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Volumn 63, Issue 6, 2003, Pages 1911-1934

On effective stopping time selection for visco-plastic nonlinear BV diffusion filters used in image denoising

Author keywords

Image processing; Nonlinear diffusion filtering; Stability; Variational methods; Visco plastic fluids

Indexed keywords

APPROXIMATION THEORY; ASYMPTOTIC STABILITY; BOUNDARY CONDITIONS; CONFORMAL MAPPING; EIGENVALUES AND EIGENFUNCTIONS; FLUIDS; IMAGE ENHANCEMENT; INTEGRATION; ITERATIVE METHODS; PARTIAL DIFFERENTIAL EQUATIONS; THEOREM PROVING; VISCOPLASTICITY;

EID: 1642544678     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139902400465     Document Type: Article
Times cited : (11)

References (78)
  • 1
    • 36149030663 scopus 로고
    • Analysis of bounded variation penalty methods for ill-posed problems
    • R. Acar and C.R. Vogel, Analysis of bounded variation penalty methods for ill-posed problems, Inverse Problems, 10 (1994), pp. 1217-1229.
    • (1994) Inverse Problems , vol.10 , pp. 1217-1229
    • Acar, R.1    Vogel, C.R.2
  • 3
    • 0026883886 scopus 로고
    • Image selective smoothing and edge detection by nonlinear diffusion
    • L. Alvarez, P.-L. Lions, and J.-M. Morel, Image selective smoothing and edge detection by nonlinear diffusion. II, SIAM J. Numer. Anal., 29 (1992), pp. 845-866.
    • (1992) II, SIAM J. Numer. Anal. , vol.29 , pp. 845-866
    • Alvarez, L.1    Lions, P.-L.2    Morel, J.-M.3
  • 4
    • 84974253506 scopus 로고
    • Formalization and computational aspects of image analysis
    • Cambridge University Press, London
    • L. Alvarez and J.-M. Morel, Formalization and computational aspects of image analysis, Acta Numer. 1994, Cambridge University Press, London, 1994, pp. 1-59.
    • (1994) Acta Numer. 1994 , pp. 1-59
    • Alvarez, L.1    Morel, J.-M.2
  • 5
    • 0040305878 scopus 로고    scopus 로고
    • Geometric evolution problems, distance function and viscosity solutions
    • Springer-Verlag, New York
    • L. Ambrosio, Geometric evolution problems, distance function and viscosity solutions, in Calculus of Variations and Partial Differential Equations, Springer-Verlag, New York, 1999, pp. 5-94.
    • (1999) Calculus of Variations and Partial Differential Equations , pp. 5-94
    • Ambrosio, L.1
  • 10
    • 0036473319 scopus 로고    scopus 로고
    • Some qualitative properties for the total variation flow
    • F. Andreu, V. Caselles, J.I. Díaz, and J.M. Mazón, Some qualitative properties for the total variation flow, J. Funct. Anal., 188 (2002), pp. 516-547.
    • (2002) J. Funct. Anal. , vol.188 , pp. 516-547
    • Andreu, F.1    Caselles, V.2    Díaz, J.I.3    Mazón, J.M.4
  • 11
    • 0343193150 scopus 로고    scopus 로고
    • Computing optical flow via variational techniques
    • G. Aubert, R. Deriche, and P. Kornprobst, Computing optical flow via variational techniques, SIAM J. Appl. Math., 60 (1999), pp. 156-182.
    • (1999) SIAM J. Appl. Math. , vol.60 , pp. 156-182
    • Aubert, G.1    Deriche, R.2    Kornprobst, P.3
  • 12
    • 0011235023 scopus 로고    scopus 로고
    • A variational method in image recovery
    • G. Aubert and L. Vese, A variational method in image recovery, SIAM J. Numer. Anal., 34 (1997), pp. 1948-1979.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1948-1979
    • Aubert, G.1    Vese, L.2
  • 13
  • 14
    • 0034634843 scopus 로고    scopus 로고
    • Dynamics of cooling domes of visco-plastic fluid
    • N.J. Balmforth and R.V. Craster, Dynamics of cooling domes of visco-plastic fluid, J. Fluid Mech., 422 (2000), pp. 225-248.
