Semi-Linearized Proximal Alternating Minimization for a Discrete Mumford-Shah ModelMS78

The Mumford-Shah functional is an influential variational model in image segmentation and restoration. We propose a general formulation of the discrete counterpart of the Mumford-Shah functional, adapted to nonsmooth penalizations. Such nonsmooth penalizations require the design of a new nonconvex algorithmic scheme, that we called SL-PAM, for which convergence guarantees are derived. Numerical experiments show that the proposed method is able to detect sharp contours and to reconstruct piecewise smooth approximations with low computational cost.

This presentation is part of Minisymposium “MS78 - Recent developments in variational image modeling
organized by: Sonia Tabti (Université de Caen, CNRS) , Rabin Julien (CNRS, Normandie Univ.) .

Marion Foare (Laboratoire de Physique, ENS Lyon)
Nelly Pustelnik (CNRS, Laboratoire de Physique de l'ENS de Lyon)
Laurent Condat (Université Grenoble Alpes)