A Convex Decomposition Formula for the Mumford-Shah Functional in Dimension One
Analysis of PDEs
2017-09-29 v3
Abstract
We study the convex lift of Mumford-Shah type functionals in the space of rectifiable currents and we prove a generalized coarea formula in dimension one, for finite linear combinations of SBV graphs. We use this result to prove the equivalence between the minimum problems for the Mumford-Shah functional and the lifted one and, as a consequence, we obtain a weak existence result for calibrations in one dimension.
Keywords
Cite
@article{arxiv.1610.01846,
title = {A Convex Decomposition Formula for the Mumford-Shah Functional in Dimension One},
author = {Marcello Carioni},
journal= {arXiv preprint arXiv:1610.01846},
year = {2017}
}