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):

A Novel Technique for Wideband Spectrum Sensing in Cognitive Radio Through Phase-Field Segmentation

Mohammad Eslami and Seyed Mohammad-Sajad Sadough
Wireless Personal Communications 68 (1) 115 (2013)
DOI: 10.1007/s11277-011-0442-0
See this article

Multiscale Joint Segmentation and Registration of Image Morphology

M. Droske and M. Rumpf
IEEE Transactions on Pattern Analysis and Machine Intelligence 29 (12) 2181 (2007)
DOI: 10.1109/TPAMI.2007.1120
See this article

Application of Level Set Method in Medical Image Segmentation

秀 马
Advances in Applied Mathematics 05 (01) 63 (2016)
DOI: 10.12677/AAM.2016.51010
See this article

Mesh adaptation-aided image segmentation

Alberto Silvio Chiappa, Stefano Micheletti, Riccardo Peli and Simona Perotto
Communications in Nonlinear Science and Numerical Simulation 74 147 (2019)
DOI: 10.1016/j.cnsns.2019.03.010
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

Fracture Phenomena in Nature and Technology

C. Maurini, B. Bourdin, G. Gauthier and V. Lazarus
Fracture Phenomena in Nature and Technology 75 (2014)
DOI: 10.1007/978-3-319-04397-5_7
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

A discretization method for the numerical solution of Dieudonné-Rashevsky type problems with application to edge detection within noisy image data

Lucas Franek, Marzena Franek, Helmut Maurer and Marcus Wagner
Optimal Control Applications and Methods 33 (3) 276 (2012)
DOI: 10.1002/oca.996
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

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

Crack patterns obtained by unidirectional drying of a colloidal suspension in a capillary tube: experiments and numerical simulations using a two-dimensional variational approach

C. Maurini, B. Bourdin, G. Gauthier and V. Lazarus
International Journal of Fracture 184 (1-2) 75 (2013)
DOI: 10.1007/s10704-013-9824-5
See this article

Reprint of Solution of Ambrosio–Tortorelli model for image segmentation by generalized relaxation method

Pasqua D’Ambra and Gaetano Tartaglione
Communications in Nonlinear Science and Numerical Simulation 21 (1-3) 225 (2015)
DOI: 10.1016/j.cnsns.2014.10.018
See this article

An Application of Quadratic Measure Filters to the Segmentation of Chorio-Retinal OCT Data

Marcus Wagner
Journal of Mathematical Imaging and Vision 60 (2) 216 (2018)
DOI: 10.1007/s10851-017-0752-2
See this article

Hybrid adaptation for detecting skin in color images

Michal Kawulok, Jolanta Kawulok, Jakub Nalepa, Bogdan Smolka and Eduardo Bayro-Corrochano
Intelligent Data Analysis 20 (s1) S121 (2016)
DOI: 10.3233/IDA-160850
See this article

An augmented-Lagrangian method for the phase-field approach for pressurized fractures

M.F. Wheeler, T. Wick and W. Wollner
Computer Methods in Applied Mechanics and Engineering 271 69 (2014)
DOI: 10.1016/j.cma.2013.12.005
See this article

Energy approach to brittle fracture in strain-gradient modelling

Luca Placidi and Emilio Barchiesi
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474 (2210) 20170878 (2018)
DOI: 10.1098/rspa.2017.0878
See this article

Experimental validation of a phase-field model for fracture

K. H. Pham, K. Ravi-Chandar and C. M. Landis
International Journal of Fracture 205 (1) 83 (2017)
DOI: 10.1007/s10704-017-0185-3
See this article

Multimodal image registration by elastic matching of edge sketches via optimal control

Marcus Wagner and Angel Angelov
Journal of Industrial and Management Optimization 10 (2) 567 (2013)
DOI: 10.3934/jimo.2014.10.567
See this article

A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework

Michael J. Borden, Thomas J.R. Hughes, Chad M. Landis and Clemens V. Verhoosel
Computer Methods in Applied Mechanics and Engineering 273 100 (2014)
DOI: 10.1016/j.cma.2014.01.016
See this article

Solution of Ambrosio–Tortorelli model for image segmentation by generalized relaxation method

Pasqua D’Ambra and Gaetano Tartaglione
Communications in Nonlinear Science and Numerical Simulation 20 (3) 819 (2015)
DOI: 10.1016/j.cnsns.2014.06.036
See this article

