Discrete approximation of the Mumford-Shah functional in dimension two

Antonin Chambolle; Gianni Dal Maso

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 33, Issue: 4, page 651-672
  • ISSN: 0764-583X

Abstract

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The Mumford-Shah functional, introduced to study image segmentation problems, is approximated in the sense of vergence by a sequence of integral functionals defined on piecewise affine functions.

How to cite

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Chambolle, Antonin, and Maso, Gianni Dal. "Discrete approximation of the Mumford-Shah functional in dimension two." ESAIM: Mathematical Modelling and Numerical Analysis 33.4 (2010): 651-672. <http://eudml.org/doc/197453>.

@article{Chambolle2010,
abstract = { The Mumford-Shah functional, introduced to study image segmentation problems, is approximated in the sense of vergence by a sequence of integral functionals defined on piecewise affine functions. },
author = {Chambolle, Antonin, Maso, Gianni Dal},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Free discontinuity problems; special bounded variation (SBV) functions; Γ-convergence; finite elements.; classes SBV and GSBV of functions of bounded variation; Mumford-Shah functional; variational approximation; -convergence; special functions of bounded variation; integral functionals},
language = {eng},
month = {3},
number = {4},
pages = {651-672},
publisher = {EDP Sciences},
title = {Discrete approximation of the Mumford-Shah functional in dimension two},
url = {http://eudml.org/doc/197453},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Chambolle, Antonin
AU - Maso, Gianni Dal
TI - Discrete approximation of the Mumford-Shah functional in dimension two
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 4
SP - 651
EP - 672
AB - The Mumford-Shah functional, introduced to study image segmentation problems, is approximated in the sense of vergence by a sequence of integral functionals defined on piecewise affine functions.
LA - eng
KW - Free discontinuity problems; special bounded variation (SBV) functions; Γ-convergence; finite elements.; classes SBV and GSBV of functions of bounded variation; Mumford-Shah functional; variational approximation; -convergence; special functions of bounded variation; integral functionals
UR - http://eudml.org/doc/197453
ER -

Citations in EuDML Documents

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  1. Luca Lussardi, Enrico Vitali, Non-local approximation of free-discontinuity problems with linear growth
  2. Luca Lussardi, Annibale Magni, Γ-limits of convolution functionals
  3. Andrea Braides, Anneliese Defranceschi, Enrico Vitali, A compactness result for a second-order variational discrete model
  4. Andrea Braides, Anneliese Defranceschi, Enrico Vitali, A compactness result for a second-order variational discrete model
  5. Xiaobing Feng, Andreas Prohl, Analysis of gradient flow of a regularized Mumford-Shah functional for image segmentation and image inpainting
  6. Xiaobing Feng, Andreas Prohl, Analysis of gradient flow of a regularized Mumford-Shah functional for image segmentation and image inpainting
  7. Andrea Braides, Giuseppe Riey, A variational model in image processing with focal points

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