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Volumn 20, Issue 1-2, 2004, Pages 19-42

An Inexact Newton-CG-Type Active Contour Approach for the Minimization of the Mumford-Shah Functional

Author keywords

Active contours; Image segmentation; Level set method; Mumford Shah functional; Newton algorithm; Shape sensitivity analysis

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; CONTOUR MEASUREMENT; FUNCTION EVALUATION; GRADIENT METHODS; MATHEMATICAL MODELS; OPTIMIZATION; SENSITIVITY ANALYSIS;

EID: 17544385421     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1023/b:jmiv.0000011317.13643.3a     Document Type: Conference Paper
Times cited : (52)

References (41)
  • 1
    • 0002108952 scopus 로고    scopus 로고
    • The fast construction of extension velocities in level set methods
    • D. Adalsteinsson and J.A. Sethian, "The fast construction of extension velocities in level set methods," J. Comput. Phys., Vol. 148, No. 1, pp. 2-22, 1999.
    • (1999) J. Comput. Phys. , vol.148 , Issue.1 , pp. 2-22
    • Adalsteinsson, D.1    Sethian, J.A.2
  • 3
    • 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," Comm. Pure Appl. Math., Vol. 43, No. 8, pp. 999-1036, 1990.
    • (1990) Comm. Pure Appl. Math. , vol.43 , Issue.8 , pp. 999-1036
    • Ambrosio, L.1    Tortorelli, V.M.2
  • 5
    • 0013091709 scopus 로고    scopus 로고
    • Springer-Verlag, New York. Partial differential equations and the calculus of variations, With a foreword by Olivier Faugeras
    • G. Aubert and P. Kornprobst, Mathematical Problems in Image Processing. Springer-Verlag, New York, 2002. Partial differential equations and the calculus of variations, With a foreword by Olivier Faugeras.
    • (2002) Mathematical Problems in Image Processing
    • Aubert, G.1    Kornprobst, P.2
  • 6
    • 85031738381 scopus 로고    scopus 로고
    • Topology design of structures, materials and mechanisms - Status and perspectives
    • M.J.D. Powell and S. Scholtes (Eds.), July 12-16, Boston, MA. Kluwer Academic Publishers
    • M.P. Bendsœ, "Topology design of structures, materials and mechanisms - status and perspectives," in System modelling and optimization, Proceedings of the 19th IFIP TC7 Conference held in Cambridge, M.J.D. Powell and S. Scholtes (Eds.), July 12-16, 1999, pp. 1-17, Boston, MA, 2000. Kluwer Academic Publishers.
    • (1999) System Modelling and Optimization, Proceedings of the 19th IFIP TC7 Conference Held in Cambridge , pp. 1-17
    • Bendsœ, M.P.1
  • 7
    • 0004293575 scopus 로고
    • MIT Press Series in Artificial Intelligence. MIT Press, Cambridge, MA
    • A. Blake and A. Zisserman, Visual Reconstruction, MIT Press Series in Artificial Intelligence. MIT Press, Cambridge, MA, 1987.
    • (1987) Visual Reconstruction
    • Blake, A.1    Zisserman, A.2
  • 8
    • 0034412473 scopus 로고    scopus 로고
    • Implementation of an adaptive finite-element approximation of the Mumford-Shah functional
    • B. Bourdin and A. Chambolle, "Implementation of an adaptive finite-element approximation of the Mumford-Shah functional," Numer. Math., Vol. 85, No. 4, pp. 609-646, 2000.
    • (2000) Numer. Math. , vol.85 , Issue.4 , pp. 609-646
    • Bourdin, B.1    Chambolle, A.2
  • 9
    • 0000121920 scopus 로고    scopus 로고
    • Non-local approximation of the Mumford-Shah functional
    • A. Braides and G. Dal Maso, "Non-local approximation of the Mumford-Shah functional," Calc. Var. Partial Differential Equations, Vol. 5, No. 4, pp. 293-322, 1997.
    • (1997) Calc. Var. Partial Differential Equations , vol.5 , Issue.4 , pp. 293-322
    • Braides, A.1    Dal Maso, G.2
  • 12
    • 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
  • 13
    • 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
  • 14
    • 0033438682 scopus 로고    scopus 로고
    • Discrete approximation of the Mumford-Shah functional in dimension two
    • A. Chambolle and G.D. Maso, "Discrete approximation of the Mumford-Shah functional in dimension two," M2AN Math. Model. Numer. Anal., Vol. 33, No. 4, pp. 651-672, 1999.
    • (1999) M2AN Math. Model. Numer. Anal. , vol.33 , Issue.4 , pp. 651-672
    • Chambolle, A.1    Maso, G.D.2
