Rational and affine expressions for image description

In this paper, the representation, generation and inference of images using automata-theoretic techniques is investigated. It is shown that highly complex images, including ‘fractal’ (self-similar) images, can be manipulated by the application of these techniques. Languages and relations over some alphabet are interpreted as images by treating strings as rational coordinates. In particular rational relations, specified by rational expressions, are considered. It is shown how texture of an image can be defined by probabilistic finite generators. Affine expressions are introduced as a generalization of both rational expressions and the IFS method to define images. Finally, two efficient methods to implement rational expressions are presented.