Free Access
Volume 39, Number 2, March-April 2005
Page(s) 231 - 251
Published online 15 April 2005
  1. L. Alvarez, F. Guichard, P.-L. Lions and J.-M. Morel, Axioms and fundamental equations of image processing. Arch. Rational Mech. Anal. 123 (1993) 199–257. [Google Scholar]
  2. A. Belahmidi, Équations aux dérivées partielles appliquées à la restauration et à l'agrandissement des images. Ph.D. thesis, CEREMADE, Université de Paris-Dauphine, Paris (2003). Available at [Google Scholar]
  3. J. Canny, A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8 (1986) 679–698. [Google Scholar]
  4. 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]
  5. P.G. Ciarlet, Introduction à l'analyse numérique matricielle et à l'optimisation. Collection Mathématiques Appliquées pour la Maîtrise. Masson, Paris (1982). [Google Scholar]
  6. G.H. Cottet and M. El-Ayyadi, A volterra type model for image processing. IEEE Trans. Image Process. 7 (1998) 292–303. [CrossRef] [PubMed] [Google Scholar]
  7. S. Esedoḡlu, An analysis of the Perona-Malik scheme. Comm. Pure Appl. Math. 54 (2001) 1442–1487. [CrossRef] [MathSciNet] [Google Scholar]
  8. Y. Giga and S. Goto, Motion of hypersurfaces and geometric equations. J. Math. Soc. Japan 44 (1992) 99–111. [CrossRef] [MathSciNet] [Google Scholar]
  9. D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order. Classics in Mathematics. Springer-Verlag, Berlin (2001). Reprint of the 1998 edition. [Google Scholar]
  10. E. Heinz, An elementary analytic theory of the degree of mapping in n-dimensional space. J. Math. Mech. 8 (1959) 231–247. [MathSciNet] [Google Scholar]
  11. K. Höllig and J.A. Nohel, A diffusion equation with a nonmonotone constitutive function, in Systems of nonlinear partial differential equations (Oxford, 1982), Reidel, Dordrecht. NATO Adv. Sci. Inst. Ser. C: Math. Phys. Sci. 111 (1983) 409–422. [Google Scholar]
  12. O. Kavian, Introduction à la théorie des points critiques et applications aux problèmes elliptiques, volume 13 of Mathématiques & Applications (Berlin). Springer-Verlag, Paris (1993). [Google Scholar]
  13. B. Kawohl and N. Kutev, Maximum and comparison principle for one-dimensional anisotropic diffusion. Math. Ann. 311 (1998) 107–123. [CrossRef] [MathSciNet] [Google Scholar]
  14. S. Kichenassamy, The Perona-Malik paradox. SIAM J. Appl. Math. 57 (1997) 1328–1342. [CrossRef] [MathSciNet] [Google Scholar]
  15. D. Marr and E. Hildreth, Theory of edge detection. Proc. Roy. Soc. London B. 207 (1980) 187–217. [Google Scholar]
  16. N.G. Meyers, An Lpe-estimate for the gradient of solutions of second order elliptic divergence equations. Ann. Scuola Norm. Sup. Pisa 17 (1963) 189–206. [MathSciNet] [Google Scholar]
  17. M. Nitzberg and T. Shiota, Nonlinear image filtering with edge and corner enhancement. IEEE Trans. Pattern Anal. Mach. Intell. 14 (1992) 826–833. [CrossRef] [Google Scholar]
  18. P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12 (1990) 629–639. [CrossRef] [Google Scholar]
  19. R.T. Whitaker and S.M. Pizer, A multi-scale approach to nonuniform diffusion. CVGIP: Image Underst. 57 (1993) 99–110. [CrossRef] [Google Scholar]
  20. Y. You, W. Xu, A. Tannenbaum and M. Kaveh, Behavioral analysis of anisotropic diffusion in image processing. IEEE Trans. Image Process. 5 (1996) 1539–1553. [CrossRef] [PubMed] [Google Scholar]

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