Two dimensional parameterized matching

Two equal length strings, or two equal sized two dimensional texts, parameterize match (p-match) if there is a one-one mapping (relative to the alphabet) of their characters. Two dimensional parameterized matching is the task of finding all m x m substrings of an n x n text that p-match to an m x m pattern. This models, for example, searching for color images with changing of color maps. We present an algorithm that solves the two dimensional parameterized matching problem in O(n(2) + m(2.5 .) polylog(m)) time.