We present an asymptotic description of local minimization problems, and of quasistatic and dynamic evolutions of discrete one-dimensional scaled Perona-Malik functionals. The scaling is chosen in such a way that these energies Γ-converge to the Mumford-Shah functional by a result by Morini and Negri. This continuum approximation still provides a good description of quasistatic and gradient-flow type evolutions, while it must be suitably corrected to maintain the pattern of local minima and to account for long-time evolution.

Static, Quasistatic and Dynamic Analysis for Scaled Perona-Malik Functionals / Braides, A.; Vallocchia, V.. - In: ACTA APPLICANDAE MATHEMATICAE. - ISSN 0167-8019. - 156:1(2018), pp. 79-107. [10.1007/s10440-018-0155-4]

Static, Quasistatic and Dynamic Analysis for Scaled Perona-Malik Functionals

Braides A.;Vallocchia V.
2018-01-01

Abstract

We present an asymptotic description of local minimization problems, and of quasistatic and dynamic evolutions of discrete one-dimensional scaled Perona-Malik functionals. The scaling is chosen in such a way that these energies Γ-converge to the Mumford-Shah functional by a result by Morini and Negri. This continuum approximation still provides a good description of quasistatic and gradient-flow type evolutions, while it must be suitably corrected to maintain the pattern of local minima and to account for long-time evolution.
2018
156
1
79
107
https://arxiv.org/abs/1610.08295
Braides, A.; Vallocchia, V.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/139610
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