Predictability and redundancy of natural images

One aspect of human image understanding is the ability to estimate missing parts of a natural image. This ability depends on the redundancy of the representation used to describe the class of images. In 1951, Shannon Bell. Syst. Tech. J. 30, 50 (1951) showed how to estimate bounds on the entropy and redundancy of an information source from predictability data. The entropy, in turn, gives a measure of the limits to error-free information compaction. An experiment was devised in which human observers interactively restored missing gray levels from 128 X 128 pixel pictures with 16 gray levels. For eight images, the redundancy ranged from 46%, for a complicated picture of foliage, to 74%, for a picture of a face. For almost-complete pictures, but not for noisy pictures, this performance can be matched by a nearest-neighbor predictor.