Optimal transportation theory is a powerful tool to deal with image interpolation. This was first investigated by [Benamou and Brenier, Numer. Math. 84 (2000) 375–393.] 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.
DOI : 10.1051/m2an/2015038
Mots clés : Optimal transportation, image multiphysics, proximal splitting method, non-convex optimization
@article{M2AN_2015__49_6_1671_0, author = {Hug, Romain and Maitre, Emmanuel and Papadakis, Nicolas}, title = {Multi-physics optimal transportation and image interpolation}, journal = {ESAIM: Mathematical Modelling and Numerical Analysis }, pages = {1671--1692}, publisher = {EDP-Sciences}, volume = {49}, number = {6}, year = {2015}, doi = {10.1051/m2an/2015038}, zbl = {1348.94006}, mrnumber = {3423271}, language = {en}, url = {http://www.numdam.org/articles/10.1051/m2an/2015038/} }
TY - JOUR AU - Hug, Romain AU - Maitre, Emmanuel AU - Papadakis, Nicolas TI - Multi-physics optimal transportation and image interpolation JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2015 SP - 1671 EP - 1692 VL - 49 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2015038/ DO - 10.1051/m2an/2015038 LA - en ID - M2AN_2015__49_6_1671_0 ER -
%0 Journal Article %A Hug, Romain %A Maitre, Emmanuel %A Papadakis, Nicolas %T Multi-physics optimal transportation and image interpolation %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2015 %P 1671-1692 %V 49 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2015038/ %R 10.1051/m2an/2015038 %G en %F M2AN_2015__49_6_1671_0
Hug, Romain; Maitre, Emmanuel; Papadakis, Nicolas. Multi-physics optimal transportation and image interpolation. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 49 (2015) no. 6, pp. 1671-1692. doi : 10.1051/m2an/2015038. http://www.numdam.org/articles/10.1051/m2an/2015038/
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