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Volumn 1, Issue 1, 2004, Pages 25-47

A survey on multiple level set methods with applications for identifying piecewise constant functions

Author keywords

Electrical impedance tomography; Image segmentation; Inverse problems; Level set methods; Optimal shape design; Positron emission tomography; Survey

Indexed keywords


EID: 24644508476     PISSN: 17055105     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (122)

References (57)
  • 1
    • 0036609140 scopus 로고    scopus 로고
    • Refinement and coarsening indicators for adaptive parametrization: Application to the estimation of hydraulic transmissivities
    • H. Ben Ameur, G. Chavent, and J. Jaffré. Refinement and coarsening indicators for adaptive parametrization: application to the estimation of hydraulic transmissivities. Inverse Problems, 18:775-794, 2002.
    • (2002) Inverse Problems , vol.18 , pp. 775-794
    • Ben Ameur, H.1    Chavent, G.2    Jaffré, J.3
  • 2
    • 0000252505 scopus 로고    scopus 로고
    • Numerical implementation of two noniterative methods for locating inclusions by impedance tomography
    • Martin Br¨uhl and Martin Hanke. Numerical implementation of two noniterative methods for locating inclusions by impedance tomography. Inverse Problems, 16(4):1029-1042, 2000.
    • (2000) Inverse Problems , vol.16 , Issue.4 , pp. 1029-1042
    • Martin, B.1    Hanke, M.2
  • 3
    • 0034497171 scopus 로고    scopus 로고
    • Basis norm rescaling for nonlinear parameter estimation
    • electronic
    • Kari Brusdal and Trond Mannseth. Basis norm rescaling for nonlinear parameter estimation. SIAM J. Sci. Comput., 21(6):2114-2125 (electronic), 2000.
    • (2000) SIAM J. Sci. Comput , vol.21 , Issue.6 , pp. 2114-2125
    • Brusdal, K.1    Mannseth, T.2
  • 4
    • 0035473388 scopus 로고    scopus 로고
    • A level set method for inverse problems
    • M. Burger. A level set method for inverse problems. Inverse problems, 17:1327-1356, 2001.
    • (2001) Inverse Problems , vol.17 , pp. 1327-1356
    • Burger, M.1
  • 5
    • 0842267881 scopus 로고    scopus 로고
    • A framework for the construction of level set methods for shape optimization and reconstruction
    • M. Burger. A framework for the construction of level set methods for shape optimization and reconstruction. Interfaces and Free boundaries, 5:301-329, 2005.
    • (2005) Interfaces and Free Boundaries , vol.5 , pp. 301-329
    • Burger, M.1
  • 6
    • 0345655616 scopus 로고    scopus 로고
    • Augmented lagrangian and total variation methods for recovering discontinuous coefficients from elliptic equations
    • M. Bristeau, G. Etgen, W. Fitzgibbon, J. L. Lions, J. Periaux, and M. F. Wheeler, editors, John Wiley & Sons
    • T. F. Chan and X.-C. Tai. Augmented lagrangian and total variation methods for recovering discontinuous coefficients from elliptic equations. In M. Bristeau, G. Etgen, W. Fitzgibbon, J. L. Lions, J. Periaux, and M. F. Wheeler, editors, Computational Science for the 21st Century, pages 597-607. John Wiley & Sons, 1997.
    • (1997) Computational Science for the 21St Century , pp. 597-607
    • Chan, T.F.1    Tai, X.-C.2
  • 7
    • 2942612639 scopus 로고    scopus 로고
    • Identification of discontinuous coefficients in elliptic problems using total variation regularization
    • T F. Chan and X.-C. Tai. Identification of discontinuous coefficients in elliptic problems using total variation regularization. SIAM J. Sci. Comput., 25:881-904, 2003. Available online at http://www.mi.uib.no/˜tai/.
    • (2003) SIAM J. Sci. Comput , vol.25 , pp. 881-904
    • Chan, T.F.1    Tai, X.-C.2
  • 8
    • 0344550387 scopus 로고    scopus 로고
    • Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients
    • T. F. Chan and X.-C. Tai. Level set and total variation regularization for elliptic inverse problems with discontinuous coefficients. J. Comput. Phys., 193:40-66, 2003.
    • (2003) J. Comput. Phys. , vol.193 , pp. 40-66
    • Chan, T.F.1    Tai, X.-C.2
  • 14
    • 3042758075 scopus 로고    scopus 로고
    • Variational PDE models in image processing
    • Tony F. Chan, Jianhong Shen, and Luminita Vese. Variational PDE models in image processing. Notices Amer. Math. Soc., 50(1):14-26, 2003.
