# Fast rigid alignment of heterogeneous images in sliced Wasserstein distance

arXiv: https://arxiv.org/abs/2503.13756 · HTML: https://mlsanity.com/paper/2503.13756/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 53 references that are in the map.
- First posted on arXiv 17 Mar 2025.

## Builds on (most cited first, 15 of 15)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Max-Sliced Wasserstein Distance and its use for GANs](https://mlsanity.com/paper/1904.05877/) (2019)
- [Generative Modeling using the Sliced Wasserstein Distance](https://mlsanity.com/paper/1803.11188/) (2018)
- [Sliced Wasserstein Kernels for Probability Distributions](https://mlsanity.com/paper/1511.03198/) (2015)
- [The Radon cumulative distribution transform and its application to image classification](https://mlsanity.com/paper/1511.03206/) (2015)
- [Earthmover-based manifold learning for analyzing molecular conformation spaces](https://mlsanity.com/paper/1911.06107/) (2019)
- [Alignment of Density Maps in Wasserstein Distance](https://mlsanity.com/paper/2305.12310/) (2023)
- [Centering noisy images with application to cryo-EM](https://mlsanity.com/paper/2009.04810/) (2020)
- [Invariance encoding in sliced-Wasserstein space for image classification with limited training data](https://mlsanity.com/paper/2201.02980/) (2022)
- [AlignOT: An optimal transport based algorithm for fast 3D alignment with applications to cryogenic electron microscopy density maps](https://mlsanity.com/paper/2210.09361/) (2022)
- [Wasserstein K-Means for Clustering Tomographic Projections](https://mlsanity.com/paper/2010.09989/) (2020)
- [Nonequispaced Fast Fourier Transform Boost for the Sinkhorn Algorithm](https://mlsanity.com/paper/2201.07524/) (2022)
- [Ab-initio Contrast Estimation and Denoising of Cryo-EM Images](https://mlsanity.com/paper/2202.07737/) (2022)
- [The Radon Signed Cumulative Distribution Transform and its applications in classification of Signed Images](https://mlsanity.com/paper/2307.15339/) (2023)

## Built on by (most cited first, 4 of 4)

- [Quantifying the noise sensitivity of the Wasserstein metric for images](https://mlsanity.com/paper/2510.01015/) (2025)
- [Generalizations of the Normalized Radon Cumulative Distribution Transform for Limited Data Recognition](https://mlsanity.com/paper/2512.08099/) (2025)
- [Application and Evaluation of the Common Circles Method](https://mlsanity.com/paper/2602.17353/) (2026)
- [On the stability of scale-space metrics](https://mlsanity.com/paper/2606.27605/) (2026)

## Abstract (arXiv)

Many applications of computer vision rely on the alignment of similar but non-identical images. We present a fast algorithm for aligning heterogeneous images based on optimal transport. Our approach combines the speed of fast Fourier methods with the robustness of sliced probability metrics and allows us to efficiently compute the alignment between two L × L images using the sliced 2-Wasserstein distance in O(L2 log L) operations. We show that our method is robust to translations, rotations and deformations in the images.