메뉴 건너뛰기




Volumn 53, Issue 3, 2006, Pages 331-358

Weberized mumford-shah model with bose-einstein photon noise

Author keywords

; convergence; Bayesian; Bose Einstein distribution; Computational PDE; Free boundary; Light adaptivity; Mumford Shah segmentation; Noise; Retina; Variational; Weber's Law

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; GAUSSIAN NOISE (ELECTRONIC); LIGHTING; MATHEMATICAL MODELS; PHOTONS; SPURIOUS SIGNAL NOISE; THERMAL NOISE;

EID: 33646457532     PISSN: 00954616     EISSN: 14320606     Source Type: Journal    
DOI: 10.1007/s00245-005-0850-1     Document Type: Article
Times cited : (26)

References (47)
  • 1
    • 0004392136 scopus 로고    scopus 로고
    • A note on the theory of SBV functions
    • G. Alberti and C. Mantegazza. A note on the theory of SBV functions. Boll. Un. Mat. Ital. B. 7(11):375-382, 1997.
    • (1997) Boll. Un. Mat. Ital. B. , vol.7 , Issue.11 , pp. 375-382
    • Alberti, G.1    Mantegazza, C.2
  • 2
    • 0001400376 scopus 로고
    • A compactness theorem for a new class of functions of bounded variation
    • L. Ambrosio. A compactness theorem for a new class of functions of bounded variation. Boll. Un. Mat. Ital. B, 7(3):857-881, 1989.
    • (1989) Boll. Un. Mat. Ital. B , vol.7 , Issue.3 , pp. 857-881
    • Ambrosio, L.1
  • 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., 43:999-1036, 1990.
    • (1990) Comm. Pure Appl. Math. , vol.43 , pp. 999-1036
    • Ambrosio, L.1    Tortorelli, V.M.2
  • 4
    • 0000654840 scopus 로고
    • On the approximation of free discontinuity problems
    • L. Ambrosio and V. M. Tortorelli. On the approximation of free discontinuity problems. Boll. Un. Mat. Ital. B, 6:105-123, 1992.
    • (1992) Boll. Un. Mat. Ital. B , vol.6 , pp. 105-123
    • Ambrosio, L.1    Tortorelli, V.M.2
  • 6
    • 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., 29:182-193, 1992.
    • (1992) SIAM J. Numer. Anal. , vol.29 , pp. 182-193
    • Catté, F.1    Lions, P.-L.2    Morel, J.-M.3    Coll, T.4
  • 7
    • 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., 55(3):827-863, 1995.
    • (1995) SIAM J. Appl. Math. , vol.55 , Issue.3 , pp. 827-863
    • Chambolle, A.1
  • 8
    • 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., 33(2):261-288, 1999.
    • (1999) M2AN Math. Model. Numer. Anal. , vol.33 , Issue.2 , pp. 261-288
    • Chambolle, A.1
  • 9
    • 0031492191 scopus 로고    scopus 로고
    • Image recovery via Total Variational minimization and related problems
    • A. Chambolle and P. L. Lions. Image recovery via Total Variational minimization and related problems. Numer. Math., 76:167-188, 1997.
    • (1997) Numer. Math. , vol.76 , pp. 167-188
    • Chambolle, A.1    Lions, P.L.2
  • 10
    • 0037767145 scopus 로고    scopus 로고
    • Euler's elastica and curvature-based inpainting
    • T. F. Chan, S.-H. Kang, and J. Shen. Euler's elastica and curvature-based inpainting. SLAM J. Appl. Math., 63(2):564-592, 2002.
    • (2002) SLAM J. Appl. Math. , vol.63 , Issue.2 , pp. 564-592
    • Chan, T.F.1    Kang, S.-H.2    Shen, J.3
  • 11
    • 0036301838 scopus 로고    scopus 로고
    • Mathematical models for local nontexture inpaintings
    • T. F. Chan and J. Shen. Mathematical models for local nontexture inpaintings. SIAM J. Appl. Math., 62(3): 1019-1043, 2002.
    • (2002) SIAM J. Appl. Math. , vol.62 , Issue.3 , pp. 1019-1043
    • Chan, T.F.1    Shen, J.2
  • 12
    • 26244465007 scopus 로고    scopus 로고
    • On the role of the BV image model in image restoration
    • Recent Advances in Scientific Computing and Partial Differential Equations (editors: S. Y. Cheng, C.-W. Shu, and T. Tang), American Mathematical Society, Providence, RI
    • T. F. Chan and J. Shen. On the role of the BV image model in image restoration. In: Recent Advances in Scientific Computing and Partial Differential Equations (editors: S. Y. Cheng, C.-W. Shu, and T. Tang), pp. 25-41. Contemporary Mathematics, vol. 330. American Mathematical Society, Providence, RI, 2003.