  • 16
    • 0003241517 scopus 로고    scopus 로고
    • Image segmentation using level sets and the piecewise constant Mumford-Shah model
    • University of California, Los Angeles
    • T.F. Chan and L.A. Vese, "Image segmentation using level sets and the piecewise constant Mumford-Shah model," UCLA CAM Report 00-14, University of California, Los Angeles, 2000.
    • (2000) UCLA CAM Report , vol.14
    • Chan, T.F.1    Vese, L.A.2
  • 17
    • 0003273034 scopus 로고    scopus 로고
    • A level set algorithm for minimizing the Mumford-Shah functional in image processing
    • University of California, Los Angeles
    • T.F. Chan and L.A. Vese, "A level set algorithm for minimizing the Mumford-Shah functional in image processing," UCLA CAM Report 00-13, University of California, Los Angeles, 2000.
    • (2000) UCLA CAM Report , vol.13
    • Chan, T.F.1    Vese, L.A.2
  • 18
    • 0035248865 scopus 로고    scopus 로고
    • Active contours without edges
    • T.F. Chan and L.A. Vese, "Active contours without edges," IEEE Trans. Image Processing, Vol. 10, No. 2, pp. 266-277, 2001.
    • (2001) IEEE Trans. Image Processing , vol.10 , Issue.2 , pp. 266-277
    • Chan, T.F.1    Vese, L.A.2
  • 19
    • 0036891794 scopus 로고    scopus 로고
    • A multiphase level set framework for image segmentation using the mumford and shah model
    • T.F. Chan and L.A. Vese, "A multiphase level set framework for image segmentation using the mumford and shah model," Int. J. Comp. Vision, Vol. 50, No. 3, pp. 271-293, 2002.
    • (2002) Int. J. Comp. Vision , vol.50 , Issue.3 , pp. 271-293
    • Chan, T.F.1    Vese, L.A.2
  • 20
    • 0011778271 scopus 로고    scopus 로고
    • Avoiding local minima for deformable curves in image analysis
    • A. Le Méhauté, C. Rabut, and L.L. Schumaker (Eds.). Vanderbilt University Press: Nashvill, TN
    • L.D. Cohen, "Avoiding local minima for deformable curves in image analysis," in Curves and Surfaces with Applications in CAGD, A. Le Méhauté, C. Rabut, and L.L. Schumaker (Eds.), pp. 77-84. Vanderbilt University Press: Nashvill, TN, 1997.
    • (1997) Curves and Surfaces with Applications in CAGD , pp. 77-84
    • Cohen, L.D.1
  • 21
    • 0031213363 scopus 로고    scopus 로고
    • Global minimum for active contour models: A minimum path approach
    • L.D. Cohen and R. Kimmel, "Global minimum for active contour models: A minimum path approach," International Journal of Computer Vision, Vol. 24, No. 1, pp. 57-78, 1997.
    • (1997) International Journal of Computer Vision , vol.24 , Issue.1 , pp. 57-78
    • Cohen, L.D.1    Kimmel, R.2
  • 22
    • 0038500200 scopus 로고    scopus 로고
    • Society for Industrial and Applied Mathematics (SIAM): Philadelphia, PA. Analysis, differential calculus, and optimization
    • M.C. Delfour and J.-P. Zolésio, Shapes and Geometries. Society for Industrial and Applied Mathematics (SIAM): Philadelphia, PA, 2001. Analysis, differential calculus, and optimization.
    • (2001) Shapes and Geometries
    • Delfour, M.C.1    Zolésio, J.-P.2
  • 25
    • 0021518209 scopus 로고
    • Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images
    • D. Geman and S. Geman, "Stochastic relaxation, Gibbs distribution, and the Bayesian restoration of images," IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 6, No. 6, pp. 721-741, 1984.
    • (1984) IEEE Transactions on Pattern Analysis and Machine Intelligence , vol.6 , Issue.6 , pp. 721-741
    • Geman, D.1    Geman, S.2
  • 27
    • 24444467035 scopus 로고    scopus 로고
    • A level set approach for the solution of a state constrained optimal control problem
    • Technical Report 212, Special Research Center on Optimization and Control, University of Graz, Austria
    • M. Hintermüller and W. Ring, "A level set approach for the solution of a state constrained optimal control problem," Technical Report 212, Special Research Center on Optimization and Control, University of Graz, Austria, 2001. To appear in Numerische Mathematik.
    • (2001) Numerische Mathematik.
    • Hintermüller, M.1    Ring, W.2
  • 28
    • 24444444438 scopus 로고    scopus 로고
    • A second order shape optimization approach for image segmentation