    • (2000) J. Fluid Mech. , vol.422 , pp. 225-248
    • Balmforth, N.J.1    Craster, R.V.2
  • 15
    • 85040958291 scopus 로고
    • Theory of fluid flows through natural rocks
    • Kluwer Academic Publishers, Nowell, MA
    • G.I. Barenblatt, V.M. Entov, and V.M. Ryzhik, Theory of Fluid Flows Through Natural Rocks, Kluwer Academic Publishers, Nowell, MA, 1990.
    • (1990)
    • Barenblatt, G.I.1    Entov, V.M.2    Ryzhik, V.M.3
  • 18
    • 0029772518 scopus 로고    scopus 로고
    • The robust estimation of multiple motions: Parametric and piecewise-smooth flow fields
    • M.J. Black and P. Anandan, The robust estimation of multiple motions: Parametric and piecewise-smooth flow fields, Comput. Vision Image Understanding, 63 (1996), pp. 75-104.
    • (1996) Comput. Vision Image Understanding , vol.63 , pp. 75-104
    • Black, M.J.1    Anandan, P.2
  • 19
    • 0004291558 scopus 로고
    • Operateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert
    • North-Holland, Amsterdam
    • H. Brezis, Operateurs Maximaux Monotones et Semi-Groupes de Contractions dans les Espaces de Hilbert, North-Holland, Amsterdam, 1973.
    • (1973)
    • Brezis, H.1
  • 20
    • 0020648263 scopus 로고
    • The rheology and flow of viscoplastic materials
    • R. Byron-Bird, G.C. Dai, and B.J. Yarusso, The rheology and flow of viscoplastic materials, Rev. Chem. Engrg., 1 (1983), pp. 2-70.
    • (1983) Rev. Chem. Engrg. , vol.1 , pp. 2-70
    • Byron-Bird, R.1    Dai, G.C.2    Yarusso, B.J.3
  • 21
    • 0026821645 scopus 로고
    • Image selective smoothing and edge detection by nonlinear diffusion
    • F. Catté, P.-L. Lions, J.-M. Morel, and T. Coll, Image selective smoothing and edge detection by nonlinear diffusion, SIAM J. Numer. Anal., 29 (1992), pp. 182-193.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 182-193
    • Catté, F.1    Lions, P.-L.2    Morel, J.-M.3    Coll, T.4
  • 22
    • 0031492191 scopus 로고    scopus 로고
    • Image recovery via total variation minimization and related problems
    • A. Chambolle and P.L. Lions, Image recovery via total variation minimization and related problems, Numer. Math., 76 (1997), pp. 167-188.
    • (1997) Numer. Math. , vol.76 , pp. 167-188
    • Chambolle, A.1    Lions, P.L.2
  • 23
    • 0033295350 scopus 로고    scopus 로고
    • A nonlinear primal-dual method for total variation-based image restoration
    • T.F. Chan, G.H. Golub, and P. Mulet, A nonlinear primal-dual method for total variation-based image restoration, SIAM J. Sci. Comput., 20 (1999), pp. 1964-1977.
    • (1999) SIAM J. Sci. Comput. , vol.20 , pp. 1964-1977
    • Chan, T.F.1    Golub, G.H.2    Mulet, P.3
  • 24
    • 0000668458 scopus 로고    scopus 로고
    • On the convergence of the lagged diffusivity fixed point method in total variation image restoration
    • T.F. Chan and P. Mulet, On the convergence of the lagged diffusivity fixed point method in total variation image restoration, SIAM J. Numer. Anal., 36 (1999), pp. 354-367.
    • (1999) SIAM J. Numer. Anal. , vol.36 , pp. 354-367
    • Chan, T.F.1    Mulet, P.2
  • 26
    • 84996143333 scopus 로고    scopus 로고
    • Regularization of linear least problems by total bounded variation
    • G. Chavent and K. Kunisch, Regularization of linear least squares problems by total bounded variation, ESAIM Control Optim. Calc. Var., 2 (1997), pp. 359-376.
