Weighted finite transducers in image processing

Culik and Karhumäki studied weighted finite automata (WFA) as devices computing real functions. The main motivation was to give specifications of graytone images as local grayness functions. Culik and Kari gave an algorithm for automatic image encoding using WFA as a basis for a practical image data compression method. In this paper the authors introduce k-tape weighted finite automata. They are mainly interested in the case of 2 tapes called weighted finite transducers (WFT). The authors show that the most commonly used image transformations can be defined by WFTs. They also show that WFT transformations are close under union and composition and that the family of WFA images is closed under WFT transformations.