Articles citing this article

The Citing articles tool gives a list of articles citing the current article.
The citing articles come from EDP Sciences database, as well as other publishers participating in CrossRef Cited-by Linking Program. You can set up your personal account to receive an email alert each time this article is cited by a new article (see the menu on the right-hand side of the abstract page).

Cited article:

This article has been cited by the following article(s):

Mumford–Shah regularization in electrical impedance tomography with complete electrode model

Jyrki Jauhiainen, Aku Seppänen and Tuomo Valkonen
Inverse Problems 38 (6) 065004 (2022)
DOI: 10.1088/1361-6420/ac5f3a
See this article

Anisotropic mesh adaptation for region-based segmentation accounting for image spatial information

Matteo Giacomini and Simona Perotto
Computers & Mathematics with Applications 121 1 (2022)
DOI: 10.1016/j.camwa.2022.06.025
See this article

Non-local approximation of the Griffith functional

Giovanni Scilla and Francesco Solombrino
Nonlinear Differential Equations and Applications NoDEA 28 (2) (2021)
DOI: 10.1007/s00030-021-00682-y
See this article

A discrete approximation of Blake and Zisserman energy in image denoising with optimal choice of regularization parameters

Anis Theljani and Zakaria Belhachmi
Mathematical Methods in the Applied Sciences 44 (5) 3857 (2021)
DOI: 10.1002/mma.6991
See this article

A comparative accuracy and convergence study of eigenerosion and phase-field models of fracture

A. Pandolfi, K. Weinberg and M. Ortiz
Computer Methods in Applied Mechanics and Engineering 386 114078 (2021)
DOI: 10.1016/j.cma.2021.114078
See this article

Two-stage image segmentation based on nonconvex ℓ2−ℓp approximation and thresholding

Tingting Wu, Jinbo Shao, Xiaoyu Gu, Michael K. Ng and Tieyong Zeng
Applied Mathematics and Computation 403 126168 (2021)
DOI: 10.1016/j.amc.2021.126168
See this article

Approximation of the Mumford–Shah functional by phase fields of bounded variation

Sandro Belz and Kristian Bredies
Analysis and Applications 19 (02) 183 (2021)
DOI: 10.1142/S0219530520500190
See this article

Regularization of free discontinuity problem and its application in the simulation of brittle fracture of concrete

FU JIAJIA and WANG YAO
Science Journal Innovation Technologies Transfer (2020-3) 10 (2020)
DOI: 10.36381/iamsti.3.2020.10-17
See this article

A derivation of Griffith functionals from discrete finite-difference models

Vito Crismale, Giovanni Scilla and Francesco Solombrino
Calculus of Variations and Partial Differential Equations 59 (6) (2020)
DOI: 10.1007/s00526-020-01858-7
See this article

Discrete stochastic approximations of the Mumford–Shah functional

Matthias Ruf
Annales de l'Institut Henri Poincaré C, Analyse non linéaire 36 (4) 887 (2019)
DOI: 10.1016/j.anihpc.2018.10.004
See this article

A case study of a two-stage image segmentation algorithm

Xiaolong Li and Wei Li
Multimedia Tools and Applications 78 (7) 8197 (2019)
DOI: 10.1007/s11042-018-6778-7
See this article

Multi-phase image segmentation with the adaptive deformable mesh

Tuan T. Nguyen, Vedrana A. Dahl and J. Andreas Bærentzen
Pattern Recognition Letters 117 97 (2019)
DOI: 10.1016/j.patrec.2018.12.009
See this article

Consistent finite-dimensional approximation of phase-field models of fracture

Stefano Almi and Sandro Belz
Annali di Matematica Pura ed Applicata (1923 -) 198 (4) 1191 (2019)
DOI: 10.1007/s10231-018-0815-z
See this article

Mumford‐Shah Mesh Processing using the Ambrosio‐Tortorelli Functional

Nicolas Bonneel, David Coeurjolly, Pierre Gueth and Jacques‐Olivier Lachaud
Computer Graphics Forum 37 (7) 75 (2018)
DOI: 10.1111/cgf.13549
See this article

Mathematical Image Processing

Kristian Bredies and Dirk Lorenz
Applied and Numerical Harmonic Analysis, Mathematical Image Processing 251 (2018)
DOI: 10.1007/978-3-030-01458-2_6
See this article

Gamma-convergence of certain modified Perona-Malik functionals

Juha Tiirola
ESAIM: Control, Optimisation and Calculus of Variations 23 (4) 1499 (2017)
DOI: 10.1051/cocv/2016062
See this article

A multiscale fourth-order model for the image inpainting and low-dimensional sets recovery

Anis Theljani, Zakaria Belhachmi, Moez Kallel and Maher Moakher
Mathematical Methods in the Applied Sciences 40 (10) 3637 (2017)
DOI: 10.1002/mma.4250
See this article