    • (1997) ESAIM Control Optim. Calc. Var. , vol.2 , pp. 359-376
    • Chavent, G.1    Kunisch, K.2
  • 30
    • 0030212858 scopus 로고    scopus 로고
    • Recovery of blocky images from noisy and blurred data
    • D.C. Dobson and F. Santosa, Recovery of blocky images from noisy and blurred data, SIAM J. Appl. Math., 56 (1996), pp. 1181-1198.
    • (1996) SIAM J. Appl. Math. , vol.56 , pp. 1181-1198
    • Dobson, D.C.1    Santosa, F.2
  • 31
    • 0009176284 scopus 로고    scopus 로고
    • Analysis of regularized total variation penalty methods for denoising
    • D. C. Dobson and O. Scherzer, Analysis of regularized total variation penalty methods for denoising, Inverse Problems, 12 (1996), pp. 601-617.
    • (1996) Inverse Problems , vol.12 , pp. 601-617
    • Dobson, D.C.1    Scherzer, O.2
  • 32
    • 0000427927 scopus 로고    scopus 로고
    • Convergence of an iterative method for total variation denoising
    • D.C. Dobson and C.R. Vogel, Convergence of an iterative method for total variation denoising, SIAM J. Numer. Anal., 34 (1997), pp. 1779-1791.
    • (1997) SIAM J. Numer. Anal. , vol.34 , pp. 1779-1791
    • Dobson, D.C.1    Vogel, C.R.2
  • 34
    • 0032324706 scopus 로고    scopus 로고
    • Uniaxial exchange flows of two Bingham fluids in a cylindrical duct
    • I.A. Frigaard and O. Scherzer, Uniaxial exchange flows of two Bingham fluids in a cylindrical duct, IMA J. Appl. Math., 61 (1998), pp. 237-266.
    • (1998) IMA J. Appl. Math. , vol.61 , pp. 237-266
    • Frigaard, I.A.1    Scherzer, O.2
  • 35
    • 0034476651 scopus 로고    scopus 로고
    • The effects of yield stress variation on uniaxial exchange flows of two Binham fluids in a pipe
    • I.A. Frigaard and O. Scherzer, The effects of yield stress variation on uniaxial exchange flows of two Binham fluids in a pipe, SIAM J. Appl. Math., 60 (2000), pp. 1950-1976.
    • (2000) SIAM J. Appl. Math. , vol.60 , pp. 1950-1976
    • Frigaard, I.A.1    Scherzer, O.2
  • 36
    • 0028385349 scopus 로고
    • On the stability of Poiseuille flow of a Bingham fluid
    • I.A. Frigaard, S.D. Howison, and I.J. Sobey, On the stability of Poiseuille flow of a Bingham fluid, J. Fluid Mech., 263 (1994), pp. 133-150.
    • (1994) J. Fluid Mech. , vol.263 , pp. 133-150
    • Frigaard, I.A.1    Howison, S.D.2    Sobey, I.J.3
  • 37
    • 0029341230 scopus 로고
    • Nonlinear image recovery with half-quadratic regularization
    • D. Geman and C. Yang, Nonlinear image recovery with half-quadratic regularization, IEEE Trans. Image Processing, 4 (1995), pp. 932-945.
    • (1995) IEEE Trans. Image Processing , vol.4 , pp. 932-945
    • Geman, D.1    Yang, C.2
  • 38
    • 0021518209 scopus 로고
    • Stochastic relaxation, Gibbs distributions, and the Bayseian restoration of images
    • S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions, and the Bayseian restoration of images, IEEE Trans. Pattern Analysis and Machine Intelligence, 6 (1984), pp. 721-741.
    • (1984) IEEE Trans. Pattern Analysis and Machine Intelligence , vol.6 , pp. 721-741
    • Geman, S.1    Geman, D.2
  • 41
    • 0036342277 scopus 로고    scopus 로고
    • Are natural images of bounded variation?
    • Y. Gousseau and J.-M. Morel, Are natural images of bounded variation?, SIAM J. Math. Anal., 33 (2001), pp. 634-648.
    • (2001) SIAM J. Math. Anal. , vol.33 , pp. 634-648
    • Gousseau, Y.1    Morel, J.-M.2
  • 42
    • 0004261332 scopus 로고
    • Cambridge University Press, Cambridge, UK
    • E.J. Hinch, Perturbation Methods, Cambridge University Press, Cambridge, UK, 1991.
