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NORIA SIGNED

Numerical Optimal tRansport for ImAging

Total Cost €

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EC-Contrib. €

0

Partnership

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 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.

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

Project "NORIA" data sheet

The following table provides information about the project.

Coordinator
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS 

Organization address
address: RUE MICHEL ANGE 3
city: PARIS
postcode: 75794
website: www.cnrs.fr

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

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS FR (PARIS) coordinator 1˙996˙720.00

Map

 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.

 Publications

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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