A selective review on Mumford–Shah minimizers

Antoine Lemenant
Bollettino dell'Unione Matematica Italiana 9 (1) 69 (2016)
DOI: 10.1007/s40574-016-0056-2
See this article

An Adaptive Approach for the Segmentation and the TV-Filtering in the Optic Flow Estimation

Z. Belhachmi and F. Hecht
Journal of Mathematical Imaging and Vision 54 (3) 358 (2016)
DOI: 10.1007/s10851-015-0608-6
See this article

Numerical minimization of a second-order functional for image segmentation

Massimo Zanetti, Valeria Ruggiero and Michele Miranda Jr
Communications in Nonlinear Science and Numerical Simulation 36 528 (2016)
DOI: 10.1016/j.cnsns.2015.12.018
See this article

Piecewise smooth reconstruction of normal vector field on digital data

David Coeurjolly, Marion Foare, Pierre Gueth and Jacques-Olivier Lachaud
Computer Graphics Forum 35 (7) 157 (2016)
DOI: 10.1111/cgf.13013
See this article

Anisotropic Mesh Adaptation for Crack Detection In Brittle Materials

Marco Artina, Massimo Fornasier, Stefano Micheletti and Simona Perotto
SIAM Journal on Scientific Computing 37 (4) B633 (2015)
DOI: 10.1137/140970495
See this article

New Challenges in Grid Generation and Adaptivity for Scientific Computing

Marco Artina, Massimo Fornasier, Stefano Micheletti and Simona Perotto
SEMA SIMAI Springer Series, New Challenges in Grid Generation and Adaptivity for Scientific Computing 5 43 (2015)
DOI: 10.1007/978-3-319-06053-8_3
See this article

Point-wise behavior of the Geman--McClure and the Hebert--Leahy image restoration models

Petteri Harjulehto, Peter Hästö and Juha Tiirola
Inverse Problems and Imaging 9 (3) 835 (2015)
DOI: 10.3934/ipi.2015.9.835
See this article

A Nash-game approach to joint image restoration and segmentation

Moez Kallel, Rajae Aboulaich, Abderrahmane Habbal and Maher Moakher
Applied Mathematical Modelling 38 (11-12) 3038 (2014)
DOI: 10.1016/j.apm.2013.11.034
See this article

A Two-Stage Image Segmentation Method for Blurry Images with Poisson or Multiplicative Gamma Noise

Raymond Chan, Hongfei Yang and Tieyong Zeng
SIAM Journal on Imaging Sciences 7 (1) 98 (2014)
DOI: 10.1137/130920241
See this article

Handbook of Mathematical Methods in Imaging

Leah Bar, Tony F. Chan, Ginmo Chung, et al.
Handbook of Mathematical Methods in Imaging 1 (2014)
DOI: 10.1007/978-3-642-27795-5_25-5
See this article

Optimization with PDE Constraints

Charles Brett, Charles M. Elliott and Andreas S. Dedner
Lecture Notes in Computational Science and Engineering, Optimization with PDE Constraints 101 25 (2014)
DOI: 10.1007/978-3-319-08025-3_2
See this article

Existence of minimizers of the Mumford-Shah functional with singular operators and unbounded data

Massimo Fornasier, Riccardo March and Francesco Solombrino
Annali di Matematica Pura ed Applicata 192 (3) 361 (2013)
DOI: 10.1007/s10231-011-0228-8
See this article

Γ-limits of convolution functionals

Luca Lussardi and Annibale Magni
ESAIM: Control, Optimisation and Calculus of Variations 19 (2) 486 (2013)
DOI: 10.1051/cocv/2012018
See this article

A Two-Stage Image Segmentation Method Using a Convex Variant of the Mumford--Shah Model and Thresholding

Xiaohao Cai, Raymond Chan and Tieyong Zeng
SIAM Journal on Imaging Sciences 6 (1) 368 (2013)
DOI: 10.1137/120867068
See this article

The Mumford–Shah variational model for image segmentation: An overview of the theory, implementation and use

Alfonso Vitti
ISPRS Journal of Photogrammetry and Remote Sensing 69 50 (2012)
DOI: 10.1016/j.isprsjprs.2012.02.005
See this article

A compactness result for a second-order variational discrete model

Andrea Braides, Anneliese Defranceschi and Enrico Vitali
ESAIM: Mathematical Modelling and Numerical Analysis 46 (2) 389 (2012)
DOI: 10.1051/m2an/2011043
See this article

Handbook of Mathematical Methods in Imaging

Leah Bar, Tony F. Chan, Ginmo Chung, et al.
Handbook of Mathematical Methods in Imaging 1095 (2011)
DOI: 10.1007/978-0-387-92920-0_25
See this article

An Adaptive Finite Element Approximation of a Variational Model of Brittle Fracture

Siobhan Burke, Christoph Ortner and Endre S�li
SIAM Journal on Numerical Analysis 48 (3) 980 (2010)
DOI: 10.1137/080741033
See this article

