Time-delay regularization of anisotropic diffusion and image processing

被引：28

作者：

Belahmidi, A ^{[1
]}

Chambolle, A

机构：

[1] Univ Paris 09, CEREMADE, CNRS, UMR 7534, F-75775 Paris, France

[2] Ecole Polytech, CMAP, CNRS, UMR 7641, F-91128 Palaiseau, France

来源：

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2005年 / 39卷 / 02期

关键词：

image restoration; edge detection; Perona-Malik equation; time-delay regularization;

D O I：

10.1051/m2an:2005010

中图分类号：

O29 [应用数学];

学科分类号：

070104 [应用数学];

摘要：

We study a time-delay regularization of the anisotropic diffusion model for image denoising of Perona and Malik [IEEE Trans. Pattern Anal. Mach. Intell 12 (1990) 629 - 639], which has been proposed by Nitzberg and Shiota [ IEEE Trans. Pattern Anal. Mach. Intell 14 ( 1998) 826 - 835]. In the two-dimensional case, we show the convergence of a numerical approximation and the existence of a weak solution. Finally, we show some experiments on images.

引用

页码：231 / 251

页数：21

共 20 条

[1]

AXIOMS AND FUNDAMENTAL EQUATIONS OF IMAGE-PROCESSING [J].

ALVAREZ, L ;

GUICHARD, F ;

LIONS, PL ;

MOREL, JM .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1993, 123 (03) :199-257

[2]

Belahmidi A., 2003, THESIS U PARIS DAUPH

[3]

A COMPUTATIONAL APPROACH TO EDGE-DETECTION [J].

CANNY, J .

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 1986, 8 (06) :679-698

[4]

IMAGE SELECTIVE SMOOTHING AND EDGE-DETECTION BY NONLINEAR DIFFUSION [J].

CATTE, F ;

LIONS, PL ;

MOREL, JM ;

COLL, T .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1992, 29 (01) :182-193

[5]

Ciarlet PG, 1982, COLLECTION MATH APPL

[6]

A Volterra type model for image processing [J].

Cottet, GH ;

El Ayyadi, M .

IEEE TRANSACTIONS ON IMAGE PROCESSING, 1998, 7 (03) :292-303

[7]

An analysis of the Perona-Malik scheme [J].

Esedoglu, S .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2001, 54 (12) :1442-1487

[8]

MOTION OF HYPERSURFACES AND GEOMETRIC EQUATIONS [J].

GIGA, Y ;

GOTO, S .

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1992, 44 (01) :99-111

[9]

Gilbarg D, 1998, Elliptic Partial Differential Equations of Second Order, V224

[10]

HEINZ E, 1959, J MATH MECH, V8, P231

← 1 2 →