# Fast computation of mutual information in the frequency domain with applications to global multimodal image alignment

arXiv: https://arxiv.org/abs/2106.14699 · HTML: https://mlsanity.com/paper/2106.14699/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 36 references that are in the map.
- First posted on arXiv 28 Jun 2021.

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

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Learning in Medical Image Registration: A Survey](https://mlsanity.com/paper/1903.02026/) (2019)
- [Deep Learning in Medical Image Registration: A Review](https://mlsanity.com/paper/1912.12318/) (2019)
- [CoMIR: Contrastive Multimodal Image Representation for Registration](https://mlsanity.com/paper/2006.06325/) (2020)
- [Is Image-to-Image Translation the Panacea for Multimodal Image Registration? A Comparative Study](https://mlsanity.com/paper/2103.16262/) (2021)
- [Fast and Robust Symmetric Image Registration Based on Distances Combining Intensity and Spatial Information](https://mlsanity.com/paper/1807.11599/) (2018)

## Built on by (most cited first, 6 of 6)

- [Let it shine: Autofluorescence of Papanicolaou-stain improves AI-based cytological oral cancer detection](https://mlsanity.com/paper/2407.01869/) (2024)
- [Can representation learning for multimodal image registration be improved by supervision of intermediate layers?](https://mlsanity.com/paper/2303.00403/) (2023)
- [PromptMID: Modal Invariant Descriptors Based on Diffusion and Vision Foundation Models for Optical-SAR Image Matching](https://mlsanity.com/paper/2502.18104/) (2025)
- [Cross-Sim-NGF: FFT-Based Global Rigid Multimodal Alignment of Image Volumes using Normalized Gradient Fields](https://mlsanity.com/paper/2110.10156/) (2021)
- [Fidelity-Imposed Displacement Editing for the Learn2Reg 2024 SHG-BF Challenge](https://mlsanity.com/paper/2410.20812/) (2024)
- [Fourier Preconditioning for Neural Feature Learning](https://mlsanity.com/paper/2607.02199/) (2026)

## Abstract (arXiv)

Multimodal image alignment is the process of finding spatial correspondences between images formed by different imaging techniques or under different conditions, to facilitate heterogeneous data fusion and correlative analysis. The information-theoretic concept of mutual information (MI) is widely used as a similarity measure to guide multimodal alignment processes, where most works have focused on local maximization of MI that typically works well only for small displacements; this points to a need for global maximization of MI, which has previously been computationally infeasible due to the high run-time complexity of existing algorithms. We propose an efficient algorithm for computing MI for all discrete displacements (formalized as the cross-mutual information function (CMIF)), which is based on cross-correlation computed in the frequency domain. We show that the algorithm is equivalent to a direct method while asymptotically superior in terms of run-time. Furthermore, we propose a method for multimodal image alignment for transformation models with few degrees of freedom (e.g. rigid) based on the proposed CMIF-algorithm. We evaluate the efficacy of the proposed method on three distinct benchmark datasets, of aerial images, cytological images, and histological images, and we observe excellent success-rates (in recovering known rigid transformations), overall outperforming alternative methods, including local optimization of MI as well as several recent deep learning-based approaches. We also evaluate the run-times of a GPU implementation of the proposed algorithm and observe speed-ups from 100 to more than 10,000 times for realistic image sizes compared to a GPU implementation of a direct method. Code is shared as open-source at urlgithub.com/MIDA-group/globalign.