메뉴 건너뛰기




Volumn 66, Issue 5, 2006, Pages 1632-1648

Algorithms for finding global minimizers of image segmentation and denoising models

Author keywords

Denoising; Segmentation

Indexed keywords

CONVEX MINIMIZATION PROBLEMS; DENOISING; DENOISING MODELS; NONCONVEX OPTIMIZATION;

EID: 33750153530     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/040615286     Document Type: Article
Times cited : (960)

References (26)
  • 1
    • 0026883172 scopus 로고
    • Digital filters as absolute norm regularizes
    • S. ALLINEY, Digital filters as absolute norm regularizes, IEEE Trans. Signal Process., 40 (1992), pp. 1548-1562.
    • (1992) IEEE Trans. Signal Process. , vol.40 , pp. 1548-1562
    • Alliney, S.1
  • 2
    • 0030169670 scopus 로고    scopus 로고
    • Recursive median filters of increasing order: A variational approach
    • S. ALLINEY, Recursive median filters of increasing order: A variational approach, IEEE Trans. Signal Process., 44 (1996), pp. 1346-1354.
    • (1996) IEEE Trans. Signal Process. , vol.44 , pp. 1346-1354
    • Alliney, S.1
  • 3
    • 0031124308 scopus 로고    scopus 로고
    • A property of the minimum vectors of a regularizing functional defined by means of the absolute norm
    • S. ALLINEY, A property of the minimum vectors of a regularizing functional defined by means of the absolute norm, IEEE Trans. Signal Process., 45 (1997), pp. 913-917.
    • (1997) IEEE Trans. Signal Process. , vol.45 , pp. 913-917
    • Alliney, S.1
  • 4
    • 34748925841 scopus 로고
    • Approximation of functional depending on jumps by elliptic functional via Gamma convergence
    • L. AMBROSIO AND V. M. TORTORELLI, Approximation of functional depending on jumps by elliptic functional via Gamma convergence, Comm. Pure Appl. Math., 43 (1990), pp. 999-1036.
    • (1990) Comm. Pure Appl. Math. , vol.43 , pp. 999-1036
    • Ambrosio, L.1    Tortorelli, V.M.2
  • 5
    • 84965008631 scopus 로고
    • A morphological scheme for mean curvature motion and applications to anisotropic diffusion and motion of level sets
    • [5] F. CATTÉ, F. DIBOS, AND G. KOEPFLER, A morphological scheme for mean curvature motion and applications to anisotropic diffusion and motion of level sets, SIAM J. Numer. Anal., 32 (1995), pp. 1895-1909.
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 1895-1909
    • Catté, F.1    Dibos, F.2    Koepfler, G.3
  • 9
    • 0042687843 scopus 로고    scopus 로고
    • Global total variation minimization
    • F. DIBOS AND G. KOEPFLER, Global total variation minimization, SIAM J. Numer. Anal., 37 (2000), pp. 646-664.
    • (2000) SIAM J. Numer. Anal. , vol.37 , pp. 646-664
    • Dibos, F.1    Koepfler, G.2
  • 10
    • 0003346795 scopus 로고
    • Measure theory and fine properties of functions
    • CRC Press, Boca Raton, FL
    • L. C. EVANS AND R. F. GARIEPY, Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1992.
    • (1992) Studies in Advanced Mathematics
    • Evans, L.C.1    Gariepy, R.F.2
  • 11
    • 0001008594 scopus 로고
    • An integral formula for total gradient variation
    • W. FLEMING, W. RISHEL, AND R. RISHEL, An integral formula for total gradient variation, Arch. Math., 11 (1960), pp. 218-222.
    • (1960) Arch. Math. , vol.11 , pp. 218-222
    • Fleming, W.1    Rishel, W.2    Rishel, R.3
  • 12
    • 0003343498 scopus 로고
    • Minimal surfaces and functions of bounded variation
    • Birkhäuser Verlag, Basel
    • E. GIUSTI, Minimal Surfaces and Functions of Bounded Variation, Monogr. Math. 80, Birkhäuser Verlag, Basel, 1984.
    • (1984) Monogr. Math. , vol.80
    • Giusti, E.1
  • 13
    • 0003316862 scopus 로고
    • Convex analysis and minimization algorithms. I. Fundamentals
    • Springer-Verlag, New York
    • J.-B. HIRIART-URRUTY AND C. LEMARECHAL, Convex Analysis and Minimization Algorithms. I. Fundamentals, Grundlehren Math. Wiss. 305, Springer-Verlag, New York, 1993.
    • (1993) Grundlehren Math. Wiss. , vol.305
    • Hiriart-Urruty, J.-B.1    Lemarechal, C.2
  • 14
    • 0003316862 scopus 로고