    • (2003) Contemporary Mathematics , vol.330 , pp. 25-41
    • Chan, T.F.1    Shen, J.2
  • 14
    • 3042758075 scopus 로고    scopus 로고
    • Variational PDE models in image processing
    • T. F. Chan, J. Shen, and L. Vese. Variational PDE models in image processing. Notices Amer. Math. Soc., 50:14-26, 2003.
    • (2003) Notices Amer. Math. Soc. , vol.50 , pp. 14-26
    • Chan, T.F.1    Shen, J.2    Vese, L.3
  • 17
    • 0002874591 scopus 로고
    • A variational method in image segmentation: Existence and approximation results
    • G. Dal Maso, J.-M. Morel, and S. Solimini. A variational method in image segmentation: existence and approximation results. Acta. Math., 168:89-151, 1992.
    • (1992) Acta. Math. , vol.168 , pp. 89-151
    • Dal Maso, G.1    Morel, J.-M.2    Solimini, S.3
  • 18
    • 0036672270 scopus 로고    scopus 로고
    • Digital inpainting based on the Mumford-Shah-Euler image model
    • S. Esedoglu and J. Shen. Digital inpainting based on the Mumford-Shah-Euler image model. European J. Appl. Math., 13:353-370, 2002.
    • (2002) European J. Appl. Math. , vol.13 , pp. 353-370
    • Esedoglu, S.1    Shen, J.2
  • 19
    • 0025160434 scopus 로고
    • Calcium and the mechanism of light adaptation in vertebrate photoreceptors
    • G. Fain and H. R. Matthews. Calcium and the mechanism of light adaptation in vertebrate photoreceptors. Trends Neurosci., 13:378-384, 1990.
    • (1990) Trends Neurosci. , vol.13 , pp. 378-384
    • Fain, G.1    Matthews, H.R.2
  • 20
    • 0012415024 scopus 로고
    • Über ein wichtiges psychophysiches grundgesetz und dessen beziehung zur schäzung der sterngrössen
    • G. T. Fechner. Über ein wichtiges psychophysiches Grundgesetz und dessen Beziehung zur Schäzung der Sterngrössen. Abh. Ges. Wissensch. Math.-Phys., K1, 4, 1858.
    • (1858) Abh. Ges. Wissensch. Math.-phys. , vol.K1 , pp. 4
    • Fechner, G.T.1
  • 21
    • 0001008594 scopus 로고
    • An integral formula for total gradient variation
    • W. H. Fleming and R. Rishel. An integral formula for total gradient variation. Arch. Math., 11:218-222, 1960.
    • (1960) Arch. Math. , vol.11 , pp. 218-222
    • Fleming, W.H.1    Rishel, R.2
  • 22
    • 0021518209 scopus 로고
    • Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images
    • S. Geman and D. Geman. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Machine Intell., 6:721-741, 1984.
    • (1984) IEEE Trans. Pattern Anal. Machine Intell. , vol.6 , pp. 721-741
    • Geman, S.1    Geman, D.2
  • 24
    • 0000532812 scopus 로고
    • Existence theorem for a minimization problem with free discontinuity set
    • E. De Giorgi, M. Carriero, and A. Leaci. existence theorem for a minimization problem with free discontinuity set. Arch. Ration. Mech. Anal., 108:195-218, 1989.
    • (1989) Arch. Ration. Mech. Anal. , vol.108 , pp. 195-218
    • De Giorgi, E.1    Carriero, M.2    Leaci, A.3
  • 29
    • 0004148844 scopus 로고    scopus 로고
    • American Mathematical Society, Providence, RI
    • E. H. Lieb and M. Loss. Analysis, 2nd edn. American Mathematical Society, Providence, RI, 2001.
    • (2001) Analysis, 2nd Edn.
    • Lieb, E.H.1    Loss, M.2
  • 31
    • 0025307013 scopus 로고
    • Light response of vertebrate photoreceptors
    • P. A. McNaughton. Light response of vertebrate photoreceptors. Physiological Rev., 70:847-883, 1990.
    • (1990) Physiological Rev. , vol.70 , pp. 847-883
    • McNaughton, P.A.1
  • 34
    • 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., 42:577-685, 1989.
    • (1989) Comm. Pure Appl. Math. , vol.42 , pp. 577-685
    • Mumford, D.1    Shah, J.2
  • 35
    • 0018333443 scopus 로고
    • The effects of background illumination on the photoresponses of red and green cones
    • R. A. Norman and I. Perlman. The effects of background illumination on the photoresponses of red and green cones. J. Physiology. 286:491-507, 1979.
