… Radon transform of a measure µ ∈ M(Rd) as the measure … sliced-Wasserstein discrepancy
on the sphere and discuss some of its properties. Notably, we derive a new spherical Radon …

… a new two-dimensional Radon transform and develop its … sliced OT from even measures
to arbitrary probability … with barycenters with respect to our new sliced Wasserstein distances …

… For any p ≥ 1, we define Pp(Rd) as the set of Borel probability measures with finite p-th …
) Radon transform maps, which are key to the notion of (generalized) sliced-Wasserstein …

… If µ and ν are continuous one-dimensional measures defined … spatial Radon transformwhich
includes the Radon transform … color transferring and Wasserstein barycenters. What remains …

… Transform (HRT) which is constructed by applying Radon … between measures, named
Hierarchical Sliced Wasserstein (HSW… the Radon Transform, we can define the sliced Wasserstein …

… In TSW-SL, we use a variant of the Radon Transform to project measures onto a system
of lines, resulting in measures on a space with a tree metric, then leverage TW to efficiently …

… spherical measures using the stereographic projection and the generalized Radon transform,
… This section will review the classic Radon transform in the general Radon measure setting. …

… the Radon transform, we introduce the vertical slice transform, … for all measures, and hence
the sliced Wasserstein distance … First, we show in section 7.1 that Wasserstein barycenters on …

… of probability measures. In particular, a Wasserstein barycenter is a probability measure that
… Due to the rich geometry of the Wasserstein distance [38], the Wasserstein barycenter can …

… measures we prove the central limit theorem and concentration results for empirical Wasserstein
barycenters. It … classes, and each of them is a Radon space (in particular, it is separable …