Image segmentation with a finite element method

Blaise Bourdin

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 33, Issue: 2, page 229-244
  • ISSN: 0764-583X

Abstract

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The Mumford-Shah functional for image segmentation is an original approach of the image segmentation problem, based on a minimal energy criterion. Its minimization can be seen as a free discontinuity problem and is based on Γ-convergence and bounded variation functions theories. Some new regularization results, make possible to imagine a finite element resolution method. In a first time, the Mumford-Shah functional is introduced and some existing results are quoted. Then, a discrete formulation for the Mumford-Shah problem is proposed and its Γ-convergence is proved. Finally, some numerical results, computed from both artificial and real images are presented and discussed.

How to cite

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Bourdin, Blaise. "Image segmentation with a finite element method." ESAIM: Mathematical Modelling and Numerical Analysis 33.2 (2010): 229-244. <http://eudml.org/doc/197511>.

@article{Bourdin2010,
abstract = { The Mumford-Shah functional for image segmentation is an original approach of the image segmentation problem, based on a minimal energy criterion. Its minimization can be seen as a free discontinuity problem and is based on Γ-convergence and bounded variation functions theories. Some new regularization results, make possible to imagine a finite element resolution method. In a first time, the Mumford-Shah functional is introduced and some existing results are quoted. Then, a discrete formulation for the Mumford-Shah problem is proposed and its Γ-convergence is proved. Finally, some numerical results, computed from both artificial and real images are presented and discussed. },
author = {Bourdin, Blaise},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Mumford-Shah functional; image segmentation; finite element method; convergence; numerial results},
language = {eng},
month = {3},
number = {2},
pages = {229-244},
publisher = {EDP Sciences},
title = {Image segmentation with a finite element method},
url = {http://eudml.org/doc/197511},
volume = {33},
year = {2010},
}

TY - JOUR
AU - Bourdin, Blaise
TI - Image segmentation with a finite element method
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 33
IS - 2
SP - 229
EP - 244
AB - The Mumford-Shah functional for image segmentation is an original approach of the image segmentation problem, based on a minimal energy criterion. Its minimization can be seen as a free discontinuity problem and is based on Γ-convergence and bounded variation functions theories. Some new regularization results, make possible to imagine a finite element resolution method. In a first time, the Mumford-Shah functional is introduced and some existing results are quoted. Then, a discrete formulation for the Mumford-Shah problem is proposed and its Γ-convergence is proved. Finally, some numerical results, computed from both artificial and real images are presented and discussed.
LA - eng
KW - Mumford-Shah functional; image segmentation; finite element method; convergence; numerial results
UR - http://eudml.org/doc/197511
ER -

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