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

arXiv: https://arxiv.org/abs/2608.11565 · HTML: https://mlsanity.com/paper/2608.11565/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 20 references that are in the map.
- First posted on arXiv 12 Aug 2026.

## Builds on (most cited first, 5 of 5)

- [FlowNet: Learning Optical Flow with Convolutional Networks](https://mlsanity.com/paper/1504.06852/) (2015)
- [FlowNet 2.0: Evolution of Optical Flow Estimation with Deep Networks](https://mlsanity.com/paper/1612.01925/) (2016)
- [Deep Learning in Medical Image Registration: A Survey](https://mlsanity.com/paper/1903.02026/) (2019)
- [Iterative Deep Homography Estimation](https://mlsanity.com/paper/2203.15982/) (2022)
- [AnyFlow: Arbitrary Scale Optical Flow with Implicit Neural Representation](https://mlsanity.com/paper/2303.16493/) (2023)

## Abstract (arXiv)

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.