How to create abstract color profile to encode specific color transformation?

Question

I have a set of images (48-bit TIFF) that are encoded in ProPhoto RGB.

I have a set of alternative input color profiles (related to ProPhoto RGB, but slightly different) that I can assign to the images in order to obtain various color transformations.

This is not the correct way of using color profiles though. If you need a color transformation you either want a 3DLUT (working color-space dependent, more like a device-link profile), or an abstract profile (Lab->Lab mapping, color-space independent).

Photoshop supports both 3DLUTs and abstract profiles.

I want to create either a 3DLUT, or an abstract profile that encodes the same transformation as the one achieved by changing the input profile. I don't know how to proceed further. I am a programmer and can write code, if that's helpful.

In more math notation, we have these functions:

ProPhotoRGB: RGB->XYZ
ProPhotoRGBModified: RGB->XYZ
XYZ2Lab: XYZ->Lab
Lab2XYZ: Lab->XYZ

And we want to find this function:

UnknownAbstract: Lab->Lab

Such that this equality holds:

ProPhotoRGBModified(input) == Lab2XYZ(UnknownAbstract(XYZ2Lab(ProPhotoRGB(input))))

Answer 1

You can do this by creating an RGB Color Cube as a .tif (or whatever lossless format you prefer), taking it into Photoshop, applying the transform to the image, then saving it back out. I have one that is 64x64x64:

So open that in Photoshop and tell it that it's in the source color space you want to transform from. (You may need to tell it to ignore the profile that's attached if there is any. Not sure what uploading it here does to the image.) Then do whatever you were doing to convert to the new color space. Save it back out in a loss-less, easy-to-read-with-code format. Then remove the color profile info if there is any, as that will cause it to render differently in the future. You can now use it as a 3D LUT.