A phase-field description of dynamic brittle fracture

Michael J. Borden, Clemens V. Verhoosel, Michael A. Scott, Thomas J.R. Hughes and Chad M. Landis
Computer Methods in Applied Mechanics and Engineering 217-220 77 (2012)
DOI: 10.1016/j.cma.2012.01.008
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

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

Crack nucleation in variational phase-field models of brittle fracture

E. Tanné, T. Li, B. Bourdin, J.-J. Marigo and C. Maurini
Journal of the Mechanics and Physics of Solids 110 80 (2018)
DOI: 10.1016/j.jmps.2017.09.006
See this article

Radial segmentation

Eric D. Sinzinger
Pattern Recognition Letters 25 (12) 1337 (2004)
DOI: 10.1016/j.patrec.2004.05.012
See this article

Detection of Intensity and Motion Edges within Optical Flow via Multidimensional Control

Christoph Brune, Helmut Maurer and Marcus Wagner
SIAM Journal on Imaging Sciences 2 (4) 1190 (2009)
DOI: 10.1137/080725064
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

Variational approach to the free-discontinuity problem of inverse crack identification

R. Tsotsova
Communications in Numerical Methods in Engineering 24 (12) 2216 (2007)
DOI: 10.1002/cnm.1078
See this article

Phase-field modeling through iterative splitting of hydraulic fractures in a poroelastic medium

A. Mikelić, M. F. Wheeler and T. Wick
GEM - International Journal on Geomathematics 10 (1) (2019)
DOI: 10.1007/s13137-019-0113-y
See this article

Robust variational segmentation of 3D bone CT data with thin cartilage interfaces

Tarun Gangwar, Jeff Calder, Takashi Takahashi, Joan E. Bechtold and Dominik Schillinger
Medical Image Analysis 47 95 (2018)
DOI: 10.1016/j.media.2018.04.003
See this article

Mumford–Shah based registration: a comparison of a level set and a phase field approach

Marc Droske, Wolfgang Ring and Martin Rumpf
Computing and Visualization in Science 12 (3) 101 (2009)
DOI: 10.1007/s00791-008-0084-2
See this article

The Variational Approach to Fracture

Blaise Bourdin, Gilles A. Francfort and Jean-Jacques Marigo
Journal of Elasticity 91 (1-3) 5 (2008)
DOI: 10.1007/s10659-007-9107-3
See this article

Pattern Recognition

Alexandru Telea, Tobias Preusser, Christoph Garbe, Marc Droske and Martin Rumpf
Lecture Notes in Computer Science, Pattern Recognition 4174 525 (2006)
DOI: 10.1007/11861898_53
See this article

IUTAM Symposium on Discretization Methods for Evolving Discontinuities

B. Bourdin
IUTAM Bookseries, IUTAM Symposium on Discretization Methods for Evolving Discontinuities 5 381 (2007)
DOI: 10.1007/978-1-4020-6530-9_22
See this article

A diffuse interface method for the Navier–Stokes/Darcy equations: Perfusion profile for a patient-specific human liver based on MRI scans

Stein K.F. Stoter, Peter Müller, Luca Cicalese, et al.
Computer Methods in Applied Mechanics and Engineering 321 70 (2017)
DOI: 10.1016/j.cma.2017.04.002
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

Reconstruction in the inverse crack problem by variational methods

LUCA RONDI
European Journal of Applied Mathematics 19 (6) 635 (2008)
DOI: 10.1017/S0956792508007729
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

Variational Models and Methods in Solid and Fluid Mechanics

B. Bourdin and G. A. Francfort
CISM International Centre for Mechanical Sciences, Variational Models and Methods in Solid and Fluid Mechanics 535 107 (2011)
DOI: 10.1007/978-3-7091-0983-0_3
See this article

An adaptive global–local approach for phase-field modeling of anisotropic brittle fracture

Nima Noii, Fadi Aldakheel, Thomas Wick and Peter Wriggers
Computer Methods in Applied Mechanics and Engineering 361 112744 (2020)
DOI: 10.1016/j.cma.2019.112744
See this article

Numerical experiments in revisited brittle fracture

B. Bourdin, G.A. Francfort and J-J. Marigo
Journal of the Mechanics and Physics of Solids 48 (4) 797 (2000)
DOI: 10.1016/S0022-5096(99)00028-9
See this article

Hierarchical models in statistical inverse problems and the Mumford–Shah functional

T Helin and M Lassas
Inverse Problems 27 (1) 015008 (2011)
DOI: 10.1088/0266-5611/27/1/015008
See this article