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Volumn 15, Issue 5, 2006, Pages 1171-1181

A binary level set model and some applications to Mumford-Shah image segmentation

Author keywords

Image processing; Image segmentation; Level set; PDE; Piecewise constant level set functions; Variational

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; IMAGE PROCESSING; MATHEMATICAL MODELS; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS; SET THEORY;

EID: 33646013275     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2005.863956     Document Type: Article
Times cited : (331)

References (46)
  • 1
    • 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., vol. 79, no. 1, pp. 12-49, 1988.
    • (1988) J. Comput. Phys. , vol.79 , Issue.1 , pp. 12-49
    • Osher, S.1    Sethian, J.A.2
  • 2
    • 0035248865 scopus 로고    scopus 로고
    • "Active contours without edges"
    • Feb
    • T. F. Chan and L. A. Vese, "Active contours without edges," IEEE Trans. Image Process., vol. 10, no. 2, pp. 266-277, Feb. 2001.
    • (2001) IEEE Trans. Image Process. , vol.10 , Issue.2 , pp. 266-277
    • Chan, T.F.1    Vese, L.A.2
  • 3
    • 28144444111 scopus 로고
    • "A level set approach for computing solutions to incompressible two phase flow"
    • M. Sussman, P. Smereka, and S. Osher, "A level set approach for computing solutions to incompressible two phase flow," J. Comput. Phys., vol. 114, pp. 146-159, 1994.
    • (1994) J. Comput. Phys. , vol.114 , pp. 146-159
    • Sussman, M.1    Smereka, P.2    Osher, S.3
  • 4
    • 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., vol. 193, pp. 40-66, 2003.
    • (2003) J. Comput. Phys. , vol.193 , pp. 40-66
    • Chan, T.F.1    Tai, X.-C.2
  • 5
    • 0037337788 scopus 로고    scopus 로고
    • "Shock capturing, level sets, and PDE based methods in computer vision and image processing: A review of Osher's contributions"
    • R. P. Fedkiw, G. Sapiro, and C.-W. Shu, "Shock capturing, level sets, and PDE based methods in computer vision and image processing: A review of Osher's contributions," J. Comput. Phys., vol. 185, no. 2, pp. 309-341, 2003.
    • (2003) J. Comput. Phys. , vol.185 , Issue.2 , pp. 309-341
    • Fedkiw, R.P.1    Sapiro, G.2    Shu, C.-W.3
  • 6
    • 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," Interf. Free Bound, vol. 5, no. 3, pp. 301-329, 2003.
    • (2003) Interf. Free Bound , vol.5 , Issue.3 , pp. 301-329
    • Burger, M.1
  • 7
    • 2542438832 scopus 로고    scopus 로고
    • "A second order shape optimization approach for image segmentation"
    • (electronic)
    • M. Hintermüller and W. Ring, "A second order shape optimization approach for image segmentation," SIAM J. Appl. Math., vol. 64, no. 2, pp. 442-467, 2003/2004. (electronic).
    • (2003) SIAM J. Appl. Math. , vol.64 , Issue.2 , pp. 442-467
    • Hintermüller, M.1    Ring, W.2
  • 8
    • 0842312288 scopus 로고    scopus 로고
    • "Incorporating topological derivatives into level set methods"
    • M. Burger, B. Hackl, and W. Ring, "Incorporating topological derivatives into level set methods," J. Comput. Phys., vol. 194, no. 1, pp. 344-362, 2004.
    • (2004) J. Comput. Phys. , vol.194 , Issue.1 , pp. 344-362
    • Burger, M.1    Hackl, B.2    Ring, W.3
  • 9
    • 0000653947 scopus 로고    scopus 로고
    • "Level set methods: An overview and some recent results"
    • S. Osher and R. Fedkiw, "Level set methods: An overview and some recent results," J. Comput. Phys., vol. 169, no. 2, pp. 463-502, 2001.
    • (2001) J. Comput. Phys. , vol.169 , Issue.2 , pp. 463-502
    • Osher, S.1    Fedkiw, R.2
  • 11
    • 0003661003 scopus 로고    scopus 로고
    • 2nd ed. Cambridge, MA: Harvard Univ. Press, Cambridge Monographs on Applied and Computational Mathematics. Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science
