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

Georgia Institute of Technology
Long Beach VA and University of California

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

36 Citations (Scopus)

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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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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KW - Interpolation of measures

KW - Optimal mass transport

KW - Splines

KW - Wasserstein geometry

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JF - SIAM Journal on Mathematical Analysis

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Measure-valued spline curves: An optimal transport viewpoint

Abstract

Keywords

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