Parallelly Sliced Optimal Transport on Spheres and on the Rotation Group

Understand

Sliced optimal transport, which is basically a Radon transform followed by one-dimensional optimal transport, became popular in various applications due to its efficient computation.

• In this paper, we deal with sliced optimal transport on the sphere $\mathbb{S}^{d-1}$ and on the rotation group SO(3).
• We propose a parallel slicing procedure of the sphere which requires again only optimal transforms on the line.
• We analyze the properties of the corresponding parallelly sliced optimal transport, which provides in particular a rotationally invariant metric on the spherical probability measures.