New exact solutions to nonlinear diffusion equation that occurs in image processing

被引：0

作者：

Chouder, Rafaa ^{[1
]}

Benhamidouche, Nouredine ^{[1
]}

机构：

[1] Univ Msila, Lab Pure & Appl Math, Bp 166, Msila 28000, Algeria

来源：

INTERNATIONAL JOURNAL OF COMPUTING SCIENCE AND MATHEMATICS | 2019年 / 10卷 / 04期

关键词：

nonlinear diffusion; travelling profile solutions; exact solutions; contour enhancement; image processing; EDGE-DETECTION;

D O I：

10.1504/IJCSM.2019.102690

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we would like to seek the new exact solutions to nonlinear diffusion equation that occurs in image processing. This equation is called degenerate parabolic equation. The solutions which we seek are called 'travelling profiles solutions'. For that, we have used the 'travelling profiles method' in order to find, explicitly, new exact solutions to this equation under some conditions. An interesting particular case has been discussed, this case coincides with particular solutions called 'intermediate asymptotic solutions' used to study the contour enhancement in image processing.

引用

页码：364 / 374

页数：11

共 7 条

[1] IMAGE SELECTIVE SMOOTHING AND EDGE-DETECTION BY NONLINEAR DIFFUSION .2. [J].

ALVAREZ, L ;

LIONS, PL ;

MOREL, JM .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 1992, 29 (03) :845-866

[2] Self-similar intermediate asymptotics for nonlinear degenerate parabolic free-boundary problems that occur in image processing [J].

Barenblatt, GI .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 2001, 98 (23) :12878-12881

[3]

Barenblattt GI, 2004, INTERFACE FREE BOUND, V6, P31

[4]

Benhamidouche N., 2009, INT J NONLINEAR SCI, V7, P395

[5]

Benhamidouche N, 2008, ELECTRON J QUAL THEO, P1

[6] Image processing: Flows under min/max curvature and mean curvature [J].

Malladi, R ;

Sethian, JA .

GRAPHICAL MODELS AND IMAGE PROCESSING, 1996, 58 (02) :127-141

[7] SCALE-SPACE AND EDGE-DETECTION USING ANISOTROPIC DIFFUSION [J].

PERONA, P ;

MALIK, J .

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 1990, 12 (07) :629-639

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