Depends on what you mean by "identical images". If you want to check for copies of the same file, use something like Digest::MD5 or Digest::SHA1 and compare the generated digests (same digest, identical file contents; different digest, different pictures).

If you mean "looks the same but the file's different" (e.g. a PNG that's been converted to a JPG of identical size) that'd be much more difficult (and I can't even think of where to tell you to start looking; although it'd probably involve some sorts of deep Computer Science academic literature).