Section: New Results

Image processing

Image processing

Participant : Nicolas Papadakis.

In collaboration with the Inria team MC2 of the Bordeaux-Sud-Ouest center, we investigate the application of image assimilation to medical issues. The objective is here to use MRI images in order to monitor EDP models dealing with tumor growth in lungs or brains. Using such images, we would like to define a patient specific process allowing to calibrate the numerical model with respect to the observed tumor. First works based on convex relaxation of the binary segmentation problem [34] have been realized in this direction by proposing a 3D segmentation method dedicated to glioblastomas from a set of MRI brain images. The obtained automatic segmentation results are very close to specialist manual segmentations (errors of 5%) and will be used as pseudo-observations for an assimilation system based on the numerical model describing the tumor growth. The final issue will be to define an observation operator linking images with the model in order to realize a direct assimilation.

Next, in collaboration with Vicent Caselles (Pompeu Fabra University, Barcelona, Spain) we tackled the problem of histogram equalization of different images. Our aim has been to include spatial information on color repartition during the histogram transfer for inpainting and shadow removal purposes [18] . We also focused with Jean-François Aujol (Institut de Mathématiques de Bordeaux), on the convexification of non linear problems such as optical flow estimation and submitted a jounal paper on this subject in SIAM Journal on Imaging Sciences.

Optimal transport

Participants : Maëlle Nodet, Nicolas Papadakis, Arthur Vidard.

Within the optimal transport project TOMMI funded by the ANR white program, some new algorithms had been proposed to take into account the physics (rigidity, elesticity) of the density to transport [40] . A journal paper has been submitted on this topic in M2AN.