# AlignOT: An optimal transport based algorithm for fast 3D alignment with applications to cryogenic electron microscopy density maps

arXiv: https://arxiv.org/abs/2210.09361 · HTML: https://mlsanity.com/paper/2210.09361/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Oct 2022.

## Built on by (most cited first, 7 of 7)

- [Alignment of Density Maps in Wasserstein Distance](https://mlsanity.com/paper/2305.12310/) (2023)
- [Fast rigid alignment of heterogeneous images in sliced Wasserstein distance](https://mlsanity.com/paper/2503.13756/) (2025)
- [Robust Point Matching with Distance Profiles](https://mlsanity.com/paper/2312.12641/) (2023)
- [Quantization-based Bounds on the Wasserstein Metric](https://mlsanity.com/paper/2506.00976/) (2025)
- [Quantifying the noise sensitivity of the Wasserstein metric for images](https://mlsanity.com/paper/2510.01015/) (2025)
- [The Joint Gromov Wasserstein Objective for Multiple Object Matching](https://mlsanity.com/paper/2511.16868/) (2025)
- [Cluster-Aware Matching via Laplacian Optimal Transport](https://mlsanity.com/paper/2607.16178/) (2026)

## Abstract (arXiv)

Aligning electron density maps from Cryogenic electron microscopy (cryo-EM) is a first key step for studying multiple conformations of a biomolecule. As this step remains costly and challenging, with standard alignment tools being potentially stuck in local minima, we propose here a new procedure, called AlignOT, which relies on the use of computational optimal transport (OT) to align EM maps in 3D space. By embedding a fast estimation of OT maps within a stochastic gradient descent algorithm, our method searches for a rotation that minimizes the Wasserstein distance between two maps, represented as point clouds. We quantify the impact of various parameters on the precision and accuracy of the alignment, and show that AlignOT can outperform the standard local alignment methods, with an increased range of rotation angles leading to proper alignment. We further benchmark AlignOT on various pairs of experimental maps, which account for different types of conformational heterogeneities and geometric properties. As our experiments show good performance, we anticipate that our method can be broadly applied to align 3D EM maps.