    • (2003) Notices Amer. Math. Soc. , vol.50 , Issue.1 , pp. 14-26
    • Chan, T.F.1    Shen, J.2    Vese, L.3
  • 15
    • 84996143333 scopus 로고    scopus 로고
    • Regularization of linear least squares problems by total bounded variation
    • (electronic)
    • G. Chavent and K. Kunisch. Regularization of linear least squares problems by total bounded variation. ESAIM Control Optim. Calc. Var., 2:359-376 (electronic), 1997.
    • (1997) ESAIM Control Optim. Calc. Var. , vol.2 , pp. 359-376
    • Chavent, G.1    Kunisch, K.2
  • 16
    • 0032633972 scopus 로고    scopus 로고
    • An augmented Lagrangian method for identifying discontinuous parameters in elliptic systems
    • electronic
    • Zhiming Chen and Jun Zou. An augmented Lagrangian method for identifying discontinuous parameters in elliptic systems. SIAM J. Control Optim., 37(3):892-910 (electronic), 1999.
    • (1999) SIAM J. Control Optim , vol.37 , Issue.3 , pp. 892-910
    • Chen, Z.1    Zou, J.2
  • 17
    • 0002621641 scopus 로고    scopus 로고
    • Electrical impedance tomography
    • electronic
    • Margaret Cheney, David Isaacson, and Jonathan C. Newell. Electrical impedance tomography. SIAM Rev., 41(1):85-101 (electronic), 1999.
    • (1999) SIAM Rev , vol.41 , Issue.1 , pp. 85-101
    • Cheney, M.1    Isaacson, D.2    Newell, J.C.3
  • 19
    • 84967708673 scopus 로고
    • User’s guide to viscosity solutions of second order partial differential equations
    • Michael G. Crandall, Hitoshi Ishii, and Pierre-Louis Lions. User’s guide to viscosity solutions of second order partial differential equations. Bull. Amer. Math. Soc. (N.S.), 27(1):1-67, 1992.
    • (1992) Bull. Amer. Math. Soc. (N.S.) , vol.27 , Issue.1 , pp. 1-67
    • Crandall, M.G.1    Ishii, H.2    Lions, P.-L.3
  • 20
    • 0001341095 scopus 로고
    • An image enhancement technique for eletrical impedance tomography
    • D. C. Dobson and F. Santosa. An image enhancement technique for eletrical impedance tomography. Inverse problems, 10:317-334, 1994.
    • (1994) Inverse Problems , vol.10 , pp. 317-334
    • Dobson, D.C.1    Santosa, F.2
  • 21
    • 0034292566 scopus 로고    scopus 로고
    • A shape reconstruction method for eletronomagnetic tomography using adjoint and level sets
    • O. Dorn, E. M. Miller, and C. M. Rappaport. A shape reconstruction method for eletronomagnetic tomography using adjoint and level sets. Inverse problems, 16:1119-1156, 2000.
    • (2000) Inverse Problems , vol.16 , pp. 1119-1156
    • Dorn, O.1    Miller, E.M.2    Rappaport, C.M.3
  • 23
    • 0005316834 scopus 로고    scopus 로고
    • A mixed least-squares method for an inverse problem of a nonlinear beam equation
    • Conference on Inverse Problems, Control and Shape Optimization (Carthage, 1998)
    • Richard E. Ewing, Tao Lin, and Yanping Lin. A mixed least-squares method for an inverse problem of a nonlinear beam equation. Inverse Problems, 15(1):19-32, 1999. Conference on Inverse Problems, Control and Shape Optimization (Carthage, 1998).
    • (1999) Inverse Problems , vol.15 , Issue.1 , pp. 19-32
    • Ewing, R.E.1    Lin, T.2    Lin, Y.3
  • 24
    • 84966231637 scopus 로고
    • Falk. Error estimates for the numerical identification of a variable coefficient
    • Richard S. Falk. Error estimates for the numerical identification of a variable coefficient. Math. Comp., 40(162):537-546, 1983.
    • (1983) Math. Comp. , vol.40 , Issue.162 , pp. 537-546
    • Richard, S.1
  • 26
    • 84904325107 scopus 로고    scopus 로고
    • Level set methods and augmented lagrangian for a parameter identification problem
    • In V.Barbu, I. Lasiecka, D. Tiba, and C. Varsan, editors, Kluwer Academic Publishers, Boston/Dordrecht/London
    • B. Heimsund, T. F. Chan, T. K. Nilssen, and X.-C. Tai. Level set methods and augmented lagrangian for a parameter identification problem. In V.Barbu, I. Lasiecka, D. Tiba, and C. Varsan, editors, Analysis and optimization of differential systems, pages 189-200. Kluwer Academic Publishers, Boston/Dordrecht/London, 2003.
    • (2003) Analysis and Optimization of Differential Systems , pp. 189-200
    • Heimsund, B.1    Chan, T.F.2    Nilssen, T.K.3    Tai, X.-C.4
