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. [CrossRef] [MathSciNet]
  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
  3. J. Canny, A computational approach to edge detection. IEEE Trans. Pattern Anal. Mach. Intell. 8 (1986) 679–698. [CrossRef] [PubMed]
  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]
  5. P.G. Ciarlet, Introduction à l'analyse numérique matricielle et à l'optimisation. Collection Mathématiques Appliquées pour la Maîtrise. Masson, Paris (1982).
  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]
  7. S. Esedoḡlu, An analysis of the Perona-Malik scheme. Comm. Pure Appl. Math. 54 (2001) 1442–1487. [CrossRef] [MathSciNet]
  8. Y. Giga and S. Goto, Motion of hypersurfaces and geometric equations. J. Math. Soc. Japan 44 (1992) 99–111. [CrossRef] [MathSciNet]
  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.
  10. E. Heinz, An elementary analytic theory of the degree of mapping in n-dimensional space. J. Math. Mech. 8 (1959) 231–247. [MathSciNet]
  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.
  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).
  13. B. Kawohl and N. Kutev, Maximum and comparison principle for one-dimensional anisotropic diffusion. Math. Ann. 311 (1998) 107–123. [CrossRef] [MathSciNet]
  14. S. Kichenassamy, The Perona-Malik paradox. SIAM J. Appl. Math. 57 (1997) 1328–1342. [CrossRef] [MathSciNet]
  15. D. Marr and E. Hildreth, Theory of edge detection. Proc. Roy. Soc. London B. 207 (1980) 187–217. [CrossRef]
  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]
  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]
  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]
  19. R.T. Whitaker and S.M. Pizer, A multi-scale approach to nonuniform diffusion. CVGIP: Image Underst. 57 (1993) 99–110. [CrossRef]
  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]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you