Unification and extension of weighted finite automata applicable to image compression

Weighted finite automata (WFA), including the linear WFA due to Culik and Kari and the acyclic WFA due to Hafner, have been under investigation over the years for their applications to image compression. We shall in this work first examine in great details the underlying WFA structure and propose the most systematic extension, along with its full legitimacy analysis, to the WFA that are applicable to image compression. A new mechanism based on the concept of resolution-wise and resolution-driven image mappings is developed to create rich families of legitimate similarity images so as to reduce the overall WFA size, a property that is critically related the performance of WFA-based compression codecs. Moreover, we shall also unify the relevant WFA by showing an acyclic WFA can always be merged into a linear WFA but not vice versa.