Question

Basically, I have a context where I can’t programatically tint an image, though I can change it’s alpha value. With some experimentation, I’ve found that I can layer a red, blue, and green version of the image, with specific alpha values, to produce a wide range of colors. However, I am wondering if it’s possible to achieve a true RGB representation through this method? If so, what is the formula for converting an RGB value into different alpha values for the red, blue, and green layers.

Answer 1

The basic “equation” of alpha combination is:

alpha * (R1,G1,B1) + (1-alpha) * (R2,G2,B2)

When you have three layers with alpha you are actually combining 4 layers (the 4th one is black) so the final color is:

alpha1 * (R1,G1,B1) + (1-alpha1) * ( 
   alpha2 * (R2,G2,B2) + (1-alpha2) * (
      alpha3 * (R3,G3,B3) + (1-alpha2) * (0,0,0) ) )

Provided you have the same image on each layer and layer1 is the red channel (G1=B1=0) and layer2 is green and layer3 is blue you get:

(alpha1 * R, (1-alpha1)*alpha2 * G, (1-alpha1)*(1-alpha2)*alpha3 * B)

For a white pixel you can do any possible color. For a black pixel you cannot do anything but black. For any other pixel, you are restricted by the values of R, G and B.

Say you wanted to achieve (Rd, Gd, Bd) at a pixel where the current color is (R, G, B) then you would have to choose:

alpha1 = Rd/R
alpha2 = Gd/(G*(1-alpha1))
alpha3 = Bd/(B*(1-alpha1)*(1-alpha2))

The problem is that alpha can typically only be between 0 and 1. So, for example, if Rd > R there is nothing you can do.

You can do better if you can control the blending function (for example, in Photoshop).