    • Convex analysis and minimization algorithms. II. Advanced theory and bundle methods
    • Springer-Verlag, New York
    • J.-B. HIRIART-URRUTY AND C. LEMARECHAL, Convex Analysis and Minimization Algorithms. II. Advanced Theory and Bundle Methods, Grundlehren Math. Wiss. 306, Springer-Verlag, New York, 1993.
    • (1993) Grundlehren Math. Wiss. , vol.306
    • Hiriart-Urruty, J.-B.1    Lemarechal, C.2
  • 16
    • 0000359194 scopus 로고
    • Un esempio di Gamma-convergenza
    • L. MODICA AND S. MORTOLA, Un esempio di Gamma-convergenza, Boll. Un. Mat. Ital. B, 14 (1977), pp. 285-299.
    • (1977) Boll. Un. Mat. Ital. B , vol.14 , pp. 285-299
    • Modica, L.1    Mortola, S.2
  • 17
    • 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., 42 (1989), pp. 577-685.
    • (1989) Comm. Pure Appl. Math. , vol.42 , pp. 577-685
    • Mumford, D.1    Shah, J.2
  • 18
    • 1242284980 scopus 로고    scopus 로고
    • A variational approach to remove outliers and impulse noise
    • M. NIKOLOVA, A variational approach to remove outliers and impulse noise, J. Math. maging and Vision, 20 (2004), pp. 99-120.
    • (2004) J. Math. Maging and Vision , vol.20 , pp. 99-120
    • Nikolova, M.1
  • 19
    • 0038042413 scopus 로고    scopus 로고
    • Minimizers of cost-functions involving nonsmooth data-fidelity terms. Application to the processing of outliers
    • M. NIKOLOVA, Minimizers of cost-functions involving nonsmooth data-fidelity terms. Application to the processing of outliers, SIAM J. Numer. Anal., 40 (2002), pp. 965-994.
    • (2002) SIAM J. Numer. Anal. , vol.40 , pp. 965-994
    • Nikolova, M.1
  • 20
    • 3042841518 scopus 로고    scopus 로고
    • Level set methods and dynamic implicit surfaces
    • Springer-Verlag, New York
    • S. OSHER AND R. FEDKIW, Level Set Methods and Dynamic Implicit Surfaces, Appl. Math. Sci., 153, Springer-Verlag, New York, 2003.
    • (2003) Appl. Math. Sci. , vol.153
    • Osher, S.1    Fedkiw, R.2
  • 21
    • 44749084234 scopus 로고
    • Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
    • S. OSHER AND J. SETHIAN, Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79 (1988), pp. 12-49.
    • (1988) J. Comput. Phys. , vol.79 , pp. 12-49
    • Osher, S.1    Sethian, J.2
  • 22
    • 44049111982 scopus 로고
    • Nonlinear total variation based noise removal algorithms
    • L. RUDIN, S. 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.1    Osher, S.2    Fatemi, E.3
  • 23
    • 4243607361 scopus 로고
    • ∞ approximation of vector fields in the plane
    • Nonlinear Partial Differential Equations in Applied Science (Tokyo, 1982), North-Holland, Amsterdam
    • ∞ approximation of vector fields in the plane, in Nonlinear Partial Differential Equations in Applied Science (Tokyo, 1982), North-Holland Math. Stud. 81, North-Holland, Amsterdam, 1983, pp. 273-288.
    • (1983) North-Holland Math. Stud. , vol.81 , pp. 273-288
    • Strang, G.1
  • 24
    • 0020764041 scopus 로고
    • Maximal flow through a domain
    • G. STRANG, Maximal flow through a domain, Math. Programming, 26 (1983), pp. 123-143.
    • (1983) Math. Programming , vol.26 , pp. 123-143
    • Strang, G.1
  • 25
    • 0346316863 scopus 로고    scopus 로고
    • Edge-preserving and scale-dependent properties of total variation regularization
    • D. STRONG AND T. F. CHAN, Edge-preserving and scale-dependent properties of total variation regularization, Inverse Problems, 19 (2003), pp. S165-S187.
    • (2003) Inverse Problems , vol.19
    • Strong, D.1    Chan, T.F.2
  • 26
    • 0036891794 scopus 로고    scopus 로고
    • A multiphase level set framework for image segmentation using the Mumford and Shah model
    • L. A. VESE AND T. F. CHAN, A multiphase level set framework for image segmentation using the Mumford and Shah model, Internat. J. Comput. Vision, 50 (2002), pp. 271-293.
    • (2002) Internat. J. Comput. Vision , vol.50 , pp. 271-293
    • Vese, L.A.1    Chan, T.F.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.