    • J. A. Sethian, Level Set Methods and Fast Marching Methods, 2nd ed. Cambridge, MA: Harvard Univ. Press, 1999, vol. 3. Cambridge Monographs on Applied and Computational Mathematics. Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science.
    • (1999) Level Set Methods and Fast Marching Methods , vol.3
    • Sethian, J.A.1
  • 12
    • 24644508476 scopus 로고    scopus 로고
    • "A survey on multiple level set methods with applications for identifying piecewise constant functions"
    • X.-C. Tai and T. F. Chan, "A survey on multiple level set methods with applications for identifying piecewise constant functions," Int. J. Numer. Anal. Model., vol. 1, no. 1, pp. 25-48, 2004.
    • (2004) Int. J. Numer. Anal. Model. , vol.1 , Issue.1 , pp. 25-48
    • Tai, X.-C.1    Chan, T.F.2
  • 14
    • 24644510855 scopus 로고    scopus 로고
    • "A fast algorithm for level set based optimization"
    • Comput. Appl. Math. Rep. 02-68, Univ. California, Los Angeles
    • B. Song and T. Chan, "A fast algorithm for level set based optimization," Comput. Appl. Math. Rep. 02-68, Univ. California, Los Angeles, 2002.
    • (2002)
    • Song, B.1    Chan, T.2
  • 15
    • 84935168793 scopus 로고
    • "Minimal interface criterion for phase transitions in mixtures of Cahn-Hilliard fluids"
    • S. Baldo, "Minimal interface criterion for phase transitions in mixtures of Cahn-Hilliard fluids," Ann. Inst. H. Poincaré Anal. Non Linéaire, vol. 7, no. 2, pp. 67-90, 1990.
    • (1990) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.7 , Issue.2 , pp. 67-90
    • Baldo, S.1
  • 16
    • 20344397096 scopus 로고    scopus 로고
    • "Design-dependent loads in topology optimization"
    • (electronic)
    • B. Bourdin and A. Chambolle, "Design-dependent loads in topology optimization," ESAIM Contr. Optim. Calc. Var., vol. 9, pp. 19-48, 2003. (electronic).
    • (2003) ESAIM Contr. Optim. Calc. Var. , vol.9 , pp. 19-48
    • Bourdin, B.1    Chambolle, A.2
  • 17
    • 0000467453 scopus 로고    scopus 로고
    • "Model of surface instabilities induced by stress"
    • J. Müller and M. Grant, "Model of surface instabilities induced by stress," Phys. Rev. Lett., vol. 82, no. 8, 1999.
    • (1999) Phys. Rev. Lett. , vol.82 , Issue.8
    • Müller, J.1    Grant, M.2
  • 20
    • 34748925841 scopus 로고
    • "Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence"
    • L. Ambrosio and V. M. Tortorelli, "Approximation of functionals depending on jumps by elliptic functionals via Γ-convergence," Commun. Pure Appl. Math., vol. 43, no. 8, pp. 999-1036, 1990.
    • (1990) Commun. Pure Appl. Math. , vol.43 , Issue.8 , pp. 999-1036
    • Ambrosio, L.1    Tortorelli, V.M.2
  • 21
    • 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," Commun. Pure Appl. Math, vol. 42, pp. 577-685, 1989.
    • (1989) Commun. Pure Appl. Math , vol.42 , pp. 577-685
    • Mumford, D.1    Shah, J.2
  • 22
    • 0029328073 scopus 로고
    • "Image segmentation by variational methods: Mumford and Shah functional and the discrete approximations"
    • A. Chambolle, "Image segmentation by variational methods: Mumford and Shah functional and the discrete approximations," SIAM J. Appl. Math., vol. 55, no. 3, pp. 827-863, 1995.
    • (1995) SIAM J. Appl. Math. , vol.55 , Issue.3 , pp. 827-863
    • Chambolle, A.1
  • 23
    • 0033463011 scopus 로고    scopus 로고
    • "Finite-differences discretizations of the Mumford-Shah functional"
    • A. Chambolle, "Finite-differences discretizations of the Mumford-Shah functional," M2AN Math. Model. Numer. Anal., vol. 33, no. 2, pp. 261-288, 1999.
    • (1999) M2AN Math. Model. Numer. Anal. , vol.33 , Issue.2 , pp. 261-288
    • Chambolle, A.1
  • 24
    • 0035425439 scopus 로고    scopus 로고
    • "Curve evolution implementation of the mumford shah functional for image segmentation, denoising, interpolation, and magnification"
    • Aug
