Convex Relaxations for the Mumford-Shah Functional

Daniel Cremers
Technische Universtitat München

I will review the Mumford-Shah functional, some special cases and generalizations including the piecewise constant limit, anisotropic versions and vectorial formulations. I will discuss how respective functionals can be relaxed to convex problems which can be solved efficiently using provably convergent primal-dual algorithms. Applications to computer vision problems such as segmentation, denoising and semantic labeling demonstrate that the convex relaxations allow to compute near-optimal solutions which are independent of initialization. This is joint work with E. Strekalovskiy, A. Chambolle, T. Pock, C. Nieuwenhuis and M. Souiai.

Presentation (PDF File)

Back to Convex Relaxation Methods for Geometric Problems in Scientific Computing