MUMFORD-SHAH FUNCTIONAL o Mumford-Shah(Ms) functional F(u,)=/(-20dx+a/ bp dr+b d6 MS 9-K Q-K K Observed image Set of discontinuities o Open questions. Conjecture 4.2.1 There exists a minimizer of F such that the edges(the discontinuity set K)are the union of a finite set of Cl, embedded curves Moreover, each curve may end either as a crack tip(a free extremity, i.e., K looks like a half-line) or in triple junction, that is, three curves meeting at their endpoints with 2T /3 angle between each pair. D. Mumford and J. Shah. Optimal approximations by piecewise smooth functions and associated variational problems. Communications on Pure and applied mathematics. 42: 577-684. 1989MUMFORD-SHAH FUNCTIONAL  Mumford-Shah (MS) functional:  Open questions: Observed Image Set of Discontinuities