An improved robust hierarchical registration algorithm

This note describes an improvement to an accurate, robust, and fast registration algorithm (Alexander, M.E. and Somorjai, R.L., Mag. Reson. Imaging, 14:453–468, 1996). A computationally inexpensive preregistration method is proposed, consisting of simply aligning the image centroids, from which estimates of the translation shifts are derived. The method has low sensitivity to noise, and provides starting values of sufficient accuracy for the iterative registration algorithm to allow accurate registration of images that have significant levels of noise and/or large misalignments. Also, it requires a smaller computational effort than the Fourier Phase Matching (FPM) preregistration method used previously. The FPM method provides accurate preregistration for low-noise images, but fails when significant noise is present. For testing the various methods, a 256 × 256 pixel T2∗-weighted image was translated, rotated, and scaled to produce large misalignments and occlusion at the image boundaries. The two situations of no noise being present in the images and in which Gaussian noise is added, were tested. After preregistration, the images were registered by applying one or several passes of the iterative algorithm at different levels of preblurring of the input images. Results of using the old and new preregistration methods, as well as no preregistration, are compared for the final accuracy of recovery of registration parameters. In addition, the performance of three robust estimators: Least Median of Squares, Least Trimmed Squares, and Least Winsorized Mean, are compared with those of the nonrobust Least Squares and Woodsʹ methods, and found to converge to correct solutions in cases where the nonrobust methods do not.