Some reversible image operators from the point of view of cellular automata

In this paper image operators and cellular automata are treated from an unified point of view. A class of non-linear operators is described, which is characterized by a typical structure of its transition function and meets sufficient conditions for reversibility. These conditions are then extended to some other operators, featuring a more general structure, and numerous concrete examples, with particular reference to image processing, are given. Cascading reversible operators in opposite scan directions can provide a mean for obtaining processing windows, which surround symmetrically the respective central cells. The conditions to be met by the structure of the single operators and by their processing windows in order to yield a reversible cascade are examined and illustrated by means of examples. In spite of the severe limitations imposed by the reversibility requirement, a number of interesting and useful non-linear reversible operators remain available for image processing and cellular process simulation purposes.