates/position in the gamut for Adobe RGB as it is for ProPhoto RGB.

For me the explanations are not convincing, so far.

Let's have a look at a gradient test image, made by Photoshop CS6 in sRGB:

1. The distance x=0.0 to 1.0 is divided linearly.

2.  R is constant, G and B are not linear.

3.  L is not linear

4. G and B are not linear with gamma encoding taken into account (center is at 127/128)

5. The gradient is visually far from being perfect: we have almost equal lightnesses in the three

     columns at the red end.

I don't know the mathematical function. There are many possibilities, linear in R, G, B or linear

in R', G', B' ( Gamma encoded) or linear in L of Lab*) or linear in Lab, or linear in HSB (HSL,HLS)

or last but not least linear in XYZ, which would be physically reasonable.

where linear means a straight line in the respective color space with equidistant interpolation.

*) Choosing colors sorted by L instead of linearly interpolating in Lab is for me not understandable.

Not all gradients have the same hue or its equivalent in Lab, the same ratio a:b.

Or my test is wrong...

Best regards --Gernot Hoffmann

Two things are happening here. First, a B/W gradient is obviously monochrome, so all R=G=B.

But then something interesting happens. These calculations are done in the luminance component of the data, ignoring the color component. When you dive deep into the heart of Photoshop's engine room, things operate in Lab color mode (or something very similar, but let's just say Lab for now).

And in Lab, separating luminance and color components, the inherent lightness of any color is accounted for. It's easier to illustrate than to describe:

Hi

Gradient map uses the Lightness value (see Lab values in the colour picker) and maps those onto your gradient.

Dave