One of the major challenges related to image registration is the estimation of large motions without prior knowledge. This work presents a Fourier-based approach that estimates large translations, scalings, and rotations. The algorithm uses the pseudopolar (PP) Fourier transform to achieve substantial improved approximations of the polar and log-polar Fourier transforms of an image. Thus, rotations and scalings are reduced to translations which are estimated using phase correlation. By utilizing the PP grid, we increase the performance (accuracy, speed, and robustness) of the registration algorithms. Scales up to 4 and arbitrary rotation angles can be robustly recovered, compared to a maximum scaling of 2 recovered by state-of-the-art algorithms. The algorithm only utilizes one-dimensional fast Fourier transform computations whose overall complexity is significantly lower than prior works. Experimental results demonstrate the applicability of the proposed algorithms.