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This paper presents a new direct Fourier-based algorithm for performing image-to-image registration to subpixel accuracy, where the image differences are restricted to translations and uniform changes of illumination. The algorithm detects the Fourier components that have become unreliable estimators of shift due to aliasing, and removes them from the shift-estimate computation. In the presence of aliasing, the average precision of the registration is a few hundredths of a pixel. Experimental data presented here show that the new algorithm yields superior registration precision in the presence of aliasing when compared to several earlier methods and has comparable precision to the iterative method of P. Thevenaz et al. (1998)