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I have three images; An "original" 16x16 image, a recoloured 16x16 image, and a 32x32 image which is basically the same as the original image, but with a higher resolution. What I want to do, is to obtain a 32x32 recoloured image; it should have the same colours as the recoloured 16x16 image.

In other words, if we call the images I have A, B and C, and the one I want to make D, D should be to C as B is to A. More precisely, I want to map all colours in the original 16x16 image to the colour at the same position in the recoloured 16x16 image, and apply the mapping to the 32x32 image.

Is there any way to do this? I usually use GIMP for image editing.

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    Depends heavily on the images in question, please show us some pictures. Welcome to GD.SE – joojaa May 3 '15 at 16:04
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If you are really interested in recoloring and not in the transformation of any sort, then standard technique is to use a "Color" mode for a layer that sets the colors.
So, in the back layer you put the 32x32 image with correct details, but wrong colors.
On top of it in the separate layer you take a 16x16 image with correct colors. Then rescale it to 32x32 so that it matches the background. Then for the top layer set the "Color" layer mode.
P.S. And on top of it you may have a final layer to retouch the result of course.

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