Gabriel Peyré. Wasserstein Methods in Imaging.

In this talk I will review the use of optimal transport methods to tackle
various imaging problems such as texture synthesis and mixing, color
transfer, and shape retrieval. Representing texture variations as well as
shapes geometry can be achieved by recording histograms of high
dimensional feature distributions. I will present a fast approximate
Wasserstein distance to achieve fast optimal transport manipulations of
these high dimensional histograms. The resulting approximate distance can
be optimized using standard first order optimization schemes to perform
color equalization and texture synthesis. It is also possible to use this
optimal transport as a data fidelity term in standard inverse problems
regularization. One can try online several ideas related to Wasserstein
imaging (as many other imaging methods) by visiting
www.numerical-tours.com (computer graphics section). This is a joint work
with Julien Rabin, Julie Delon and Marc Bernot.