A new method for image description, compression, and manipulation based on finite automata is studied. A Weighted Finite Automaton (WFA) computes a real function on 0,1, .., n. For n = 2, such a function can be interpreted as the grayscale function specifying an image. The most important application of WFA is the new image- compression method based on the WFA inference algorithm. This method can be classified as a fractal compression method, but it is different and performs considerably better than the previous fractal methods for image compression. It produces an excellent compression size to quality ratio for the widest variety of images. The current image-data compression software performs well; however, it does not reach the full potential of WFA for image compression. One of the main goals of this project is to optimize the compression algorithm to make it faster and to produce better quality regenerated images for the same compression rate. Weighted Finite Transducers (WFT) are a tool for the description and implementation of image transformations. The project will investigate the WFT and their applications, their efficient implementation, and the design of inference algorithms for WFT.