An Edge-Preserving Multigrid-Like Technique for Image Denoising

  • Carolina Toledo Ferraz
  • Luis Gustavo Nonato
  • José Alberto Cuminato
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4141)


Techniques based on the Well-Balanced Flow Equation have been employed as efficient tools for edge preserving noise removal. Although effective, this technique demands high computational effort, rendering it not practical in several applications. This work aims at proposing a multigrid like technique for speeding up the solution of the Well-Balanced Flow equation. In fact, the diffusion equation is solved in a coarse grid and a coarse-to-fine error correction is applied in order to generate the desired solution. The transfer between coarser and finer grids is made by the Mitchell-Filter, a well known interpolation scheme that is designed for preserving edges. Numerical results are compared quantitative and qualitatively with other approaches, showing that our method produces similar image quality with much smaller computational time.


Edge Detection Coarse Grid Noisy Image Multigrid Method Image Denoising 
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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  1. 1.
    Acton, S.T.: Multigrid anisotropic diffusion. IEEE Transaction on Image Processing 7(3), 280–291 (1998)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Alvarez, L., Lions, P., Morel, J.: Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29(3), 182–193 (1992)CrossRefMathSciNetGoogle Scholar
  3. 3.
    Barcelos, C.A.Z., Boaventura, M., Castro Silva Jr., E.: Edge detection and noise removal by use of a partial differential equation with automatic selection of parameters. Computational and Applied Mathematics 24(1), 131–150 (2005)MathSciNetGoogle Scholar
  4. 4.
    Barcelos, C.A.Z., Boaventura, M., Castro Silva Jr., E.: A well-balanced flow equation for noise removal and edge detection. IEEE Transaction on Image Processing 12(7), 751–763 (2003)CrossRefGoogle Scholar
  5. 5.
    Briggs, W.L.: A Multigrid Tutorial. Society for Industrial and Applied Mathematics (1987)Google Scholar
  6. 6.
    Duff, T.: Splines in Animation and Modeling. State of the Art in Image Synthesis. In: SIGGRAPH 1986 Course Notes (1986)Google Scholar
  7. 7.
    Hou, H.S., Andrews, H.C.: Cubic splines for image interpolation and digital filtering. IEEE Trans. Acoust., Speech, Signal Processing ASSP-26, 508–517 (1978)Google Scholar
  8. 8.
    Keys, R.: Cubic convolution interpolation for digital image processing. IEEE Trans. Acoust., Speech, Signal Processing ASSP-29, 1153–1160 (1981)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Koenderink, J.: The structure of images. Biol. Cybernet 50, 363–370 (1984)CrossRefMathSciNetzbMATHGoogle Scholar
  10. 10.
    Marr, D., Hildreth, E.: Theory of edge detection. Proc. Roy. Soc. 207, 187–217 (1980)CrossRefGoogle Scholar
  11. 11.
    McCormick, S.F. (ed.): Multigrid methods. Frontiers in Applied Mathematics, vol. 3. Society for Industrial and Applied Mathematics (SIAM), Philadelphia (1987)zbMATHGoogle Scholar
  12. 12.
    Mitchell, D., Netravali, A.: Reconstruction filters in computer graphics. Computer Graphics 22(4), 221–228 (1988)CrossRefGoogle Scholar
  13. 13.
    Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Transaction on Pattern Analysis and Machine Intelligence 12(7), 629–639 (1990)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Carolina Toledo Ferraz
    • 1
  • Luis Gustavo Nonato
    • 1
  • José Alberto Cuminato
    • 1
  1. 1.São Paulo University – ICMCSão CarlosBrazil

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