Ah, right, anything that's a function purely of what's in the image - no randomness, no external context/'knowledge' to interpret it semantically, is as you say

Ah, right, anything that's a function purely of what's in the image - no randomness, no external context/'knowledge' to interpret it semantically, is as you say 'encoding the same information in different ways'? If it can be computed (deterministically) from the image alone, then it was already there.