White = transparency ?

Question

Hi everyone.
This has bugged me for a long time now, maybe some clever folks can help ?
I would like to make an image semi-transparent in such a way, that it looks as before when adding a white layer underneath it.
That's not a big feat with a grayscale image (see left side of the illustration). Command-Click the RGB channel, invert the selection, add a black (colour fill) layer (the selection is automatically added as layer mask), then add a white layer underneath. Done. The image looks the same as when we started out.
Now how can this be done with a colour image (see right side of the illustration) ?
I need a solution for ANY image, not just the example here (for which the problem can of course easily be solved as you can see, even in colour). And I would need an exact solution, not an approximation (e.g. via blend if or select >> color range, etc.).
Granted, it does seem tricky, but on the other hand, it must be solvable. Because let's imagine we would have started out with the example image in the bottom/right corner (or any other semi-transparent image for that matter) and would have added a white layer underneath. We would have obtained the example image in the upper/right corner. So we know, that there must be an image that fulfills the requirements. And merging with a white layer doesn't seem like a destructive/irreversible action, so there must be a way to reverse the process ...
any ideas how ?
my sincere thanks in advance.
(PS: Cybia Alphaworks and the Whiteout plugin won't do the job as needed.)

Answer 1

Your problem is not as simple as it sounds, and there can be no one click solution that will work for all images. What you want to do, would be to take out what you are calling "white", and all intermediate colours,  leaving transparency values in their place
The problem is that what I am calling the intermediate colours can have almost any value. Your "white" may be not completely white (2% yellow for example). There has to be a clear way of interpreting what the bleed values are, and distinguishing those from values that you want to keep. Impossible without some judgment per image.
Producing alpha channels, in some way and recreating the image, which you have said you don't want to do, would be the only way. This would have to be done differently per image and case.