Some Unexpected Uses of Total Variation Minimization
Antonin Chambolle, CMAP - Ecole Polytechnique - CNRS, Paris, France

Seminar • 08 October 2009 • MEB10

Abstract
In this talk I will discuss a few recent work in collaboration with Daniel Cremers (Bonn) and Tom Pock (U. Graz) on the minimization of "nonconvex" problems. (We'll see that there is no miracle, though.) I will explain how one can construct simple representations to minimize reconstruction problems (in stereo, optical flow...) with a convex interaction term by minimizing a globally convex energy, in some kind of continuous variant of Ishikawa and Geiger's representation for MRFs. We will then try to extend this to truly nonconvex problems, such as the Mumford-Shah functional and the optimal partition problem.