Unbalanced Optimal Transport: Geometry and Kantorovich Formulation

21 Aug 2015Lenaic ChizatGabriel PeyréBernhard SchmitzerFrançois-Xavier Vialard

This article presents a new class of "optimal transportation"-like distances between arbitrary positive Radon measures. These distances are defined by two equivalent alternative formulations: (i) a "fluid dynamic" formulation defining the distance as a geodesic distance over the space of measures (ii) a static "Kantorovich" formulation where the distance is the minimum of an optimization program over pairs of couplings describing the transfer (transport, creation and destruction) of mass between two measures... (read more)

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