Robust image alignment using improved third-order global motion estimation

The estimation of parametric global motion using non-linear optimization is a fundamental technique in computer vision. Such schemes are able to recover various motion models (translation, rotation, affine, projective) with subpixel accuracy. The parametric motion is computed using a first order Taylor expansions of the registered images. But, it is limited to the estimation of small motions, and while large translations and rotations can be coarsely estimated by Fourier domain algorithms, no such techniques exist for affine and projective motions. This paper offers two contributions: First, we improve the convergence properties by an order of magnitude using a second order Taylor expansion. A third order convergence rate is achieved, compared to the second order convergence of prior schemes. Second, we extend the third order algorithm using a symmetrical formulation which further improves the convergence properties. The results are verified by rigorous analysis and experimental trials.