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All issues Volume 30 (2024) ESAIM: COCV, 30 (2024) 44 References
Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 44
Number of page(s) 45
DOI https://doi.org/10.1051/cocv/2024035
Published online 24 May 2024
  1. P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion. Technical report, EECS Department, University of California, Berkeley (1988). [Google Scholar]
  2. 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) 182–193. [CrossRef] [MathSciNet] [Google Scholar]
  3. S. Kichenassamy, The Perona–Malik paradox. SIAM J. Appl. Math. 57 (1997) 1328–1342. [CrossRef] [MathSciNet] [Google Scholar]
  4. E. De Giorgi, Conjectures Concerning Some Evolution Problems. Vol. 81. (1996) 255–268. [Google Scholar]
  5. S. Esedoglu, An analysis of the Perona–Malik scheme. Commun. Pure Appl. Math. 54 (2001) 1442–1487. [CrossRef] [Google Scholar]
  6. H. Amann, Time-delayed Perona–Malik type problems. Acta Math. Univ. Comenian. (N.S.) 76 (2007) 15–38. [MathSciNet] [Google Scholar]
  7. P. Guidotti, A new nonlocal nonlinear diffusion of image processing. J. Differ. Equ. 246 (2009) 4731–4742. [CrossRef] [Google Scholar]
  8. F. Smarrazzo and A. Tesei, Degenerate regularization of forward-backward parabolic equations: the regularized problem Arch. Ration. Mech. Anal. 204 (2012) 85–139. [CrossRef] [MathSciNet] [Google Scholar]
  9. M. Gobbino and N. Picenni, A quantitative variational analysis of the staircasing phenomenon for a second order regularization of the Perona–Malik functional. Trans. Amer. Math. Soc. 376 (2023) 5307–5375. [CrossRef] [MathSciNet] [Google Scholar]
  10. L. Ambrosio, N. Fusco and D. Pallara, Functions of Bounded Variation and Free Discontinuity Problems. Oxford Mathematical Monographs (2000). [Google Scholar]
  11. G. Alberti and S. Müller, A new approach to variational problems with multiple scales. Commun. Pure Appl. Math. 54 (2001) 761–825. [CrossRef] [Google Scholar]
  12. M. Ghisi and M. Gobbino, Gradient estimates for the Perona–Malik equation. Math. Ann. 337 (2007) 557–590. [CrossRef] [MathSciNet] [Google Scholar]
  13. M. Morini and M. Negri, Mumford–Shah functional as Γ-limit of discrete Perona–Malik energies. Math. Models Methods Appl. Sci. 13 (2003) 785–805. [CrossRef] [MathSciNet] [Google Scholar]
  14. G. Bellettini, M. Novaga, M. Paolini and C. Tornese, Convergence of discrete schemes for the Perona–Malik equation. J. Differ. Equ. 245 (2008) 892–924. [CrossRef] [Google Scholar]
  15. G. Bellettini, M. Novaga, M. Paolini and C. Tornese, Classification of equilibria and Γ-convergence for the discrete Perona–Malik functional. Calcolo 46 (2009) 221–243. [CrossRef] [MathSciNet] [Google Scholar]
  16. G. Bellettini, M. Novaga and M. Paolini, Convergence for long-times of a semidiscrete Perona–Malik equation in one dimension. Math. Models Methods Appl. Sci. 21 (2011) 241–265. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Colombo and M. Gobbino, Slow time behavior of the semidiscrete Perona–Malik scheme in one dimension. SIAM J. Math. Anal. 43 (2011) 2564–2600. [CrossRef] [MathSciNet] [Google Scholar]
  18. A. Braides and V. Vallocchia, Static, quasistatic and dynamic analysis for scaled Perona–Malik functionals. Acta Appl. Math. 156 (2018) 79–107. [CrossRef] [MathSciNet] [Google Scholar]
  19. M. Gobbino and N. Picenni, Monotonicity properties of limits of solutions to the semidiscrete scheme for a class of Perona–Malik type equations. SIAM J. Math. Anal. 56 (2024) 2034–2062. [CrossRef] [MathSciNet] [Google Scholar]
  20. M. Gobbino and M.G. Mora, Finite-difference approximation of free-discontinuity problems. Proc. Roy. Soc. Edinburgh Sect. A 131 (2001) 567–595. [CrossRef] [MathSciNet] [Google Scholar]
  21. R. Alicandro, A. Braides and M.S. Gelli, Free-discontinuity problems generated by singular perturbation. Proc. Roy. Soc. Edinburgh Sect. A 128 (1998) 1115–1129. [CrossRef] [MathSciNet] [Google Scholar]
  22. G. Bellettini and G. Fusco, The Γ-limit and the related gradient flow for singular perturbation functionals of Perona-Malik type. Trans. Amer. Math. Soc. 360 (2008) 4929–4987. [CrossRef] [MathSciNet] [Google Scholar]

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