    • (1991) Perturbation Methods
    • Hinch, E.J.1
  • 43
    • 0029328892 scopus 로고
    • On the determination of the plug flow region in Bingham fluids through the application of variational inequalities
    • R.R. Huilgol and M.P. Panizza, On the determination of the plug flow region in Bingham fluids through the application of variational inequalities, J. Non-Newtonian Fluid Mech., 58 (1995), pp. 207-217.
    • (1995) J. Non-Newtonian Fluid Mech. , vol.58 , pp. 207-217
    • Huilgol, R.R.1    Panizza, M.P.2
  • 45
    • 0000299558 scopus 로고    scopus 로고
    • Augmented Lagrangian methods for nonsmooth, convex optimization in Hilbert spaces
    • K. Ito and K. Kunisch, Augmented Lagrangian methods for nonsmooth, convex optimization in Hilbert spaces, Nonlinear Anal., 41A (2000), pp. 591-616.
    • (2000) Nonlinear Anal. , vol.41 A , pp. 591-616
    • Ito, K.1    Kunisch, K.2
  • 46
    • 0031256990 scopus 로고    scopus 로고
    • The Perona-Malik paradox
    • S. Kichenassamy, The Perona-Malik paradox, SIAM J. Appl. Math., 57 (1997), pp. 1328-1342.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 1328-1342
    • Kichenassamy, S.1
  • 47
    • 0024750060 scopus 로고
    • Slow spreading of a sheet of Bingham fluid on an inclined plane
    • K.F. Liu and C.C. Mei, Slow spreading of a sheet of Bingham fluid on an inclined plane, J. Fluid Mech., 207 (1989), pp. 505-529.
    • (1989) J. Fluid Mech. , vol.207 , pp. 505-529
    • Liu, K.F.1    Mei, C.C.2
  • 50
    • 0001056433 scopus 로고
    • Variational methods in the theory of the fluidity of a viscous plastic medium
    • P.P. Mossolov and V.P. Miasnikov, Variational methods in the theory of the fluidity of a viscous plastic medium, J. Mech. Appl. Math., 29 (1965), pp. 468-492.
    • (1965) J. Mech. Appl. Math. , vol.29 , pp. 468-492
    • Mossolov, P.P.1    Miasnikov, V.P.2
  • 51
    • 0023446912 scopus 로고
    • On the estimation of optical flow: Relations between new approaches and some new results
    • N.H. Nagel, On the estimation of optical flow: Relations between new approaches and some new results, Artificial Intelligence, 33 (1987), pp. 299-324.
    • (1987) Artificial Intelligence , vol.33 , pp. 299-324
    • Nagel, N.H.1
  • 52
    • 0000951271 scopus 로고
    • An investigation of smoothness constraints for the estimation of displacement vector fields from image sequences
    • N.H. Nagel and W. Enkelmann, An investigation of smoothness constraints for the estimation of displacement vector fields from image sequences, IEEE Trans. Pattern Anal. Machine Intelligence, 12 (1990), pp. 629-629.
    • (1990) IEEE Trans. Pattern Anal. Machine Intelligence , vol.12 , pp. 629-629
    • Nagel, N.H.1    Enkelmann, W.2
  • 53
    • 0001357011 scopus 로고    scopus 로고
    • Stable approximations of nondifferentiable optimization problems with variational inequalities
    • M.Z. Nashed and O. Scherzer, Stable approximations of nondifferentiable optimization problems with variational inequalities, Contemp. Math., 204 (1997), pp. 155-170.
    • (1997) Contemp. Math. , vol.204 , pp. 155-170
    • Nashed, M.Z.1    Scherzer, O.2
  • 54
    • 0032165154 scopus 로고    scopus 로고
    • Least squares and bounded variation regularization with nondifferentiable functional
    • M.Z. Nashed and O. Scherzer, Least squares and bounded variation regularization with nondifferentiable functional, Numer. Funct. Anal. Optim., 19 (1998), pp. 873-901.
