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A Note on Two Classical Shock Filters and Their Asymptotics

  • Frédéric Guichard
  • Jean-Michel Morel
Conference paper
Part of the Lecture Notes in Computer Science 2106 book series (LNCS, volume 2106)

Abstract

We establish in 2D, the PDE associated with a classical debluring ?lter, the Kramer operator and compare it with another classical shock ?lter.

Keywords

Heat Equation Edge Detector Monotone Operator Image Enhancement Canny Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    L. Alvarez, F. Guichard, P.L. Lions, and J.M. Morel. Axioms and fundamental equations of image processing. Archive for Rational Mechanics and Analysis., 16(9):200–257, 1993.MathSciNetGoogle Scholar
  2. 2.
    F. Cao. Partial differential equation and mathemetical morphology. Journal de Mathematiques Pures et Appliquees, 77(9):909–941, 1998.MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    F. Guichard and J.-M. Morel. Image Iterative Smoothing and PDE’s. downloadable manuscript: please write email to fguichard@poseidon.fr, 2000.Google Scholar
  4. 4.
    H.P. Kramer and J.B. Bruckner. Iterations of a non-linear transformation for enhancement of digital images. Pattern Recognition, 7, 1975.Google Scholar
  5. 5.
    M. Lindenbaum, M. Fischer, and A.M. Bruckstein. On gabor contribution to image-enhancement. PR, 27(1):1–8, January 1994.CrossRefGoogle Scholar
  6. 6.
    P. Maragos. Slope transfroms: Theory and application to nonlinear signal processing. IEEE Transactions on signal processing, 43:864–877, 1995.CrossRefGoogle Scholar
  7. 7.
    P. Maragos and R.W. Schafer. Morphological filters. part II: Their relations to median, order-statistic, and stack filters. ASSP, 35:1170–1184, 1987.MathSciNetCrossRefGoogle Scholar
  8. 8.
    G. Matheron. Random Sets and Integral Geometry. John Wiley, N.Y., 1975.zbMATHGoogle Scholar
  9. 9.
    F. Meyer and J. Serra. Contrasts and activity lattice. Signal Processing, 16:303–317, 1989.MathSciNetCrossRefGoogle Scholar
  10. 10.
    Leonid I. Rudin, Stanley Osher, and Emad Fatemi. Nonlinear total variation based noise removal algorithms. Physica D 60,No.1-4, 259–268. [ISSN 0167-2789], 1992.zbMATHCrossRefGoogle Scholar
  11. 11.
    Osher, Stanley and Leonid I. Rudin. Feature-oriented image enhancement using shock filters. SIAM J. Numer. Anal. 27,No.4, 919–940. [ISSN 0036-1429], 1990.zbMATHCrossRefGoogle Scholar
  12. 12.
    J.G.M Schavemaker, M.J.T Reinders, J.J. Gerbrands, and E. Backer. Image sharpening by morphological filtering. submitted to Pattern Recognition, 1999.Google Scholar
  13. 13.
    J. Serra. Image Analysis and Mathematical Morphology. Academic Press, 1982.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Frédéric Guichard
    • 1
  • Jean-Michel Morel
    • 2
  1. 1.Poseidon-TechnologiesBoulogne-BillancourtFrance
  2. 2.CMLA, ENSCac hanCachan cedexFrance

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