In usual discourse, when looking at an photographed image (A) - which is a JPG - and a slightly photoshopped version of it (A2), most people can intuitively compare the two and visually assess that they are, indeed, the same image except for a small number of differences.
However, that isn't a formal proof that the two images are "nearly identical", and as such, may be challenged in a setting where more stringent standard of proof is needed (legal setting, or Skeptics.SE).
If it was a pair text files, one could run a
diff command on them, and establish close similarity by the result of the diff being significantly smaller than the file size.
But since these are JPG images, I would expect that the effect of photoshopping and saving a second version - with a slightly different compression ratio, to boot - would cause the straight up diff to be 100% useless.
Are there formal methodologies in image processing that can be used to "diff" the two photo images saved used lossy compression (JPG)?
The methodology should be vetted (e.g. via peer review process as far as publication in a well known image processing/computer vision/etc... publication).
The desired output is either numerical % of change; or some visualization method.
The methodology should be insensitive to slight post-processing, such as minor edge cropping, resizing and saving with a different compression ratio which causes minor losses.
If so, are there publicly available web sites or freeware programs that (a) can have 2 JPGs uploaded and produce the "diff"; (b) Publish the exact methodology they use, which fits #1.