Description

The construction of interpolations between two images is an old problem with applications e.g. in the recovery of lost or damaged data in video captures issued from scientific experiments. Methods based on optimal transportation are currently unable to take into account the physics of the represented objects: the optimal transport plan often has the very undesirable effect of splitting regions into smaller pieces during the interpolation and to merge them back at the end.

The name TOMMI stands for Transport optimal, m├ęthodes multiphysiques et image.

October 3-4, 2013: Workshop "Modelisation and optimal transport". New!

Objectives

The objectives of this project, funded by the French ANR, are the following:
  • Study formulations of optimal transport where a physical model is attached to the images.
  • Develop efficient algorithms and numerical schemes for this formulation.
  • Apply these tools in image processing and assimilation.

Gallery

Optimal transport with and without penalization of nonrigidity

OT interpolation between two Gaussians rigid OT interpolation between two Gaussians

Quadratic optimal transport using convex optimization