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Around unbalanced optimal transport: fluid dynamic, growth model, applications.

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GFSW03 - Shape analysis and computational anatomy

In this talk, we present the so-called Wasserstein-Fisher-Rao metric (also called Hellinger-Kantorovich) by its dynamical and static formulation. The link between these two formulations is made clear by generalizing the Riemannian submersion of Otto to this new setting. Then the link with the Camassa-Holm equation can be made with this metric, in the same way Brenier made it between optimal transport and incompressible Euler. Passing by, we prove that the Camassa-Holm equation is actually an incompressible Euler equation on a bigger space. We also show the use of this metric to interpret a particular Hele-Shaw model as a gradient flow. We then finish with some examples of use of this new metric as a similarity measure on diffeomorphic registration of shapes.

This talk is part of the Isaac Newton Institute Seminar Series series.

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