Computational Mathematics and Scientific Computing Seminar

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Optimization methods for optimal transport in imaging

Speaker: Dirk Lorenz, TU-Braunschweig

Location: Warren Weaver Hall 1302

Date: Dec. 9, 2016, 10 a.m.

Synopsis:

The problem of optimal transport asks "How to move some pile of mass to form another pile of mass with the least effort?" and has triggered contributions from many different fields of mathematics such as linear programming, partial differential equations, measure theory or Riemannian geometry in its over 200 years of history. Today, optimal transport can be viewed from many different angles and has found applications in many different fields, probably most prominently in economics.

In this talk we will investigate applications of techniques from optimal transport in the context of mathematical imaging. Distances based on optimal transport can be used to capture spatial geometric features and can lead to interesting effects. We will introduce optimal transport, treat different formulations and then focus on a particular functional analytic framework which is well suited for optimization in applications in imaging. We also highlight challenges in the numerical treatment of optimal transport problems, present some concrete applications and illustrate the effects with pictures.