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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Pages (de - à)	5947-5968
Nombre de pages	22
journal	SIAM Journal on Mathematical Analysis
Volume	50
Numéro de publication	6
Les DOIs	https://doi.org/10.1137/18M1166249
état	Publié - 1 janv. 2018

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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.\}",

note = "Publisher Copyright: {\textcopyright} 2018 Society for Industrial and Applied Mathematics.",

year = "2018",

month = jan,

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doi = "10.1137/18M1166249",

language = "English",

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journal = "SIAM Journal on Mathematical Analysis",

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T2 - An optimal transport viewpoint

AU - Chen, Yongxin

AU - Conforti, Giovanni

AU - Georgiou, Tryphon T.

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Y1 - 2018/1/1

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AB - 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.

KW - Interpolation of measures

KW - Optimal mass transport

KW - Splines

KW - Wasserstein geometry

UR - https://www.scopus.com/pages/publications/85060534785

U2 - 10.1137/18M1166249

DO - 10.1137/18M1166249

M3 - Article

AN - SCOPUS:85060534785

SN - 0036-1410

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EP - 5968

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

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ER -

Measure-valued spline curves: An optimal transport viewpoint

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