  • 27
    • 0344361062 scopus 로고    scopus 로고
    • A second order shape optimization approach for image segmentation
    • to appear
    • Michael Hintermuller and Wolgang Ring. A second order shape optimization approach for image segmentation. SIAM J. Appl. Math., to appear.
    • SIAM J. Appl. Math
    • Hintermuller, M.1    Ring, W.2
  • 28
    • 33746362425 scopus 로고    scopus 로고
    • Cand. scient thesis, Department of Mathematics, University of Bergen, Available online at
    • Erlend Hodneland. Segmentation of digital images. Cand. scient thesis, Department of Mathematics, University of Bergen, 2003. Available online at http://www.mi.uib.no/%7Etai.
    • (2003) Segmentation of Digital Images
    • Hodneland, E.1
  • 29
    • 0025208790 scopus 로고
    • The augmented lagrangian method for parameter estimation in elliptic systems
    • K. Ito and K. Kunisch. The augmented lagrangian method for parameter estimation in elliptic systems. SIAM J. Control Optim., 28:113-136, 1990.
    • (1990) SIAM J. Control Optim. , vol.28 , pp. 113-136
    • Ito, K.1    Kunisch, K.2
  • 31
    • 0035473295 scopus 로고    scopus 로고
    • Level-set function approach to an inverse interface problem
    • K. Ito, K. Kunisch, and Z. Li. Level-set function approach to an inverse interface problem. Inverse Problems, 17:1225-1242, 2001.
    • (2001) Inverse Problems , vol.17 , pp. 1225-1242
    • Ito, K.1    Kunisch, K.2    Li, Z.3
  • 32
    • 0002501641 scopus 로고    scopus 로고
    • Sequential and parallel splitting methods for bilinear control problems in Hilbert spaces
    • K. Kunisch and X.-C. Tai. Sequential and parallel splitting methods for bilinear control problems in Hilbert spaces. SIAM J. Numer. Anal., 34:91-118, 1997.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 91-118
    • Kunisch, K.1    Tai, X.-C.2
  • 38
    • 0035075370 scopus 로고    scopus 로고
    • Explicit algorithms for a new time dependent model based on level set motion for nonlinear deblurring and noise removal
    • electronic
    • Antonio Marquina and Stanley Osher. Explicit algorithms for a new time dependent model based on level set motion for nonlinear deblurring and noise removal. SIAM J. Sci. Comput., 22(2):387-405 (electronic), 2000.
    • (2000) SIAM J. Sci. Comput , vol.22 , Issue.2 , pp. 387-405
    • Marquina, A.1    Osher, S.2
  • 39
    • 84990602490 scopus 로고
    • Optimal approximation by piecewise smooth functions and assosiated variational problems
    • D. Mumford and J. Shah. Optimal approximation by piecewise smooth functions and assosiated variational problems. Comm. Pure Appl. Math, 42:577-685, 1989.
    • (1989) Comm. Pure Appl. Math , vol.42 , pp. 577-685
    • Mumford, D.1    Shah, J.2
  • 41
    • 0000653947 scopus 로고    scopus 로고
    • Level set methods: An overview and some recent results
    • S. Osher and R. P. Fedkiw. Level set methods: an overview and some recent results. J. Comput. Phys., 169(2):463-502, 2001.
    • (2001) J. Comput. Phys. , vol.169 , Issue.2 , pp. 463-502
    • Osher, S.1    Fedkiw, R.P.2
  • 43
    • 44749084234 scopus 로고
    • Fronts propagating with curvature dependent speed: Algorithms based on hamilton-jacobi formulations
    • S. Osher and J. A. Sethian. Fronts propagating with curvature dependent speed: Algorithms based on hamilton-jacobi formulations. J. Comput. Phys., 79:12-49, 1988.
    • (1988) J. Comput. Phys. , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.A.2
  • 44
    • 0001167356 scopus 로고    scopus 로고
    • A PDE-based fast local level set method
    • Danping Peng, Barry Merriman, Stanley Osher, Hongkai Zhao, and Myungjoo Kang. A PDE-based fast local level set method. J. Comput. Phys., 155(2):410-438, 1999.
    • (1999) J. Comput. Phys , vol.155 , Issue.2 , pp. 410-438
    • Peng, D.1    Merriman, B.2    Osher, S.3    Zhao, H.4    Kang, M.5
  • 45
    • 85019595680 scopus 로고    scopus 로고
    • Enhanced electrical impedance tomography via the mumford-shah functional
    • L. Rondi and F. Santosa. Enhanced electrical impedance tomography via the mumford-shah functional. Control, Optimisation, and Calculus of Variations, to appear. Available online at http://www.math.umn.edu/%7Esantosa/fs.html.
