Global parametric image alignment via high-order approximation

The estimation of parametric global motion is one of the cornerstones of computer vision. Such schemes are able to estimate 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 both the convergence range and rate using a second order Taylor expansion and show first order methods to be a degenerate case of the proposed scheme. Second, we extend the scheme using a symmetrical formulation which further improves the convergence properties. The results are verified by rigorous analysis and experimental trials.