Journal of Mathematical Imaging and Vision

, Volume 20, Issue 1, pp 121-131

First online:

Image Sharpening by Flows Based on Triple Well Potentials

  • Guy GilboaAffiliated withDepartment of Electrical Engineering, Technion—Israel Institute of Technology
  • , Nir SochenAffiliated withDepartment of Applied Mathematics, University of Tel-Aviv Ramat-Aviv
  • , Yehoshua Y. ZeeviAffiliated withDepartment of Electrical Engineering, Technion—Israel Institute of TechnologyDepartment of Biomedical Engineering, Columbia University

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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