# Scale and Rotation Estimation of Similarity-Transformed Images via Cross-Correlation Maximization Based on Auxiliary Function Method

arXiv: https://arxiv.org/abs/2509.22686 · HTML: https://mlsanity.com/paper/2509.22686/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 21 references that are in the map.
- First posted on arXiv 18 Sep 2025.

## Builds on (most cited first, 6 of 6)

- [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)
- [Unsupervised Homography Estimation with Coplanarity-Aware GAN](https://mlsanity.com/paper/2205.03821/) (2022)
- [AnyFlow: Arbitrary Scale Optical Flow with Implicit Neural Representation](https://mlsanity.com/paper/2303.16493/) (2023)

## Abstract (arXiv)

This paper introduces a highly efficient algorithm capable of jointly estimating scale and rotation between two images with sub-pixel precision. Image alignment serves as a critical process for spatially registering images captured from different viewpoints, and finds extensive use in domains such as medical imaging and computer vision. Traditional phase-correlation techniques are effective in determining translational shifts; however, they are inadequate when addressing scale and rotation changes, which often arise due to camera zooming or rotational movements. In this paper, we propose a novel algorithm that integrates scale and rotation estimation based on the Fourier transform in log-polar coordinates with a cross-correlation maximization strategy, leveraging the auxiliary function method. By incorporating sub-pixel-level cross-correlation our method enables precise estimation of both scale and rotation. Experimental results demonstrate that the proposed method achieves lower mean estimation errors for scale and rotation than conventional Fourier transform-based techniques that rely on discrete cross-correlation.