Morphological Sharpening and Denoising Using a Novel Shock Filter Model

  • Cosmin Ludusan
  • Olivier Lavialle
  • Romulus Terebes
  • Monica Borda
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6134)


We present a new approach based on Partial Differential Equations (PDEs) for image enhancement in generalized “Gaussian Blur (GB) + Additive White Gaussian Noise (AWGN)” scenarios. The inability of the classic shock filter to successfully process noisy images is overcome by the introduction of a complex shock filter framework. Furthermore, the proposed method allows for better control and anisotropic, contour-driven, shock filtering via its control functions f 1 and f 2. The main advantages of our method consist in the ability of successfully enhancing GB+AWGN images while preserving a stable-convergent time behavior.


PDEs shock filters image denoising image sharpening image enhancement 


  1. 1.
    Osher, S., Rudin, L.: Feature-oriented Image Enhancement Using Shock Filters. SIAM J. on Num. Anal. 27, 919–940 (1990)zbMATHCrossRefGoogle Scholar
  2. 2.
    Alvarez, L., Mazorra, L.: Signal and Image restoration Using Shock Filters and Anisotropic Diffusion. SIAM J. on Num. Anal. 31, 590–605 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Kornprobst, P., Deriche, R., Aubert, G.: Image Coupling, Restoration and Enhancement via PDEs. In: International Conference on Image Processing (ICIP) Proceedings, vol. 2, pp. 458–461 (1997)Google Scholar
  4. 4.
    Remaki, L., Cheriet, M.: Numerical Schemes of Shock Filter Models for Image Enhancement and Restoration. J. of Math. Imag. And Vis. 18, 129–143 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Gilboa, G., Sochen, N.A., Zeevi, Y.Y.: Regularized Shock Filters and Complex Diffusion. In: Heyden, A., Sparr, G., Nielsen, M., Johansen, P. (eds.) ECCV 2002. LNCS, vol. 2350, pp. 399–413. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Gilboa, G., Zeevi, Y.Y., Sochen, N.A.: Complex Diffusion Processes for Image Filtering. In: Kerckhove, M. (ed.) Scale-Space 2001. LNCS, vol. 2106, pp. 299–307. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  7. 7.
    Gilboa, G.: Super-resolution Algorithms Based on Inverse Diffusion-type Processes. PhD Thesis, Technion-Israel Institute of Technology, Haifa (2004)Google Scholar
  8. 8.
    Weickert, J.: Coherence-Enhancing Shock Filters. In: Michaelis, B., Krell, G. (eds.) DAGM 2003. LNCS, vol. 2781, pp. 1–8. Springer, Heidelberg (2003)Google Scholar
  9. 9.
    Tschumperle, D., Deriche, R.: Constrained and Unconstrained PDEs for Vector Image Restoration. In: 12th Scandinavian Conference on Image Analysis, Norway, pp. 153–160 (2001)Google Scholar
  10. 10.
    Buades, A., Coll, B., Morel, J.M.: Image Enhancement by Non-local Reverse Heat Equation (Preprint CMLA 2006-22) (2006)Google Scholar
  11. 11.
    Buades, A., Coll, B., Morel, J.M.: The Staircasing Effect in Neighborhood Filters and its Solution. IEEE Transactions on Image Processing 15(6), 1499–1505 (2006)CrossRefGoogle Scholar
  12. 12.
    Rudin, L.: Images, Numerical Analysis of Singularities and Shock Filters. PhD Thesis, California Institute of Technology, Pasadena CA (1987)Google Scholar
  13. 13.
    Barash, D.: One-step Deblurring and Denoising Color Images Using Partial Differential Equations. HP Laboratories, Israel (2001)Google Scholar
  14. 14.
    Welk, M., Theis, D., Borx, T., Weickert, J.: PDE-based Deconvolution with Forward-Backward Diffusivities and Diffusion Tensors. In: Kimmel, R., Sochen, N.A., Weickert, J. (eds.) Scale-Space 2005. LNCS, vol. 3459, pp. 585–597. Springer, Heidelberg (2005)Google Scholar
  15. 15.
    Bettahar, S., Stambouli, A.B.: Shock Filter Coupled to Curvature Diffusion for Image Denoising and Sharpening. Imag. and Vis. Comp. 26(11), 1481–1489 (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Cosmin Ludusan
    • 1
    • 2
  • Olivier Lavialle
    • 2
  • Romulus Terebes
    • 1
  • Monica Borda
    • 1
  1. 1.Technical University of Cluj-NapocaCluj-NapocaRomania
  2. 2.Bordeaux 1 UniversityTalenceFrance

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