Inserted: 28 nov 2005
Last Updated: 12 dec 2006
Journal: Nonlinear Analysis - Theory, Methods and Applications
We show the $\Gamma$-convergence of a family of discrete functionals to the Mumford and Shah image segmentation functional. The functionals of the family are constructed by modifying the elliptic approximating functionals proposed by Ambrosio and Tortorelli. The quadratic term of the energy related to the edges of the segmentation is replaced by a nonconvex functional.