    • A. Tsai, J. Anthony Yezzi, and A. S. Willsky, "Curve evolution implementation of the mumford shah functional for image segmentation, denoising, interpolation, and magnification," in IEEE Trans. Image Process., vol. 10, Aug. 2001, pp. 1169-1186.
    • (2001) IEEE Trans. Image Process. , vol.10 , pp. 1169-1186
    • Tsai, A.1    Yezzi, J.A.2    Willsky, A.S.3
  • 25
    • 0036892825 scopus 로고    scopus 로고
    • "Diffusion snakes: Introducing statistical shape knowledge into the Mumford-Shah functional"
    • D. Cremers, F. Tischhäuser, J. Weickert, and C. Schnörr, "Diffusion snakes: Introducing statistical shape knowledge into the Mumford-Shah functional," Int. J. Comput. Vis., vol. 50, no. 3, pp. 295-313, 2002.
    • (2002) Int. J. Comput. Vis. , vol.50 , Issue.3 , pp. 295-313
    • Cremers, D.1    Tischhäuser, F.2    Weickert, J.3    Schnörr, C.4
  • 26
    • 0036891794 scopus 로고    scopus 로고
    • "A multiphase level set framevork for image segmentation using the mumford and shah model"
    • L. A. Vese and T. F. Chan, "A multiphase level set framevork for image segmentation using the mumford and shah model," Int. J. Comput. Vis., vol. 50, no. 3, pp. 271-293, 2002.
    • (2002) Int. J. Comput. Vis. , vol.50 , Issue.3 , pp. 271-293
    • Vese, L.A.1    Chan, T.F.2
  • 27
    • 33645962045 scopus 로고    scopus 로고
    • "A variant of the levelset method and applications to image segmentation"
    • to be published
    • J. Lie, M. Lysaker, and X.-C. Tai, "A variant of the levelset method and applications to image segmentation," AMS Math. Comput., to be published.
    • AMS Math. Comput.
    • Lie, J.1    Lysaker, M.2    Tai, X.-C.3
  • 28
    • 33645983049 scopus 로고    scopus 로고
    • "Image segmentation using a multilayer level-set approach"
    • Univ. California, Los Angeles, CAM 03-53
    • J. T. Chung and L. A. Vese, "Image segmentation using a multilayer level-set approach," Univ. California, Los Angeles, CAM 03-53, 2003.
    • (2003)
    • Chung, J.T.1    Vese, L.A.2
  • 29
    • 0036570978 scopus 로고    scopus 로고
    • "Rapid and accurate computation of the distance function using grids"
    • Y. R. Tsai, "Rapid and accurate computation of the distance function using grids," J. Comput. Phys., vol. 178, pp. 175-195, 2002.
    • (2002) J. Comput. Phys. , vol.178 , pp. 175-195
    • Tsai, Y.R.1
  • 30
    • 0029373106 scopus 로고
    • "Efficient algorithms for globally optimal trajectories"
    • Sep
    • J. N. Tsitsiklis, "Efficient algorithms for globally optimal trajectories," IEEE Trans. Autom. Contr., vol. 40, no. 9, pp. 1528-1538, Sep. 1995.
    • (1995) IEEE Trans. Autom. Contr. , vol.40 , Issue.9 , pp. 1528-1538
    • Tsitsiklis, J.N.1
  • 31
    • 1942479348 scopus 로고    scopus 로고
    • "Fast sweeping algorithms for a class of Hamilton-Jacobi equations"
    • (electronic)
    • Y.-H. 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., vol. 41, no. 2, pp. 673-694, 2003. (electronic).
    • (2003) SIAM J. Numer. Anal. , vol.41 , Issue.2 , pp. 673-694
    • Tsai, Y.-H.R.1    Cheng, L.-T.2    Osher, S.3    Zhao, H.-K.4
  • 32
    • 22544433263 scopus 로고    scopus 로고
    • "A review of level set and fast marching methods for image processing"
    • ser. NATO Sci. Ser. II Math. Phys. Chem. Norwell, MA: Kluwer
    • J. A. Sethian, "A review of level set and fast marching methods for image processing," in Modern Methods in Scientific Computing and Applications, ser. NATO Sci. Ser. II Math. Phys. Chem.. Norwell, MA: Kluwer, 2002, vol. 75, pp. 365-396.
    • (2002) Modern Methods in Scientific Computing and Applications , vol.75 , pp. 365-396
    • Sethian, J.A.1
  • 34
    • 34249767150 scopus 로고
    • "A geometric model for active contours in image processing"
    • V. Caselles, F. Carte, T. Coll, and F. Dibos, "A geometric model for active contours in image processing," Numer. Math., vol. 66, pp. 1-31, 1993.
