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