A new and compact algorithm for simultaneously matching and estimation

Abstract

Feature matching and transformation estimation are two fundamental problems in computer vision research. These two problems are often related and even interlocked, solving one is solving the other's precondition. Such makes them hard to solve. In order to overcome such difficulty, this paper presents a new and compact algorithm where less than 10 lines of matlab codes suffice. We show that the solutions of correspondence and transformation are merely two factors of two Grammian matrices, and can be worked out with factorization method. A Newton-Schulz numerical iteration algorithm is used for such factorization. The two interlocked problems are solved in an alternate(flip-flop) way, The effectiveness and efficiency are illustrated by experiments on both synthetic and real images. Global and fast convergence attained even start from random chosen initial guesses.