Alignment of Similarity-Transformed Images Based on Fourier--Mellin Transform Using Auxiliary Function Method

Abstract

This paper proposes an algorithm for estimating the similarity transformation, namely translation, scale, and rotation, between two images with subpixel accuracy. Image registration is a fundamental technique for aligning images acquired under different viewpoints and imaging conditions, and a representative approach based on maximizing discrete cross-correlation is the Fourier--Mellin registration. However, the Fourier--Mellin approach often fails to achieve sufficient alignment accuracy when subpixel-level estimation is required. The proposed method integrates (i) scale-and-rotation estimation from the Fourier magnitude spectrum in a log-polar representation and (ii) maximization of phase-only correlation based on the auxiliary function method. This integration enables a two-stage estimation procedure: it first estimates scale and rotation without being affected by translation, and then estimates translation with subpixel precision in the spatial domain using the corrected image pair. A simulation experiment on image pairs subjected to random similarity transformations demonstrates that the proposed method reduces estimation errors in scale, rotation, and translation compared with Fourier--Mellin-based registration methods using discrete cross-correlation.