    • (1993) Numer. Math. , vol.66 , pp. 1-31
    • Caselles, V.1    Carte, F.2    Coll, T.3    Dibos, F.4
  • 35
    • 0004095766 scopus 로고
    • ser. Graduate Texts in Mathematics New York: Springer-Verlag, Sobolev spaces and functions of bounded variation
    • W. P. Ziemer, Weakly Differentiable Functions, ser. Graduate Texts in Mathematics. New York: Springer-Verlag, 1989, vol. 120. Sobolev spaces and functions of bounded variation.
    • (1989) Weakly Differentiable Functions , vol.120
    • Ziemer, W.P.1
  • 36
    • 2442711821 scopus 로고    scopus 로고
    • "Analysis of iterative algorithms of uzawa type for saddle point problems"
    • M.-R. Cui, "Analysis of iterative algorithms of uzawa type for saddle point problems," Appl. Numer. Math., vol. 50, no. 2, pp. 133-146, 2004.
    • (2004) Appl. Numer. Math. , vol.50 , Issue.2 , pp. 133-146
    • Cui, M.-R.1
  • 38
    • 0003982971 scopus 로고    scopus 로고
    • ser. Springer Series in Operations Research New York: Springer-Verlag
    • J. Nocedal and S. J. Wright, Numerical Optimization, ser. Springer Series in Operations Research. New York: Springer-Verlag, 1999.
    • (1999) Numerical Optimization
    • Nocedal, J.1    Wright, S.J.2
  • 39
    • 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., vol. 34, pp. 91-118, 1997.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 91-118
    • Kunisch, K.1    Tai, X.-C.2
  • 40
    • 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., vol. 25, pp. 881-904, 2003.
    • (2003) SIAM J. Sci. Comput. , vol.25 , pp. 881-904
    • Chan, T.F.1    Tai, X.-C.2
  • 41
    • 0019226085 scopus 로고
    • "Thresholding using the ISODATA clustering algorithm"
    • Nov
    • F. R. Dias Velasco, "Thresholding using the ISODATA clustering algorithm," IEEE Trans. Syst., Man, Cybern., vol. 10, no. 11, pp. 771-774, Nov. 1980.
    • (1980) IEEE Trans. Syst., Man, Cybern. , vol.10 , Issue.11 , pp. 771-774
    • Dias Velasco, F.R.1
  • 42
    • 33645961738 scopus 로고    scopus 로고
    • "A binary level set model and some applications to image processing"
    • Univ. California, Los Angeles, CAM 04-31
    • J. Lie, M. Lysaker, and X.-C. Tai, "A binary level set model and some applications to image processing," Univ. California, Los Angeles, CAM 04-31, 2004.
    • (2004)
    • Lie, J.1    Lysaker, M.2    Tai, X.-C.3
  • 43
    • 17544385421 scopus 로고    scopus 로고
    • "An inexact Newton-cg-type active contour approach for the minimization of the Mumford-Shah functional"
    • M. Hintermüller and W. Ring, "An inexact Newton-cg-type active contour approach for the minimization of the Mumford-Shah functional," J. Math. Imag. Vis., vol. 20, no. 1, pp. 19-42, 2004.
    • (2004) J. Math. Imag. Vis. , vol.20 , Issue.1 , pp. 19-42
    • Hintermüller, M.1    Ring, W.2
  • 44
    • 0032681559 scopus 로고    scopus 로고
    • "On the topological derivative in shape optimization"
    • (electronic)
    • J. Sokolowski and A. Zochowski, "On the topological derivative in shape optimization," SIAM J. Contr. Optim., vol. 37, no. 4, pp. 1251-1272, 1999. (electronic).
    • (1999) SIAM J. Contr. Optim. , vol.37 , Issue.4 , pp. 1251-1272
    • Sokolowski, J.1    Zochowski, A.2
  • 45
    • 33645974428 scopus 로고    scopus 로고
    • Brainweb: Simulated Brain Database [Online]. Available
    • Brainweb: Simulated Brain Database [OnliHe]. Available: http://www.bic. mni.mcgill.ca/brainweb
  • 46
    • 21544432712 scopus 로고    scopus 로고
    • "Brainweb: Online interface to a 3d mri simulated brain database"
    • C. Cocosco, V. Kollokian, R.-S. Kwan, and A. Evans, "Brainweb: Online interface to a 3d mri simulated brain database," NeuroImage, vol. 5, no. 4, 1997. part 2/4, S425.
    • (1997) NeuroImage , vol.5 , Issue.4 PART 2 and 4
    • Cocosco, C.1    Kollokian, V.2    Kwan, R.-S.3    Evans, A.4


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