    • Report 237, Special Research Center on Optimization and Control, University of Graz, Austria, March
    • M. Hintermüller and W. Ring, "A second order shape optimization approach for image segmentation," Report 237, Special Research Center on Optimization and Control, University of Graz, Austria, March 2002. To appear in SIAM J. Appl. Math.
    • (2002) SIAM J. Appl. Math.
    • Hintermüller, M.1    Ring, W.2
  • 30
    • 0035507080 scopus 로고    scopus 로고
    • Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces
    • F. Mémoli and G. Sapiro, "Fast computation of weighted distance functions and geodesics on implicit hyper-surfaces," J. Comput. Phys., Vol. 173, No. 2, pp. 730-764, 2001.
    • (2001) J. Comput. Phys. , vol.173 , Issue.2 , pp. 730-764
    • Mémoli, F.1    Sapiro, G.2
  • 32
    • 84990602490 scopus 로고
    • Optimal approximations by piecewise smooth functions and associated variational problems
    • D. Mumford and J. Shah, "Optimal approximations by piecewise smooth functions and associated variational problems," Comm. Pure Appl. Math., Vol. 42, No. 5, pp. 577-685, 1989.
    • (1989) Comm. Pure Appl. Math. , vol.42 , Issue.5 , pp. 577-685
    • Mumford, D.1    Shah, J.2
  • 34
    • 0029966538 scopus 로고    scopus 로고
    • A fast marching method for monotonically advancing fronts
    • J. Sethian, "A fast marching method for monotonically advancing fronts," Proc. Nat. Acad. Sci., Vol. 93, No. 4, pp. 1591-1595, 1996.
    • (1996) Proc. Nat. Acad. Sci. , vol.93 , Issue.4 , pp. 1591-1595
    • Sethian, J.1
  • 35
    • 0032631799 scopus 로고    scopus 로고
    • Fast marching methods
    • electronic
    • J.A. Sethian, "Fast marching methods," SIAM Rev., Vol. 41, No. 2, pp. 199-235 (electronic), 1999.
    • (1999) SIAM Rev. , vol.41 , Issue.2 , pp. 199-235
    • Sethian, J.A.1
  • 36
    • 0003661003 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge. Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science
    • J.A. Sethian, Level Set Methods and Fast Marching Methods. 2nd edition, Cambridge University Press, Cambridge. 1999. Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science.
    • (1999) Level Set Methods and Fast Marching Methods. 2nd Edition
    • Sethian, J.A.1
  • 38
    • 0035425439 scopus 로고    scopus 로고
    • Curve evolution implementation of the Mumford-Shah functional for image segementation, denoising, interpolation, and magnification
    • A. Tsai, A. Yezzi, and A.S. Willsky, "Curve evolution implementation of the Mumford-Shah functional for image segementation, denoising, interpolation, and magnification," IEEE Transactions on Image Processing, Vol. 10, No. 8, pp. 1169-1186, 2001.
    • (2001) IEEE Transactions on Image Processing , vol.10 , Issue.8 , pp. 1169-1186
    • Tsai, A.1    Yezzi, A.2    Willsky, A.S.3
  • 39
    • 0003707878 scopus 로고    scopus 로고
    • Fast sweeping algorithms for a class of Hamilton-Jacobi equations
    • CAM Report 01-27. Computational and Applied Mathematics, Department of Mathematics University of California, Los Angeles
    • Y.R. Tsai, L.-T. Cheng, S. Osher, and H.-K. Zhao, "Fast sweeping algorithms for a class of Hamilton-Jacobi equations," CAM-Report 01-27, Computational and Applied Mathematics, Department of Mathematics University of California, Los Angeles, 2001.
    • (2001) CAM-report
    • Tsai, Y.R.1    Cheng, L.-T.2    Osher, S.3    Zhao, H.-K.4
  • 40
    • 0036570978 scopus 로고    scopus 로고
    • Rapid and accurate computation of the distance function using grids
    • Y.-H.R. Tsai, "Rapid and accurate computation of the distance function using grids," J. Comput. Phys., Vol. 178, No. 1, pp. 175-195, 2002.
    • (2002) J. Comput. Phys. , vol.178 , Issue.1 , pp. 175-195
    • Tsai, Y.-H.R.1
  • 41
    • 0029373106 scopus 로고
    • Efficient algorithms for globally optimal trajectories
    • J.N. Tsitsiklis, "Efficient algorithms for globally optimal trajectories," IEEE Trans. Automat. Control, Vol. 40, No. 9, pp. 1528-1538, 1995.
    • (1995) IEEE Trans. Automat. Control , vol.40 , Issue.9 , pp. 1528-1538
    • Tsitsiklis, J.N.1


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