Optimal Transport Methods in Imaging

English

Séminaire Géométrie-Images: Calcul des variations

20/12/2012 - 15:15 Gabriel Peyré (Université Paris-Dauphine) Salle 1 - Tour IRMA

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 ("optimal transport" section).