HUG, Romain; MAITRE, Emmanuel; PAPADAKIS, Nicolas

doi:10.1051/m2an/2015038

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HUG, Romain
Equations aux Dérivées Partielles [EDP]

MAITRE, Emmanuel
Equations aux Dérivées Partielles [EDP]

PAPADAKIS, Nicolas
Institut de Mathématiques de Bordeaux [IMB]

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Article de revue

Ce document a été publié dans

ESAIM: Mathematical Modelling and Numerical Analysis. 2015-11, vol. 49, n° 6, p. 1671-1692

EDP Sciences

Résumé en anglais

Optimal transportation theory is a powerful tool to deal with image interpolation. This was first investigated by Benamou and Brenier \cite{BB00} where an algorithm based on the minimization of a kinetic energy under a conservation of mass constraint was devised. By structure, this algorithm does not preserve image regions along the optimal interpolation path, and it is actually not very difficult to exhibit test cases where the algorithm produces a path of images where high density regions split at the beginning before merging back at its end. However, in some applications to image interpolation this behaviour is not physically realistic. Hence, this paper aims at studying how some physics can be added to the optimal transportation theory, how to construct algorithms to compute solutions to the corresponding optimization problems and how to apply the proposed methods to image interpolation.< Réduire

Mots clés en anglais

image multiphysics

Optimal transportation

proximal splitting method

non-convex optimization

URI

https://oskar-bordeaux.fr/handle/20.500.12278/192812

DOI

http://dx.doi.org/10.1051/m2an/2015038

Project ANR

Transport Optimal et Modèles Multiphysiques de l'Image - ANR-11-BS01-0014

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251