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Measure-Valued Spline Curves: An Optimal Transport Viewpoint

Published Web Location

https://doi.org/10.1137/18m1166249
Abstract

The aim of this article is to introduce and address the problem to smoothly interpolate (empirical) probability measures. To this end, we lift the concept of a spline curve from the setting of points in a Euclidean space to that of probability measures, using the framework of optimal transport.

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