ABSTRACT
We present in this chapter an overview of the Mumford and Shah model for image segmentation. We discuss its various formulations, some of its properties, and the mathematical framework.
An important problem in image analysis and computer vision is the segmentation that aims to partition a given image into its constituent objects or to find boundaries of such objects. This chapter is devoted to the description and analysis of the classical Mumford and Shah functional proposed for image segmentation. In [245, 247, 246], Mumford and Shah formulated an energy minimization problem that allows us to compute optimal piecewise-smooth or piecewise-constant approximations u of a given initial image g. Since then, their model has been analyzed and considered in depth by many authors who studied properties of minimizers, approximations, and applications to image segmentation, image partition, image restoration, and more generally to image analysis and computer vision.
