A new and compact algorithm for simultaneously matching and estimation

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. This makes them hard to solve. In order to overcome this difficulty, the paper presents a new compact algorithm requiring less than 10 lines of Matlab code. We show that the solutions of correspondence and transformation are merely two factors of two grammian matrices, and can be worked out by a factorization method. A Newton-Schulz numerical iteration algorithm is used for the 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 is attained, even starting from randomly chosen initial guesses.