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

2026-08-11

AI Summary

This work addresses the challenge of achieving sub-pixel registration accuracy for images undergoing translation, scaling, and rotation. To this end, a two-stage decoupled estimation framework is proposed: first, scale and rotation parameters are estimated in the log-polar domain using the Fourier magnitude spectrum; subsequently, high-precision sub-pixel translation is estimated in the spatial domain by integrating an auxiliary function method with phase correlation. By effectively combining the Fourier–Mellin transform with auxiliary-function-based phase correlation, the approach successfully decouples the parameters of the similarity transformation. Experimental results demonstrate that the proposed method significantly outperforms conventional discrete cross-correlation–based Fourier–Mellin approaches in terms of estimation accuracy for scale, rotation, and translation.

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.

Problem

• image registration
• similarity transformation
• subpixel accuracy
• Fourier–Mellin transform

Innovation

• Fourier-Mellin Transform
• subpixel registration
• auxiliary function method
• phase-only correlation
• similarity transformation