Given an image depicting a scene with several objects in it, the goal of image segmentation is to partition the image into regions that contain distinct objects. Variational models for segmentation pose the problem as finding the minimizer of a suitably chosen energy. One of the most popular among them is the model of Mumford and Shah. After reviewing how a simplified version of the Mumford-Shah model can be formulated as a convex but non-smooth optimization problem, we will describe a dual formulation that turns it into a smooth optimization problem and allows more efficient numerical solution.
|