The Uncertainty Principle in Image Processing

The uncertainty principle is recognized as one of the fundamental results in signal processing. Its role in inference is, however, less well known outside of quantum mechanics. It is the aim of this paper to provide a unified approach to the problem of uncertainty in image processing. It is shown that uncertainty can be derived from the fundamental constraints on the process of vision-the requirements for class-defining operations which are both shift-invariant and insensitive to changes in illumination. It is thus shown that uncertainty plays a key role in the language of vision, since it affects the choice of both the alphabet, the elementary signals, and the syntax, the inferential structure, of vision. The report is concluded with a number of practical illustrations of these ideas, taken from such image processing tasks as enhancement, data compression, and segmentation.