Spherical Sliced-Wasserstein
Cl\'ement Bonet, Paul Berg, Nicolas Courty, Fran\c{c}ois Septier,, Lucas Drumetz, Minh-Tan Pham

TL;DR
This paper introduces a novel Sliced-Wasserstein discrepancy tailored for spherical data, extending Wasserstein-based methods from Euclidean spaces to manifolds like the sphere, with applications in machine learning tasks involving spherical representations.
Contribution
It proposes the spherical Sliced-Wasserstein, a new discrepancy measure for data on the sphere, based on closed-form Wasserstein solutions and a spherical Radon transform, enabling manifold-aware Wasserstein computations.
Findings
Efficient algorithms for spherical Sliced-Wasserstein
Applications in sampling, density estimation, and auto-encoders on the sphere
Demonstrated advantages over Euclidean-based Wasserstein methods
Abstract
Many variants of the Wasserstein distance have been introduced to reduce its original computational burden. In particular the Sliced-Wasserstein distance (SW), which leverages one-dimensional projections for which a closed-form solution of the Wasserstein distance is available, has received a lot of interest. Yet, it is restricted to data living in Euclidean spaces, while the Wasserstein distance has been studied and used recently on manifolds. We focus more specifically on the sphere, for which we define a novel SW discrepancy, which we call spherical Sliced-Wasserstein, making a first step towards defining SW discrepancies on manifolds. Our construction is notably based on closed-form solutions of the Wasserstein distance on the circle, together with a new spherical Radon transform. Along with efficient algorithms and the corresponding implementations, we illustrate its properties in…
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Code & Models
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Taxonomy
TopicsMedical Imaging Techniques and Applications · 3D Shape Modeling and Analysis · Medical Image Segmentation Techniques
MethodsVariational Inference
