Numerical insights in the solution of Euler equations of the variational image segmentation

This paper deals with numerical insights in the approximation of Euler equa tions (Eqs) associated to the variational formulation of image segmentation , that is to the minimization problem for the Mumford-Shah functional (MSf) . Once a sequence of elliptic functionals F-convergent to the MSf is introd uced, a finite-difference method, both in one- or multi-grid computational form, is defined to solve the Eqs associated to the k-th functional of the sequence. In dealing with the computation of approximate solutions u and co ntrol function z of the Eqs, in this paper we describe numerical experiment s carried out to investigate both the special relationship linking the sequ ence index k and the mesh size h of the discrete approximation and the infl uence of multigrid components and parameters on the results. We discuss alg orithm performance by application to segmentation of synthetic images. We a nalyze computed discontinuity contours and convergence histories of method executions.