A lagrangian scheme for the solution of the optimal mass transfer problem |
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Authors: | Angelo Iollo Damiano Lombardi |
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Affiliation: | Institut de Mathématiques de Bordeaux UMR 5251 Université Bordeaux 1 and INRIA Bordeaux-Sud Ouest, équipe-projet MC2, 351, Cours de la Libération, Talence 33405, France |
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Abstract: | A lagrangian method to numerically solve the L2 optimal mass transfer problem is presented. The initial and final density distributions are approximated by finite mass particles having a gaussian kernel. Mass conservation and the Hamilton–Jacobi equation for the potential are identically satisfied by constant mass transport along straight lines. The scheme is described in the context of existing methods to solve the problem and a set of numerical examples including applications to medical imagery are presented. |
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