Affine image matching is uniform TC0-complete

Abstract

Affine image matching is a computational problem to determine for two given images A and B how much an affine transformated A can resemble B. The research in combinatorial pattern matching led to a polynomial time algorithm which solves this problem by a sophisticated search in the set D(A) of all affine transformations of A. This paper shows that polynomial time is not the lowest complexity class containing this problem by providing its TC0- completeness. This result means not only that there are extremely efficient parallel solutions but also reveals further insight into the structural properties of image matching. The completeness in TC0 relates affine image matching to a number of most basic problems in computer science, like integer multiplication and division. © Springer-Verlag Berlin Heidelberg 2010.