On a functional depending on curvature and edges (Q2568711)

This is a continuation of the study of the Mumford-Shah functional for image segmentation whose minima are functions \(u\) jumping through a fairly regular set \(S_u\). It is natural to expect some corners in the contour of the images corresponding to corners in the original. In this paper, the author approximates the closure \(\overline{S_u}\) by curves having corners and proves the existence of at least one solution of the minimum problem of a certain functional. The proof of the existence of minima for the functional relies on varifold theory.