JournalsifbVol. 9, No. 4pp. 431–453

Stable discretization of scalar and constrained vectorial Perona–Malik equation

  • Andreas Prohl

    Universität Tübingen, Germany
  • Sören Bartels

    Universität Bonn, Germany
Stable discretization of scalar and constrained vectorial Perona–Malik equation cover
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Abstract

We survey recent results on analysis and numerics of the scalar Perona–Malik equation. A vectorial Perona–Malik equation is introduced to evolve unit vector fields for directional diffusion. For both cases, scalar and vectorial, fully discrete schemes are proposed which fulfill a discrete energy law, and satisfy a discrete sphere constraint in the vectorial case. Computational experiments are provided to illustrate quantitative behaviors, and compare with scalar total variation flow and heat flow of p-harmonic maps.

Cite this article

Andreas Prohl, Sören Bartels, Stable discretization of scalar and constrained vectorial Perona–Malik equation. Interfaces Free Bound. 9 (2007), no. 4, pp. 431–453

DOI 10.4171/IFB/172