The Compression of Subsegments of Images Described by Finite Automata

We investigate how the size of the compressed version of a 2-dimensional image changes when we cut off a part of it, e.g. extracting a photo of one person from a photo of a group of people. 2-dimensional compression is considered in terms of finite automata. Let n be the size of the smallest acyclic automaton which describes an image T . We show that the tight bound for the compression size of a subsegment (subimage) in the deterministic case is (n 2:5 ) and in the weighted case is (n). We also show how to construct efficiently the compressed representation of subsegments given the compressed representation of the whole image. Two applications of subsegments compression are more efficient automata-compressed pattern-matching and the first polynomial time algorithm for the fully compressed pattern-checking problem for weighted automata