# Fast Optimal Transport Averaging of Neuroimaging Data

arXiv: https://arxiv.org/abs/1503.08596 · HTML: https://mlsanity.com/paper/1503.08596/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Mar 2015.

## Built on by (most cited first, 26 of 26)

- [Unbalanced Optimal Transport, from Theory to Numerics](https://mlsanity.com/paper/2211.08775/) (2022)
- [Averaging on the Bures-Wasserstein manifold: dimension-free convergence of gradient descent](https://mlsanity.com/paper/2106.08502/) (2021)
- [Wasserstein barycenters are NP-hard to compute](https://mlsanity.com/paper/2101.01100/) (2021)
- [Aligning individual brains with Fused Unbalanced Gromov-Wasserstein](https://mlsanity.com/paper/2206.09398/) (2022)
- [Neural Unbalanced Optimal Transport via Cycle-Consistent Semi-Couplings](https://mlsanity.com/paper/2209.15621/) (2022)
- [Non-Asymptotic Performance Guarantees for Neural Estimation of mathsff-Divergences](https://mlsanity.com/paper/2103.06923/) (2021)
- [Smooth Bilevel Programming for Sparse Regularization](https://mlsanity.com/paper/2106.01429/) (2021)
- [Learning with symmetric positive definite matrices via generalized Bures-Wasserstein geometry](https://mlsanity.com/paper/2110.10464/) (2021)
- [Unbalanced Diffusion Schr"odinger Bridge](https://mlsanity.com/paper/2306.09099/) (2023)
- [Efficient and Accurate Optimal Transport with Mirror Descent and Conjugate Gradients](https://mlsanity.com/paper/2307.08507/) (2023)
- [On Partial Optimal Transport: Revising the Infeasibility of Sinkhorn and Efficient Gradient Methods](https://mlsanity.com/paper/2312.13970/) (2023)
- [Unsupervised Ground Metric Learning using Wasserstein Singular Vectors](https://mlsanity.com/paper/2102.06278/) (2021)
- [Sampling From the Wasserstein Barycenter](https://mlsanity.com/paper/2105.01706/) (2021)
- [Diffeomorphic Measure Matching with Kernels for Generative Modeling](https://mlsanity.com/paper/2402.08077/) (2024)
- [Non-isotropic Persistent Homology: Leveraging the Metric Dependency of PH](https://mlsanity.com/paper/2310.16437/) (2023)
- [Approximate Algorithms For k-Sparse Wasserstein Barycenter With Outliers](https://mlsanity.com/paper/2404.13401/) (2024)
- [Optimal Transport Barycenter via Nonconvex-Concave Minimax Optimization](https://mlsanity.com/paper/2501.14635/) (2025)
- [Sobolev Gradient Ascent for Optimal Transport: Barycenter Optimization and Convergence Analysis](https://mlsanity.com/paper/2505.13660/) (2025)
- [Max-sliced Wasserstein concentration and uniform ratio bounds of empirical measures on RKHS](https://mlsanity.com/paper/2405.13153/) (2024)
- [Sparse Partial Optimal Transport via Quadratic Regularization](https://mlsanity.com/paper/2508.08476/) (2025)
- [Lower Bounds on Adversarial Robustness for Multiclass Classification with General Loss Functions](https://mlsanity.com/paper/2510.01969/) (2025)
- [A Homotopy Algorithm for Optimal Transport](https://mlsanity.com/paper/2112.06763/) (2021)
- [Optimal Transport Features for Morphometric Population Analysis](https://mlsanity.com/paper/2208.05891/) (2022)
- [Optimal Transport for Correctional Learning](https://mlsanity.com/paper/2304.01701/) (2023)
- [A Novel Skip Orthogonal List for Dynamic Optimal Transport Problem](https://mlsanity.com/paper/2310.18446/) (2023)
- [Generalized infinite dimensional Alpha-Procrustes based geometries](https://mlsanity.com/paper/2511.09801/) (2025)

## Abstract (arXiv)

Knowing how the Human brain is anatomically and functionally organized at the level of a group of healthy individuals or patients is the primary goal of neuroimaging research. Yet computing an average of brain imaging data defined over a voxel grid or a triangulation remains a challenge. Data are large, the geometry of the brain is complex and the between subjects variability leads to spatially or temporally non-overlapping effects of interest. To address the problem of variability, data are commonly smoothed before group linear averaging. In this work we build on ideas originally introduced by Kantorovich to propose a new algorithm that can average efficiently non-normalized data defined over arbitrary discrete domains using transportation metrics. We show how Kantorovich means can be linked to Wasserstein barycenters in order to take advantage of an entropic smoothing approach. It leads to a smooth convex optimization problem and an algorithm with strong convergence guarantees. We illustrate the versatility of this tool and its empirical behavior on functional neuroimaging data, functional MRI and magnetoencephalography (MEG) source estimates, defined on voxel grids and triangulations of the folded cortical surface.