An important thing to consider, when correcting a faded print, is that print colors are not made up of red, green, and blue (RGB), but of yellow, cyan, and magenta (YCM). So, in principle to color correct a print, you’re attempting to reconstruct the original color distributions of yellow, cyan, and magenta, which have shifted. It is IMO not correct to do curves adjustment in RGB color space, as you are unwittingly altering the shape of the distributions of yellow, cyan, and magenta. One of the key assumptions in the automated color correction algorithm, is that the shape of these color distributions remains unchanged, and that they are simply shifted to different intensities. At this point I’m using the standard RGB definition of the colors yellow, cyan, and magenta. However, real film yellow, cyan, and magenta probably are a slightly different mix of red, green, and blue. It is therefore expected that the colors will be more accurate if the approriate mixes of red, green, and yellow are used.