Classification of the equilibria for the semi-discrete Perona-Malik equation

Maurizio Paolini; Giovanni Bellettini; Matteo Novaga

doi:10.1007/s10092-009-0006-9

Classification of the equilibria for the semi-discrete Perona-Malik equation

Maurizio Paolini
, Giovanni Bellettini
, Matteo Novaga

Risultato della ricerca: Contributo in rivista › Articolo › peer review

5 Citazioni (Scopus)

Abstract

We give a complete classification of the stability properties of the equilibria for the semi-discrete one-dimensional Perona-Malik equation, with Dirichlet boundary conditions. We also give the $\Gamma$-expansion of the corresponding discretized functionals up to the order two, as the discretization parameter goes to zero.

Lingua originale	Inglese
pagine (da-a)	221-243
Numero di pagine	23
Rivista	Calcolo
Volume	46
DOI	https://doi.org/10.1007/s10092-009-0006-9
Stato di pubblicazione	Pubblicato - 2009

Keywords

anisotropy
ill-posed problems
image segmentation

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10.1007/s10092-009-0006-9

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title = "Classification of the equilibria for the semi-discrete Perona-Malik equation",

abstract = "We give a complete classification of the stability properties of the equilibria for the semi-discrete one-dimensional Perona-Malik equation, with Dirichlet boundary conditions. We also give the \$\textbackslash{}Gamma\$-expansion of the corresponding discretized functionals up to the order two, as the discretization parameter goes to zero.",

keywords = "anisotropy, ill-posed problems, image segmentation, anisotropy, ill-posed problems, image segmentation",

author = "Maurizio Paolini and Giovanni Bellettini and Matteo Novaga",

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AU - Paolini, Maurizio

AU - Bellettini, Giovanni

AU - Novaga, Matteo

PY - 2009

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N2 - We give a complete classification of the stability properties of the equilibria for the semi-discrete one-dimensional Perona-Malik equation, with Dirichlet boundary conditions. We also give the $\Gamma$-expansion of the corresponding discretized functionals up to the order two, as the discretization parameter goes to zero.

AB - We give a complete classification of the stability properties of the equilibria for the semi-discrete one-dimensional Perona-Malik equation, with Dirichlet boundary conditions. We also give the $\Gamma$-expansion of the corresponding discretized functionals up to the order two, as the discretization parameter goes to zero.

KW - anisotropy

KW - ill-posed problems

KW - image segmentation

KW - anisotropy

KW - ill-posed problems

KW - image segmentation

UR - http://hdl.handle.net/10807/11577

U2 - 10.1007/s10092-009-0006-9

DO - 10.1007/s10092-009-0006-9

M3 - Article

SN - 0008-0624

VL - 46

SP - 221

EP - 243

JO - Calcolo

JF - Calcolo

ER -

Classification of the equilibria for the semi-discrete Perona-Malik equation

Abstract

Keywords

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