Iterative Thresholding Meets Free-Discontinuity Problems

Massimo Fornasier and Rachel Ward
Foundations of Computational Mathematics 10 (5) 527 (2010)
DOI: 10.1007/s10208-010-9071-3
See this article

Joint edge detection and motion estimation of cardiac MR image sequence by a phase field method

Abouzar Eslami, Mehran Jahed and Tobias Preusser
Computers in Biology and Medicine 40 (1) 21 (2010)
DOI: 10.1016/j.compbiomed.2009.10.004
See this article

Eigenfracture: An Eigendeformation Approach to Variational Fracture

Bernd Schmidt, Fernando Fraternali and Michael Ortiz
Multiscale Modeling & Simulation 7 (3) 1237 (2009)
DOI: 10.1137/080712568
See this article

Mathematics of Surfaces XIII

M. Fornasier
Lecture Notes in Computer Science, Mathematics of Surfaces XIII 5654 143 (2009)
DOI: 10.1007/978-3-642-03596-8_9
See this article

A Phase Field Method for Joint Denoising, Edge Detection, and Motion Estimation in Image Sequence Processing

T. Preusser, M. Droske, C. S. Garbe, A. Telea and M. Rumpf
SIAM Journal on Applied Mathematics 68 (3) 599 (2008)
DOI: 10.1137/060677409
See this article

A variational model in image processing with focal points

Andrea Braides and Giuseppe Riey
ESAIM: Mathematical Modelling and Numerical Analysis 42 (5) 729 (2008)
DOI: 10.1051/m2an:2008024
See this article

Non-local approximation of free-discontinuity problems with linear growth

Luca Lussardi and Enrico Vitali
ESAIM: Control, Optimisation and Calculus of Variations 13 (1) 135 (2007)
DOI: 10.1051/cocv:2007008
See this article

Convergence of Nonlocal Finite Element Energies for Fracture Mechanics

Luca Lussardi and Matteo Negri
Numerical Functional Analysis and Optimization 28 (1-2) 83 (2007)
DOI: 10.1080/01630560701189994
See this article

A versatile segmentation procedure

W. Vanzella and V. Torre
IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 36 (2) 366 (2006)
DOI: 10.1109/TSMCB.2005.859077
See this article

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

Gilles Aubert, Laure Blanc-Féraud and Riccardo March
Nonlinear Analysis: Theory, Methods & Applications 64 (9) 1908 (2006)
DOI: 10.1016/j.na.2005.07.028
See this article

Mathematical Analysis of An Extended Mumford-Shah Model for Image Segmentation

Trevor Chi-Yuen Tao, David James Crisp and John van der Hoek
Journal of Mathematical Imaging and Vision 24 (3) 327 (2006)
DOI: 10.1007/s10851-005-3631-1
See this article

Handbook of Differential Equations: Stationary Partial Differential Equations

Andrea Braides
Handbook of Differential Equations: Stationary Partial Differential Equations 3 101 (2006)
DOI: 10.1016/S1874-5733(06)80006-9
See this article

Analysis of gradient flow of a regularized Mumford-Shah functional for image segmentation and image inpainting

Xiaobing Feng and Andreas Prohl
ESAIM: Mathematical Modelling and Numerical Analysis 38 (2) 291 (2004)
DOI: 10.1051/m2an:2004014
See this article

S. Belfiore, R. Scopigno, M. Grangetto and E. Magli
6 3915 (2004)
DOI: 10.1109/IGARSS.2004.1369982
See this article

Neuronal Oscillations in the Visual Cortex: $\Gamma$-Convergence to the Riemannian Mumford--Shah Functional

Giovanna Citti, Maria Manfredini and Alessandro Sarti
SIAM Journal on Mathematical Analysis 35 (6) 1394 (2004)
DOI: 10.1137/S0036141002398673
See this article

Self-adaptive regularization

W. Vanzella, F.A. Pellegrino and V. Torre
IEEE Transactions on Pattern Analysis and Machine Intelligence 26 (6) 804 (2004)
DOI: 10.1109/TPAMI.2004.15
See this article

From Mumford–Shah to Perona–Malik in image processing

B. Kawohl
Mathematical Methods in the Applied Sciences 27 (15) 1803 (2004)
DOI: 10.1002/mma.564
See this article

From neural oscillations to variational problems in the visual cortex

Alessandro Sarti, Giovanna Citti and Maria Manfredini
Journal of Physiology-Paris 97 (2-3) 379 (2003)
DOI: 10.1016/j.jphysparis.2003.09.014
See this article

Advances in Imaging and Electron Physics

Otmar Scherzer
Advances in Imaging and Electron Physics 128 445 (2003)
DOI: 10.1016/S1076-5670(03)80067-8
See this article

T.F. Chan and L.A. Vese
161 (2001)
DOI: 10.1109/VLSM.2001.938895
See this article

An analysis of the Perona-Malik scheme

Selim Esedo??lu
Communications on Pure and Applied Mathematics 54 (12) 1442 (2001)
DOI: 10.1002/cpa.3008
See this article