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Identifying Profiles is Hard

Given an ICC profile, identifying the colorspace it describes (e.g., “sRGB” or “Display P3) is hard.

See There Is No Single sRGB Color Profile, and note that technically Profiles Aren’t Interchangable Even When They Describe the Same Colorspace.

Relying on the description string in the profile is fraught. Not all profiles will identify the colorspace they describe, or even have useful descriptions.

Questions

The best idea I have right now is to use the profile to convert a known image (maybe an identity color LUT) into a device-independent colorspace, and then compare that image with others similarly converted with known, identified profiles.

What sort of tolerance would be desired or needed when performing the comparisons?