    • Control, Optimisation, and Calculus of Variations
    • Rondi, L.1    Santosa, F.2
  • 46
    • 84996143735 scopus 로고
    • A level-set approach for inverse problems involving obstacles
    • electronic
    • F. Santosa. A level-set approach for inverse problems involving obstacles. ESAIM Contrôle Optim. Calc. Var., 1:17-33 (electronic), 1995-1996.
    • (1995) ESAIM Contrôle Optim. Calc. Var , vol.1 , pp. 17-33
    • Santosa, F.1
  • 47
    • 0032631799 scopus 로고    scopus 로고
    • Fast marching methods
    • electronic
    • J. A. Sethian. Fast marching methods. SIAM Rev., 41(2):199-235 (electronic), 1999.
    • (1999) SIAM Rev , vol.41 , Issue.2 , pp. 199-235
    • Sethian, J.A.1
  • 49
    • 0000655661 scopus 로고
    • Crystal growth and dendritic solidification
    • J. A. Sethian and J. Strain. Crystal growth and dendritic solidification. J. Comput. Phys., 98(2):231-253, 1992.
    • (1992) J. Comput. Phys. , vol.98 , Issue.2 , pp. 231-253
    • Sethian, J.A.1    Strain, J.2
  • 50
    • 24644510855 scopus 로고    scopus 로고
    • Fast algorithm for level set segmentation
    • B. Song and T.F. Chan. Fast algorithm for level set segmentation. UCLA CAM report 02-68, 2002.
    • (2002) UCLA CAM Report , pp. 02-68
    • Song, B.1    Chan, T.F.2
  • 51
    • 0345223780 scopus 로고
    • Identification of a nonlinear parameter in a parabolic equation from a linear equation
    • X.-C. Tai and T. Karkainen. Identification of a nonlinear parameter in a parabolic equation from a linear equation. Comp. Appl. Mat., 14:157-184, 1995.
    • (1995) Comp. Appl. Mat. , vol.14 , pp. 157-184
    • Tai, X.-C.1    Karkainen, T.2
  • 52
    • 0345223789 scopus 로고
    • Error estimates for numerical identification of distributed parameters
    • Xue-Cheng Tai and Pekka Neittaanmaki. Error estimates for numerical identification of distributed parameters. J. Comp. Math., Supplementary issue:66-78, 1992.
    • (1992) J. Comp. Math., Supplementary Issue , pp. 66-78
    • Tai, X.-C.1    Neittaanmaki, P.2
  • 53
    • 0344361059 scopus 로고    scopus 로고
    • Pointwise error estimates for distributed parameter identification
    • In D. Bainov, editor, The Netherlands, International Science Publishers
    • Xue-Cheng Tai and Pekka Neittaanmaki. Pointwise error estimates for distributed parameter identification. In D. Bainov, editor, Proceedings of the seventh international colloqium on differential equations, pages 455-468, The Netherlands, 1997. International Science Publishers.
    • (1997) Proceedings of the Seventh International Colloqium on Differential Equations , pp. 455-468
    • Tai, X.-C.1    Neittaanmaki, P.2
  • 54
    • 1942479348 scopus 로고    scopus 로고
    • Fast sweeping algorithms for a class of hamilton-jacobi equations
    • to appear
    • Y.R. Tsai, L.T. Cheng, S. Osher, and H.K. Zhao. Fast sweeping algorithms for a class of hamilton-jacobi equations. SIAM J. Numer. Anal., to appear.
    • SIAM J. Numer. Anal
    • Tsai, Y.R.1    Cheng, L.T.2    Osher, S.3    Zhao, H.K.4
  • 55
    • 0036891794 scopus 로고    scopus 로고
    • A new multiphase level set framework for image segmentation via the Mumford and Shah model
    • Luminita A. Vese and Tony F. Chan. A new multiphase level set framework for image segmentation via the Mumford and Shah model. International Journal of Computer Vision, 50:271-293, 2002.
    • (2002) International Journal of Computer Vision , vol.50 , pp. 271-293
    • Vese, L.A.1    Chan, T.F.2
  • 56
    • 85019549853 scopus 로고    scopus 로고
    • Fast sweeping method for eikonal equations i
    • to appear
    • H. K. Zhao. Fast sweeping method for eikonal equations i. SIAM J. Numer. Anal., to appear.
    • SIAM J. Numer. Anal
    • Zhao, H.K.1
  • 57
    • 0030210970 scopus 로고    scopus 로고
    • A variational level set approach to multiphase motion
    • Hong-Kai Zhao, T. Chan, B. Merriman, and S. Osher. A variational level set approach to multiphase motion. J. Comput. Phys., 127(1):179-195, 1996.
    • (1996) J. Comput. Phys , vol.127 , Issue.1 , pp. 179-195
    • Zhao, H.-K.1    Chan, T.2    Merriman, B.3    Osher, S.4


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