Calculus of Variations and Geometric Measure Theory

G. Aubert - L. Blanc-Feraud - R. March

An approximation of Mumford-Shah energy by a family of discrete edge-preserving functionals

created by march on 28 Nov 2005
modified on 12 Dec 2006


Published Paper

Inserted: 28 nov 2005
Last Updated: 12 dec 2006

Journal: Nonlinear Analysis - Theory, Methods and Applications
Volume: 64
Number: 9
Pages: 1908-1930
Year: 2006


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.