Generalized finite automata with weights for states and transitions have been successfully applied to image generation for more than a decade now. Bilevel images (black and white), grayscale- or color-images and even video sequences can be effectively coded as weighted finite automata. Since each state represents a subimage within those automata the weighted transitions can exploit self-similarities for image compression. These "fractal" approaches yield remarkable results in comparison to the well-known standard JPEG- or MPEG-encodings and frequently provide advantages for images with strong contrasts. Here we will study the combination of these highly effective compression techniques with a generalization of weighted finite automata to higher dimensions, which establish d-dimensional relations between resultsets of ordinary weighted automata. For the applications we will restrict ourselves to three-dimensional Bezier spline-patches and to grayscale images as textures.

Weighted Finite Automata, image compression, self-similarity, polynomials, Bezier splines, Parametric Weighted Finite Automata, bicubic Bezier patches, textured surfaces