    • (1979) J. Physiology , vol.286 , pp. 491-507
    • Norman, R.A.1    Perlman, I.2
  • 36
    • 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): 12-49, 1988.
    • (1988) J. Comput. Phys. , vol.79 , Issue.12 , pp. 12-49
    • Osher, S.1    Sethian, J.A.2
  • 37
    • 0242705996 scopus 로고    scopus 로고
    • The mathematics of learning: Dealing with data
    • T. Poggio and S. Smale. The mathematics of learning: dealing with data. Notices Amer. Math. Soc., 50(5):537-544, 2003.
    • (2003) Notices Amer. Math. Soc. , vol.50 , Issue.5 , pp. 537-544
    • Poggio, T.1    Smale, S.2
  • 38
    • 0025572721 scopus 로고
    • Cyclic GMP and calcium: Messengers of excitation and adaptation in vertebrate photoreceptors
    • E. N. Pugh and T. D. Lamb. Cyclic GMP and calcium: messengers of excitation and adaptation in vertebrate photoreceptors. Vision Res., 30:1923-1948, 1990.
    • (1990) Vision Res. , vol.30 , pp. 1923-1948
    • Pugh, E.N.1    Lamb, T.D.2
  • 39
    • 84996774871 scopus 로고
    • Total variation based image restoration with free local constraints
    • L. Rudin and S. Osher. Total variation based image restoration with free local constraints. Proc. 1st IEEE ICIP, vol. 1, pp. 31-35, 1994.
    • (1994) Proc. 1st IEEE ICIP , vol.1 , pp. 31-35
    • Rudin, L.1    Osher, S.2
  • 40
    • 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, 60:259-268, 1992.
    • (1992) Phys. D , vol.60 , pp. 259-268
    • Rudin, L.1    Osher, S.2    Fatemi, E.3
  • 41
    • 48749137111 scopus 로고
    • Visual adaptation and retinal gain controls
    • (Editors: N. Osborne and G. Chader), Pergamon Press, London
    • R. M. Shapley and C. Enroth-Cugell. Visual adaptation and retinal gain controls. In: Progress in Retinal Research (Editors: N. Osborne and G. Chader), pp. 263-346. Pergamon Press, London, 1984.
    • (1984) Progress in Retinal Research , pp. 263-346
    • Shapley, R.M.1    Enroth-Cugell, C.2
  • 42
    • 0344077277 scopus 로고    scopus 로고
    • Inpainting and the fundamental problem of image processing
    • J. Shen. Inpainting and the fundamental problem of image processing. SIAM News, 36, 2003.
    • (2003) SIAM News , vol.36
    • Shen, J.1
  • 43
    • 0037297047 scopus 로고    scopus 로고
    • On the foundations of vision modeling, I. Weber's law and Weberized TV (total variation) restoration
    • J. Shen. On the foundations of vision modeling, I. Weber's law and Weberized TV (total variation) restoration. Phys. D, 175:241-251, 2003.
    • (2003) Phys. D , vol.175 , pp. 241-251
    • Shen, J.1
  • 44
    • 0021215492 scopus 로고
    • Retinal light adaptation - Evidence for a feedback mechanism
    • D. Tranchina, J. Gordon, and R. Shapley. Retinal light adaptation - evidence for a feedback mechanism. Nature, 310:314-316, 1984.
    • (1984) Nature , vol.310 , pp. 314-316
    • Tranchina, D.1    Gordon, J.2    Shapley, R.3
  • 45
    • 0024184756 scopus 로고
    • Light adaptation in the turtle retina: Embedding a parametric family of linear models in a single nonlinear model
    • D. Tranchina and C. S. Peskin. Light adaptation in the turtle retina: embedding a parametric family of linear models in a single nonlinear model. Vis. Neurosci., 1:339-348, 1988.
    • (1988) Vis. Neurosci. , vol.1 , pp. 339-348
    • Tranchina, D.1    Peskin, C.S.2
  • 46
    • 0035425439 scopus 로고    scopus 로고
    • Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation and magnification
    • A. Tsai, Jr., A. Yezzi, and A. S. Willsky. Curve evolution implementation of the Mumford-Shah functional for image segmentation, denoising, interpolation and magnification. IEEE Trans. Image Process., 10(8):1169-1186, 2001.
    • (2001) IEEE Trans. Image Process. , vol.10 , Issue.8 , pp. 1169-1186
    • Tsai Jr., A.1    Yezzi, A.2    Willsky, A.S.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.