Measure-valued spline curves: An optimal transport viewpoint

Yongxin Chen; Giovanni Conforti; Tryphon T. Georgiou

doi:10.1137/18M1166249

Measure-valued spline curves: An optimal transport viewpoint

Yongxin Chen
, Giovanni Conforti
, Tryphon T. Georgiou

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	5947-5968
Number of pages	22
Journal	SIAM Journal on Mathematical Analysis
Volume	50
Issue number	6
DOIs	https://doi.org/10.1137/18M1166249
Publication status	Published - 1 Jan 2018

Keywords

Interpolation of measures
Optimal mass transport
Splines
Wasserstein geometry

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10.1137/18M1166249

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title = "Measure-valued spline curves: An optimal transport viewpoint",

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.",

keywords = "Interpolation of measures, Optimal mass transport, Splines, Wasserstein geometry",

author = "Yongxin Chen and Giovanni Conforti and Georgiou, \{Tryphon T.\}",

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year = "2018",

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AU - Conforti, Giovanni

AU - Georgiou, Tryphon T.

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KW - Interpolation of measures

KW - Optimal mass transport

KW - Splines

KW - Wasserstein geometry

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DO - 10.1137/18M1166249

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JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

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Measure-valued spline curves: An optimal transport viewpoint

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