how to infer alpha value from pair of opaque images

Question

I have two images, one with a white background, and one with a black background, I want to convert these images into one semi transparent image

I have found that

color*alpha=blackBackgroundImage
color*alpha+(1-alpha)=whiteBackgroundImage

I want a function that takes blackBackgroundImage and whiteBackgroundImage and outputs the color and the alpha

I'm bad at math

This doesn't really have anything to do with programming. It should be on [math.se]. But: `black-white=alpha-1`. — Teepeemm, Jun 16 '15 at 14:20
@Teepeemm I know it could be a general math question, but I'm looking for a glsl specific solution. — william malo, Jun 16 '15 at 14:58

score 1 · Accepted Answer · answered Jun 16 '15 at 14:21

1

You're almost there. You just need to solve the system of equations:

    color*alpha=blackBackgroundImage
<=> color = blackBackgroundImage / alpha

Plugging that into the second equation:

    blackBackgroundImage / alpha * alpha + (1 - alpha)*(1,1,1) = whiteBackgroundImage
<=> blackBackgroundImage + (1 - alpha)*(1,1,1) = whiteBackgroundImage
<=> (1 - alpha)*(1,1,1) = whiteBackgroundImage - blackBackgroundImage

So alpha should be 1 + blackBackgroundImage.r - whiteBackgroundImage.r. The same applies to any other channel.

answered Jun 16 '15 at 14:21

Nico Schertler

32,049
4
39
70

What about color? How do I get the color? c=b/(b-w+1) ? – william malo Jun 16 '15 at 14:55
Once you have calculated `alpha`, you can use the second formula to calculate `color`. – Nico Schertler Jun 16 '15 at 14:58

how to infer alpha value from pair of opaque images

1 Answers1