A Wasserstein-type distance in the space of Gaussian Mixture Models - Archive ouverte HAL Access content directly
Journal Articles SIAM Journal on Imaging Sciences Year : 2020

A Wasserstein-type distance in the space of Gaussian Mixture Models

Julie Delon
Agnès Desolneux
  • Function : Author
  • PersonId : 927839

Abstract

In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We derive a very simple discrete formulation for this distance, which makes it suitable for high dimensional problems. We also study the corresponding multi-marginal and barycenter formulations. We show some properties of this Wasserstein-type distance, and we illustrate its practical use with some examples in image processing.
Fichier principal
Vignette du fichier
WassersteinGMM-arxiv-final2.pdf (8.11 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-02178204 , version 1 (09-07-2019)
hal-02178204 , version 2 (27-10-2019)
hal-02178204 , version 3 (09-05-2020)
hal-02178204 , version 4 (09-06-2020)

Identifiers

Cite

Julie Delon, Agnès Desolneux. A Wasserstein-type distance in the space of Gaussian Mixture Models. SIAM Journal on Imaging Sciences, 2020, 13 (2), pp.936-970. ⟨10.1137/19M1301047⟩. ⟨hal-02178204v4⟩
1233 View
865 Download

Altmetric

Share

Gmail Facebook X LinkedIn More