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How to find the alpha layer that sends one image to another?

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If you have 2 images, one a non-uniform shade of the other, is it possible to derive the exact transparent layer so that image1 + transparent layer = image2 (not through trial and error, but through a formulated process)?

More technically, if you have 2 colors and their rgb/hsl values, is there some known formula that yields the rgb/hsl and alpha values of the 'difference' of the 2 colors?

Thanks! :D

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