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

Research output: Contribution to journal › Article › peer-review

5 Citations (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.

Original language	English
Pages (from-to)	221-243
Number of pages	23
Journal	Calcolo
Volume	46
DOIs	https://doi.org/10.1007/s10092-009-0006-9
Publication status	Published - 2009

Keywords

anisotropy
ill-posed problems
image segmentation

Access to Document

10.1007/s10092-009-0006-9

Cite this

@article{66eb971a34ee446fad3dd5aa8c41d579,

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 $\Gamma$-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",

year = "2009",

doi = "10.1007/s10092-009-0006-9",

language = "English",

volume = "46",

pages = "221--243",

journal = "Calcolo",

issn = "0008-0624",

publisher = "Roma : Springer Verlag Italia",

}

TY - JOUR

T1 - Classification of the equilibria for the semi-discrete Perona-Malik equation

AU - Paolini, Maurizio

AU - Bellettini, Giovanni

AU - Novaga, Matteo

PY - 2009

Y1 - 2009

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

Access to Document

Other files and links

Fingerprint

Cite this