    • (1998) Numer. Funct. Anal. Optim. , vol.19 , pp. 873-901
    • Nashed, M.Z.1    Scherzer, O.2
  • 56
    • 0003268344 scopus 로고    scopus 로고
    • Scale-space theories in computer vision
    • M. Nielsen, P. Johansen, O.F. Olsen, and J. Weickert, eds.; Springer-Verlag, Berlin
    • M. Nielsen, P. Johansen, O.F. Olsen, and J. Weickert, eds., Scale-Space Theories in Computer Vision, Lecture Notes in Comput. Sci. 1682, Springer-Verlag, Berlin, 1999.
    • (1999) Lecture Notes in Comput. Sci. , vol.1682
  • 57
    • 0142176890 scopus 로고    scopus 로고
    • Local strong homogeneity of a regularized estimator
    • M. Nikolova, Local strong homogeneity of a regularized estimator, SIAM J. Appl. Math., 61 (2000), pp. 633-658.
    • (2000) SIAM J. Appl. Math. , vol.61 , pp. 633-658
    • Nikolova, M.1
  • 58
    • 0025521920 scopus 로고
    • Biased anisotropic diffusion - A unified regularization and diffusion approach to edge detection
    • N. Nordström, Biased anisotropic diffusion - A unified regularization and diffusion approach to edge detection, Image Vision Comput., 8 (1990), pp. 318-327.
    • (1990) Image Vision Comput. , vol.8 , pp. 318-327
    • Nordström, N.1
  • 59
    • 84959618660 scopus 로고
    • Two-dimensional plastic flow of a Bingham solid
    • J.G. Oldroyd, Two-dimensional plastic flow of a Bingham solid, Proc. Camb. Phil. Soc., 43 (1947), pp. 383-395.
    • (1947) Proc. Camb. Phil. Soc. , vol.43 , pp. 383-395
    • Oldroyd, J.G.1
  • 60
    • 1642535468 scopus 로고
    • Fast numerical methods for total variation minimization in image reconstruction
    • SPIE, Bellingham, WA
    • M.E. Oman and C. Vogel, Fast numerical methods for total variation minimization in image reconstruction, in Advanced Signal Processing Algorithms, SPIE Proceedings Vol. 256, SPIE, Bellingham, WA, 1995.
    • (1995) Advanced Signal Processing Algorithms, SPIE Proceedings , vol.256
    • Oman, M.E.1    Vogel, C.2
  • 62
    • 0025474774 scopus 로고
    • Feature-oriented image enhancement using shock filters
    • S. Osher and L.I. Rudin, Feature-oriented image enhancement using shock filters, SIAM J. Numer. Anal., 27 (1990), pp. 919-940.
    • (1990) SIAM J. Numer. Anal. , vol.27 , pp. 919-940
    • Osher, S.1    Rudin, L.I.2
  • 65
    • 84948132487 scopus 로고    scopus 로고
    • Scale-space properties of regularization methods
    • in Scale-Space Theories in Computer Vision, M. Nielsen, P. Johansen, O.F. Olsen, and J. Weickert, eds.; Springer-Verlag, Berlin
    • E. Radmoser, O. Scherzer, and J. Weickert, Scale-space properties of regularization methods, in Scale-Space Theories in Computer Vision, M. Nielsen, P. Johansen, O.F. Olsen, and J. Weickert, eds., Lecture Notes in Comput. Sci. 1682, Springer-Verlag, Berlin, 1999, pp. 211-222.
    • (1999) Lecture Notes in Comput. Sci. , vol.1682 , pp. 211-222
    • Radmoser, E.1    Scherzer, O.2    Weickert, J.3
  • 67
    • 0035836040 scopus 로고    scopus 로고
    • Thin-film flow of a viscoplastic material round a large horizontal stationary or rotating cylinder
    • A.B. Ross, S.K. Wilson, and B.R. Duffy, Thin-film flow of a viscoplastic material round a large horizontal stationary or rotating cylinder, J. Fluid Mech., 430 (2001), pp. 309-333.
    • (2001) J. Fluid Mech. , vol.430 , pp. 309-333
    • Ross, A.B.1    Wilson, S.K.2    Duffy, B.R.3
  • 68
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • L.I. Rudin, St. Osher, and E. Fatemi, Nonlinear total variation based noise removal algorithms, Phys. D, 60 (1992), pp. 259-268.
