# Linear Spherical Sliced Optimal Transport: A Fast Metric for Comparing Spherical Data

arXiv: https://arxiv.org/abs/2411.06055 · HTML: https://mlsanity.com/paper/2411.06055/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 83 references that are in the map.
- First posted on arXiv 9 Nov 2024.

## Builds on (most cited first, 5 of 5)

- [Large-Scale Optimal Transport and Mapping Estimation](https://mlsanity.com/paper/1711.02283/) (2017)
- [Expected Sliced Transport Plans](https://mlsanity.com/paper/2410.12176/) (2024)
- [Stereographic Spherical Sliced Wasserstein Distances](https://mlsanity.com/paper/2402.02345/) (2024)
- [Validating Climate Models with Spherical Convolutional Wasserstein Distance](https://mlsanity.com/paper/2401.14657/) (2024)
- [LCOT: Linear circular optimal transport](https://mlsanity.com/paper/2310.06002/) (2023)

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

- [A User's Guide to Sampling Strategies for Sliced Optimal Transport](https://mlsanity.com/paper/2502.02275/) (2025)
- [SOTAlign: Semi-Supervised Alignment of Unimodal Vision and Language Models via Optimal Transport](https://mlsanity.com/paper/2602.23353/) (2026)
- [Constrained Sliced Wasserstein Embedding](https://mlsanity.com/paper/2506.02203/) (2025)
- [Partial Optimal Transport on the Circle for All Transported Masses in O(N log N)](https://mlsanity.com/paper/2608.23910/) (2026)

## Abstract (arXiv)

Efficient comparison of spherical probability distributions becomes important in fields such as computer vision, geosciences, and medicine. Sliced optimal transport distances, such as spherical and stereographic spherical sliced Wasserstein distances, have recently been developed to address this need. These methods reduce the computational burden of optimal transport by slicing hyperspheres into one-dimensional projections, i.e., lines or circles. Concurrently, linear optimal transport has been proposed to embed distributions into ( L2 ) spaces, where the ( L2 ) distance approximates the optimal transport distance, thereby simplifying comparisons across multiple distributions. In this work, we introduce the Linear Spherical Sliced Optimal Transport (LSSOT) framework, which utilizes slicing to embed spherical distributions into ( L2 ) spaces while preserving their intrinsic geometry, offering a computationally efficient metric for spherical probability measures. We establish the metricity of LSSOT and demonstrate its superior computational efficiency in applications such as cortical surface registration, 3D point cloud interpolation via gradient flow, and shape embedding. Our results demonstrate the significant computational benefits and high accuracy of LSSOT in these applications.