On generalizations of weighted finite automata and graphics applications

Abstract

Already computations of ordinary finite automata can be interpreted as discrete grayscale or colour images. Input words are treated as addresses of pixel-components in a very natural way. In this well understood context already meaningful operations on images like zooming or self-similarity can be formally introduced. We will turn then to finite automata with states and transitions labeled by real numbers as weights. These Weighted Finite Automata (WFA), as introduced by Culik II, Karhumäki and Kari, have turned out to be powerful tools for image- and video-compression. The recursive inference-algorithm for WFA can exploit self-similarities within single pictures, between colour components and also in sequences of pictures. We will generalize WFA further to Parametric WFA by allowing different interpretations of the computed real vectors. These vector-components can be chosen as grayscale or colour intensities or e.g. as 3D-coordinates. Applications will be provided including well-known fractal sets and 3D polynomial spline-patches with textures. © Springer-Verlag Berlin Heidelberg 2007.