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Numerical Optimal tRansport for ImAging

Total Cost €


EC-Contrib. €






 NORIA project word cloud

Explore the words cloud of the NORIA project. It provides you a very rough idea of what is the project "NORIA" about.

computational    neuroimaging    ing    rely    restricted    quantization    ot    sense    noria    schemes    fast    data    reaching    mathematical    geometric    sciences    compare    favorably    color    interfaced    transport    intuitive    theoretical    substantial    stochastic    generation    time    probability    favorable    graphics    imag    provides    exploration    standard    metric    regularization    imaging    mathematically    framework    metrics    computer    parallelizable    language    tool    confidential    wealth    gradient    notably    optimal    practical    algorithmic    point    numerical    bregman    codes    texture    niche    opportunity    distributions    bottlenecks    naively    euclidean    visual    flagship    scripting    clouds    entropic    breakthroughs    principles    barely    give    cortex    flows    synthesis    science    algorithms    spaces    embodiment    divergences    vision    players    computations    powerful    broad    consumes    distances    material    outputs    hinders    sensitive    alternatives    school    members    routinely    theory    optimization    suitable    manipulate   

Project "NORIA" data sheet

The following table provides information about the project.


Organization address
address: RUE MICHEL ANGE 3
city: PARIS
postcode: 75794

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country France [FR]
 Total cost 1˙996˙720 €
 EC max contribution 1˙996˙720 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-COG
 Funding Scheme ERC-COG
 Starting year 2017
 Duration (year-month-day) from 2017-10-01   to  2022-09-30


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

Optimal Transport (OT) theory provides a powerful framework to manipulate probability distributions using simple and intuitive geometric principles. OT distances compare favorably to all other alternatives, notably Euclidean metrics or information divergences, whose outputs are particularly sensitive to changes in quantization and are not suitable to compare point clouds. Because of these and many more favorable properties, OT should be a standard tool in imaging sciences where probability distributions are routinely used. However, at this time, OT is but a confidential tool restricted to niche applications. OT is barely used because it is complex mathematically, which hinders its dissemination in more applied fields, and because it consumes substantial computational resources when used naively. NORIA will address these two bottlenecks and develop the next generation of theoretical, numerical and algorithmic advances to enable large-scale optimal transport computations in imag- ing sciences. The algorithms developed by NORIA will rely on several mathematical breakthroughs: highly parallelizable entropic regularization schemes, Bregman stochastic optimization and gradient flows for metric spaces. They will be implemented using fast optimization codes that will be interfaced through a high-level, easy to use, scripting language. These algorithms will have far reaching applications in imaging sciences and data science in a broad sense. In particular, they will be used in three flagship applications: color and material processing in computer graphics, texture analysis and synthesis in computer vision, and exploration of the visual cortex in neuroimaging. NORIA’s members are key players in the European mathematical school of optimal transport, which is very strong. NORIA is the unique opportunity to give a computational and practical embodiment to this wealth of theoretical knowledge.


year authors and title journal last update
List of publications.
2019 A. Genevay, L. Chizat, F. Bach, M. Cuturi, G. Peyré
Sample Complexity of Sinkhorn divergences
published pages: , ISSN: , DOI:
Proc AISTATS2019 2019-08-05
2018 Jingwei Liang, Jalal Fadili, Gabriel Peyré
Local linear convergence analysis of Primal–Dual splitting methods
published pages: 821-853, ISSN: 0233-1934, DOI: 10.1080/02331934.2018.1426584
Optimization 67/6 2019-08-06
2018 Lénaïc Chizat, Gabriel Peyré, Bernhard Schmitzer, François-Xavier Vialard
An Interpolating Distance Between Optimal Transport and Fisher–Rao Metrics
published pages: 1-44, ISSN: 1615-3375, DOI: 10.1007/s10208-016-9331-y
Foundations of Computational Mathematics 18/1 2019-08-06
2019 C. Poon, N. Keriven, G. Peyré
Support localization and the fisher metric for off-the-grid sparse regularization
published pages: , ISSN: , DOI:
Proc AISTATS 2019 2019-08-05
2018 Marco Cuturi, Gabriel Peyré
Semidual Regularized Optimal Transport
published pages: 941-965, ISSN: 0036-1445, DOI: 10.1137/18m1208654
SIAM Review 60/4 2019-08-06
2018 Lénaïc Chizat, Gabriel Peyré, Bernhard Schmitzer, François-Xavier Vialard
Unbalanced optimal transport: Dynamic and Kantorovich formulations
published pages: 3090-3123, ISSN: 0022-1236, DOI: 10.1016/j.jfa.2018.03.008
Journal of Functional Analysis 274/11 2019-08-06
2018 Gabriel Peyré, Marco Cuturi
Computational Optimal Transport
published pages: 355-206, ISSN: 1935-8237, DOI: 10.1561/2200000073
Foundations and Trends® in Machine Learning 11/5-6 2019-08-05
2019 Clarice Poon, Gabriel Peyré
MultiDimensional Sparse Super-Resolution
published pages: 1-44, ISSN: 0036-1410, DOI: 10.1137/17m1147822
SIAM Journal on Mathematical Analysis 51/1 2019-08-05
2018 Jalal Fadili, Jérôme Malick, Gabriel Peyré
Sensitivity Analysis for Mirror-Stratifiable Convex Functions
published pages: 2975-3000, ISSN: 1052-6234, DOI: 10.1137/17m113825x
SIAM Journal on Optimization 28/4 2019-08-06
2019 J. Fadili, G. Garrigos, J. Malick, G. Peyré
Model Consistency for Learning with Mirror-Stratifiable Regularizers
published pages: , ISSN: , DOI:
Proc AISTATS2019 2019-08-05

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