Calculus of Variations and Geometric Measure Theory

D. Bucur - I. FragalĂ  - A. Giacomini

The Multiphase Mumford-Shah Problem

created by bucur on 09 Jan 2019


Submitted Paper

Inserted: 9 jan 2019
Last Updated: 9 jan 2019

Year: 2019


We perform a rigorous analysis of the multiphase version of the Mumford-Shah functional. A characteristic property of the formulation is the presence of a true partition of the image (so in two dimensions of {\it closed} contours), each cell of the partition possibly containing inner jumps. The nontrivial partitioning naturally occurs as a consequence of the presence in the energy functional of statistical terms or of phase depending weights. In particular, we prove a multiphase version of De Giorgi-Carriero-Leaci result.