# Correlation Ratio for Unsupervised Learning of Multi-modal Deformable Registration

arXiv: https://arxiv.org/abs/2504.12265 · HTML: https://mlsanity.com/paper/2504.12265/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Apr 2025.

## Built on by (most cited first, 2 of 2)

- [Surrogate Supervision for Robust and Generalizable Deformable Image Registration](https://mlsanity.com/paper/2509.09869/) (2025)
- [Domain-Shift Immunity in Deep Deformable Registration via Local Feature Representations](https://mlsanity.com/paper/2512.23142/) (2025)

## Abstract (arXiv)

In recent years, unsupervised learning for deformable image registration has been a major research focus. This approach involves training a registration network using pairs of moving and fixed images, along with a loss function that combines an image similarity measure and deformation regularization. For multi-modal image registration tasks, the correlation ratio has been a widely-used image similarity measure historically, yet it has been underexplored in current deep learning methods. Here, we propose a differentiable correlation ratio to use as a loss function for learning-based multi-modal deformable image registration. This approach extends the traditionally non-differentiable implementation of the correlation ratio by using the Parzen windowing approximation, enabling backpropagation with deep neural networks. We validated the proposed correlation ratio on a multi-modal neuroimaging dataset. In addition, we established a Bayesian training framework to study how the trade-off between the deformation regularizer and similarity measures, including mutual information and our proposed correlation ratio, affects the registration performance.