Journal of Mathematical Imaging and Vision

, Volume 20, Issue 1, pp 121–131

Image Sharpening by Flows Based on Triple Well Potentials

  • Guy Gilboa
  • Nir Sochen
  • Yehoshua Y. Zeevi

DOI: 10.1023/B:JMIV.0000011320.81911.38

Cite this article as:
Gilboa, G., Sochen, N. & Zeevi, Y.Y. Journal of Mathematical Imaging and Vision (2004) 20: 121. doi:10.1023/B:JMIV.0000011320.81911.38


Image sharpening in the presence of noise is formulated as a non-convex variational problem. The energy functional incorporates a gradient-dependent potential, a convex fidelity criterion and a high order convex regularizing term. The first term attains local minima at zero and some high gradient magnitude, thus forming a triple well-shaped potential (in the one-dimensional case). The energy minimization flow results in sharpening of the dominant edges, while most noisy fluctuations are filtered out.

image filtering image enhancement image sharpening nonlinear diffusion hyper-diffusion variational image processing 

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Guy Gilboa
    • 1
  • Nir Sochen
    • 2
  • Yehoshua Y. Zeevi
    • 1
    • 3
  1. 1.Department of Electrical EngineeringTechnion—Israel Institute of TechnologyTechnion City, HaifaIsrael
  2. 2.Department of Applied MathematicsUniversity of Tel-Aviv Ramat-AvivTel-AvivIsrael
  3. 3.Department of Biomedical EngineeringColumbia UniversityNew YorkUSA

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