New Fourier-Mellin algorithm improves image alignment to subpixel accuracy

A team of researchers led by Shinji Yamashita, Yuma Kinoshita, and Hitoshi Kiya has developed a new algorithm for aligning images that differ by translation, scaling, and rotation (similarity transformations) with subpixel accuracy, an important task in computer vision and image processing. Their paper, accepted to APSIPA ASC 2026 and posted on arXiv, targets the limitations of classic Fourier-Mellin registration, which often fails when subpixel-level estimation is required.

The algorithm works in two stages. First, it estimates scale and rotation from the Fourier magnitude spectrum converted to a log-polar representation, which elegantly separates these parameters from translation. Second, it fine-tunes translation using phase-only correlation (POC) optimized with an auxiliary function method—a technique that maximizes the correlation function more effectively than simple discrete cross-correlation. By splitting the problem this way, the method avoids translation interference during scale/rotation estimation and then locks on to subpixel translation in the spatial domain.

In simulation experiments with randomly similarity-transformed image pairs, the proposed method consistently reduced estimation errors for scale, rotation, and translation compared with conventional Fourier-Mellin-based registrations using discrete cross-correlation. The paper includes 6 pages and 4 figures, demonstrating the technique's practical viability for applications like image stitching, satellite imagery alignment, and medical imaging, where subpixel precision is critical.