    • (1992) Phys. D , vol.60 , pp. 259-268
    • Rudin, L.I.1    Osher, St.2    Fatemi, E.3
  • 69
    • 0342514018 scopus 로고    scopus 로고
    • Stable evaluation of differential operators and linear and nonlinear multi-scale filtering
    • O. Scherzer, Stable evaluation of differential operators and linear and nonlinear multi-scale filtering, Electronic J. Differential Equations, 15 (1997), pp. 1-12.
    • (1997) Electronic J. Differential Equations , vol.15 , pp. 1-12
    • Scherzer, O.1
  • 70
    • 0034135395 scopus 로고    scopus 로고
    • Relations between regularization and diffusion filtering
    • O. Scherzer and J. Weickert, Relations between regularization and diffusion filtering, J. Math. Imag. Vision, 12 (2000), pp. 43-63.
    • (2000) J. Math. Imag. Vision , vol.12 , pp. 43-63
    • Scherzer, O.1    Weickert, J.2
  • 71
    • 0004115152 scopus 로고    scopus 로고
    • Exact solutions to the total variation regularization problem
    • Technical report CAM 96-41, University of California, Los Angeles
    • D. Strong and T.F. Chan, Exact Solutions to the Total Variation Regularization Problem, Technical report CAM 96-41, University of California, Los Angeles, 1996.
    • (1996)
    • Strong, D.1    Chan, T.F.2
  • 72
    • 0026943363 scopus 로고
    • Flow of viscoplastic fluids in eccentric annular geometries
    • P. Szabo and O. Hassager, Flow of viscoplastic fluids in eccentric annular geometries, J. Non-Newtonian Fluid Mech., 45 (1992), pp. 149-169.
    • (1992) J. Non-Newtonian Fluid Mech. , vol.45 , pp. 149-169
    • Szabo, P.1    Hassager, O.2
  • 73
    • 0242676282 scopus 로고
    • A multigrid method for total variation-based image denoising
    • K. Bowers and J. Lunds, eds., Birkhäuser, Boston, Cambridge, MA
    • C. Vogel, A multigrid method for total variation-based image denoising, in Computation and Control IV, Progr. Systems Control Theory 20, K. Bowers and J. Lunds, eds., Birkhäuser, Boston, Cambridge, MA, 1995.
    • (1995) Computation and Control IV, Progr. Systems Control Theory , vol.20
    • Vogel, C.1
  • 74
    • 0001556589 scopus 로고    scopus 로고
    • Iterative methods for total variation denoising
    • C.R. Vogel and M.E. Oman, Iterative methods for total variation denoising, SIAM J. Sci. Comput., 17 (1996), pp. 227-238.
    • (1996) SIAM J. Sci. Comput. , vol.17 , pp. 227-238
    • Vogel, C.R.1    Oman, M.E.2
  • 75
    • 0026051064 scopus 로고
    • The axial flow of a Bingham plastic in a narrow eccentric annulus
    • I.C. Walton and S.H. Bittleston, The axial flow of a Bingham plastic in a narrow eccentric annulus, J. Fluid Mech., 222 (1991), pp. 39-60.
    • (1991) J. Fluid Mech. , vol.222 , pp. 39-60
    • Walton, I.C.1    Bittleston, S.H.2
  • 77
    • 0027606845 scopus 로고
    • Squeezing flow of a Bingham material
    • S.D.R. Wilson, Squeezing flow of a Bingham material, J. Non-Newtonian Fluid Mech., 47 (1993), pp. 211-219.
    • (1993) J. Non-Newtonian Fluid Mech. , vol.47 , pp. 211-219
    • Wilson, S.D.R.1
  • 78
    • 0030211677 scopus 로고    scopus 로고
    • The channel entry problem for a yield-stress fluid
    • S.D.R. Wilson and A.J. Taylor, The channel entry problem for a yield-stress fluid, J. Non-Newtonian Fluid Mech., 65 (1996), pp. 165-176.
    • (1996) J. Non-Newtonian Fluid Mech. , vol.65 , pp. 165-176
    • Wilson, S.D.R.1    Taylor, A.J.2


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