We propose an efficient method for image registration based on iteratively fitting a parametric model to the output of an elastic registration. It combines the flexibility of elastic registration - able to estimate complex deformations - with the robustness of parametric registration - able to estimate very large displacement. Our approach is made feasible by using the recent Local All-Pass (LAP) algorithm; a fast and accurate filter-based method for estimating the local deformation between two images. Moreover, at each iteration we
fit a linear parametric model to the local deformation which is equivalent to solving a linear system of equations (very fast and efficient). We use a quadratic polynomial model however the framework can easily be extended to more complicated models. The significant advantage of the proposed method is its robustness to model mis-match (e.g. noise and blurring). Experimental results on synthetic images and real images demonstrate that the proposed algorithm is highly accurate and outperforms a selection of image registration approaches.