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

• URL: http://arxiv.org/abs/2608.11565v1
• Date: Wed, 12 Aug 2026 02:12:33 GMT
• Title: Alignment of Similarity-Transformed Images Based on Fourier--Mellin Transform Using Auxiliary Function Method
• Abstract summary: The paper proposes an algorithm for estimating the similarity transformation, namely translation, scale, and rotation, between two images with subpixel accuracy.<n>A simulation experiment on image pairs subjected to random similarity transformations shows that the proposed method reduces estimation errors in scale, rotation, and translation.
• Score: 2.192057999494216
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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