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1 REO - Numerical simulation of biological flows LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt, UPMC - Université Pierre et Marie Curie - Paris 6 2 EDP - Equations aux Dérivées Partielles LJK - Laboratoire Jean Kuntzmann

Abstract : Benamou and Brenier formulation of Monge transportation problem Numer. Math. 84:375-393, 2000 has proven to be of great interest in image processing to compute warpings and distances between pair of images SIAM J. Math. Analysis, 35:61-97, 2003. One requirement for the algorithm to work is to interpolate densities of same mass. In most applications to image interpolation, this is a serious limitation. Existing approaches to overcome this caveat are reviewed, and discussed. Due to the mix between transport and $L^2$ interpolation, these models can produce instantaneous motion at finite range. In this paper we propose new methods, parameter-free, for interpolating unbalanced densities. One of our motivations is the application to interpolation of growing tumor images.

Keywords : Optimal transport Unbalanced Tumor Interpolation Algorithm Image

Author: Damiano Lombardi - Emmanuel Maitre -



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