Implementation of an adaptive finite-element approximation of the Mumford-Shah functional

where Ω ⊂ R2 is the image domain (a bounded open two-dimensional domain), g ∈ L∞(Ω) is the original image, that has to be segmented, K is a closed set of Hausdorff one-dimensional measure H1(K) and u ∈ C1(Ω \K). The set K is supposed to represent the edges of the segmented image u that is regular out of K and can be discontinuous across K (see Appendix A.2 for details). The actual minimization of G is a difficult problem, that has been addressed by many authors. Mumford and Shah themselves derived their energy from discrete energies introduced by D. Geman and S. Geman [24]