Proximity operator of a sum of functions: Application to image segmentationMS10

Proximal splitting algorithms are of main interest in a large number of image processing applications. The main advantage of this class of algorithms is to make possible to split a criterion in a sum of functions easier to handle with (e.g. split differentiable and non-smooth functions). However, the larger the splitting, the slower the convergence. In this work, we show how to compute the proximity operator of a sum of two functions, for a certain type of functions operating on objects having a graph structure. The gain provided by avoiding unnecessary splitting is illustrated on image segmentation.

This presentation is part of Minisymposium “MS10 - Advanced optimization methods for image processing (2 parts)
organized by: Marco Prato (University of Modena and Reggio Emilia) , Ignace Loris (Université Libre de Bruxelles) .

Nelly Pustelnik (CNRS, Laboratoire de Physique de l'ENS de Lyon)
Laurent Condat (Université Grenoble Alpes)
image segmentation, nonlinear optimization