An ω-automata approach to the representation of bilevel images

We use ω-automata (i.e., automata over infinite words) as a device for representing bilevel images. A major advantage of our approach, as opposed to using the conventional finite automata, lies in that ω-automata are capable of representing image objects of zero size, such as lines and points. To demonstrate the feasibility of our approach, we also show how a number of image processing operations, including shift, flip, rotation, complement, boundary, difference, union, intersection, and size, can be effectively carried out in the framework of ω-automata. In particular, the size of an image represented by an ω-automaton is measured based on the theory of Markov chains. In comparison with other automata-based image representation schemes reported in the literature, our approach is capable of supporting a richer set of operations, which can be performed on the automata directly and easily.