ANR ROOT: RegressiOn with Optimal Transport, for computer graphics and vision
Aug. 2016 - Sept. 2021
Presentation
ROOT is a project funded by the ANR throught the young researchers program JCJC. ROOT aims at developping numerical methods for solving regression problems involving optimal transport, with applications in computer graphics and vision.
These problems include data fitting, supervised or unsupervised learning, or statistical inference, applied to histogram features.
Histograms are frequently encountered in computer graphics (e.g., reflectance functions, color
palettes, distance histograms etc.) and vision (e.g., SIFT or HoG descriptors). Optimal transport offers a framework with a
meaningful way of comparing histograms as the amount of work required to move a pile of sand representing one histogram to match another. It also proposes
a way of interpolating histograms as the intermediate distribution produced during this motion.
The ROOT project explores the use of optimal transport, but, as a metric in the context of
inverse problems for graphics and vision, and machine learning.
Challenges addressed by ROOT include:
- Computationally efficient optimal transport solvers between histograms, for use within regression iterations.
- Solving inverse problems in graphics and vision involving histograms via regressions within the optimal transport framework.
Team
Permanents
- Nicolas Bonneel (LIRIS, coordinator)
- Gabriel Peyré (ENS)
- Marco Cuturi (CREST - ENSAE)
- Bruno Lévy (INRIA Nancy Grand-Est)
- David Coeurjolly (LIRIS)
- Julie Digne (LIRIS)
Students
- Matthieu Heitz (PhD student, started Oct. 2016 ; supervision: N. Bonneel, D. Coeurjolly, G. Peyré, M. Cuturi)
- Agathe Herrou (PhD student, started in Sept. 2018 ; supervision: N.Bonneel, J. Digne, B. Lévy).
- Guillaume Cherreau (Master's student ; supervision: N. Bonneel, J. Digne, F. Santambrogio).
- Julien Lacombe (Master's student ; supervision: N. Bonneel, J. Digne).
Publications
Morgan A. Schmitz, Matthieu Heitz, Nicolas Bonneel, Fred Maurice Ngolè Mboula, David Coeurjolly, Marco Cuturi, Gabriel Peyré, Jean-Luc Starck
Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning
SIAM Journal on Imaging Sciences (SIIMS) (2018, to appear)
Preprint
Bibtex
Morgan A. Schmitz, Matthieu Heitz, Nicolas Bonneel, Fred Maurice Ngolè Mboula, David Coeurjolly, Marco Cuturi, Gabriel Peyré, Jean-Luc Starck
Optimal transport-based dictionary learning and its application to Euclid-like Point Spread Function representation
SPIE Wavelets and Sparsity XVII
Paper
Poster
Bibtex
