Geodesic
Stable discretization of scalar and constrained vectorial Perona–Malik equation
Sören Bartels1 orcid ; Andreas Prohl2
1Universität Bonn, Germany
2Universität Tübingen, Germany
Interfaces and free boundaries, Tome 9 (2007) no. 4, pp. 431-453

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DOI

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.
DOI : 10.4171/ifb/172
Classification : 35-XX, 65-XX, 76-XX, 92-XX
Mots-clés : Total variation, Perona–Malik, <em>p</em>-harmonic map, finite elements, full discretization, discrete energy law <em>p</em>-harmonic map, finite elements, full discretization, discrete energy law

Sören Bartels  1   ; Andreas Prohl  2

1 Universität Bonn, Germany
2 Universität Tübingen, Germany 
Sören Bartels; Andreas Prohl. Stable discretization of scalar and constrained vectorial Perona–Malik equation. Interfaces and free boundaries, Tome 9 (2007) no. 4, pp. 431-453. doi: 10.4171/ifb/172
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     title = {Stable discretization of scalar and constrained vectorial {Perona{\textendash}Malik} equation},
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     pages = {431--453},
     year = {2007},
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     number = {4},
     doi = {10.4171/ifb/172},
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