pHash.org: Home of pHash, the open source perceptual hash library
http://www.phash.org/

a fingerprint of an audio, video or image file that is mathematically based on the audio or visual content contained within. Unlike cryptographic hash functions which rely on the avalanche effect of small changes in input leading to drastic changes in the output, perceptual hashes are "close" to one another if the inputs are visually or auditorily similar

A method for producing hashes so that similar objects produce similar hashes. Applied mostly to audio and video. Doesn't appear to be a general theory. Rather, special cases for files such as pictures and audio are derived. This is an open source library that runs under linux only at the moment.