Computational Efficiency of Structural Image Matching

This paper addresses computational efficiency issues of a new algebraic method for imagery registration/conflation. An algebraic approach to conflation/registration of images does not depend on identifying common points. It uses the method of algebraic invariants to provide a common set of coordinates to images using chains of line segments formally described as polylines with possible gaps between segments. The original design of the method operates with matrixes and has complexity O(n) for entire matrixes and complexity O(n) for individual binary comparisons. This paper shows that this polynomial complexity can be significantly reduced by converting each matrix to the special linear structures with n elements. Generation of the special linear structure itself requires n log n binary comparisons for sorting, and the complexity of comparing two polylines overall is O(nlogn). The ability to perform these matching computations quickly is essential in correlating images containing large quantities of polylines.