Reverse engineering a semi-transparent image

Question

I want to match the appearance of an image that is partly transparent. The problem is that I cannot obtain the original image. I can only obtain screenshots of it against different backgrounds.

Using images of it against black and white backgrounds, is there a way to derive the original image? Ideally, I'd like to derive the non-transparent version of it, along with its transparency level. I want to edit it, then re-apply the transparency.

I'm working with GIMP 2.6 on Linux, but I could obtain other software as needed.

Answer 1

Colors>Color to alpha and remove the white (if you think the original background is white). Don't forget to add an alpha channel if necessary

The "contract" of color-to-alpha is that stacking the final image over a layer filled with the removed color will give the starting image. And C2A will always shoot for maximum transparency: over a white background, a grey could be a totally opaque grey or a partially opaque black: Gimp will produce the partially opaque black.