A class of quasi-linear elliptic systems arising in image segmentation

被引：2

作者：

Birindelli, Isabeau ^{[1
,2
]}

Finzi Vita, Stefano ^{[1
]}

机构：

[1] Univ Roma La Sapienza, I-00185 Rome, Italy

[2] Univ Cergy Pontoise, F-95302 Cergy Pontoise, France

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 1998年 / 5卷 / 04期

关键词：

Numerical Experiment; Large Class; Image Segmentation; Efficient Algorithm; Elliptic System;

D O I：

10.1007/s000300050056

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a quasi-linear system arising in image segmentation in order to determine the minimum of the Mumford-Shah functional. We prove the existence of a solution for a larger class of systems including the previous one. The recursive method used in the proof produces as well an efficient algorithm that can be easily implemented in connection for example with finite element techniques. Results of some numerical experiments are also discussed.

引用

页码：445 / 459

页数：15

共 50 条

[1] A class of quasi-linear elliptic systems arising in image segmentation
Isabeau Birindelli
Stefano Finzi Vita
Nonlinear Differential Equations and Applications NoDEA, 1998, 5 : 445 - 459
[2] A CLASS OF QUASI-LINEAR ELLIPTIC-SYSTEMS WITH NATURAL GROWTH CONDITION
SHEN, YT
GUO, XK
ACTA MATHEMATICA SCIENTIA, 1991, 11 (02) : 121 - 127
[3] Global compactness for a class of quasi-linear elliptic problems
Mercuri, Carlo
Squassina, Marco
MANUSCRIPTA MATHEMATICA, 2013, 140 (1-2) : 119 - 144
[4] Morse theory methods for a class of quasi-linear elliptic systems of higher order
Lu, Guangcun
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2019, 58 (04)
[5] Study of a class of quasi-linear elliptic systems deriving from a potential RN
Ali, Djellit
Saadia, Tas
ESAIM: Mathematical Modelling and Numerical Analysis, 2007, 20 : 105 - 117
[6] ON A CLASS OF NONUNIFORMLY ELLIPTIC QUASI-LINEAR EQUATIONS IN THE PLANE
MEYERS, NG
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1963, 12 (05) : 367 - 391
[7] A PRIORI ESTIMATES FOR A CLASS OF QUASI-LINEAR ELLIPTIC EQUATIONS
Daners, Daniel
Drabek, Pavel
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 361 (12) : 6475 - 6500
[8] On Explosive Solutions for a Class of Quasi-linear Elliptic Equations
Gladiali, Francesca
Squassina, Marco
ADVANCED NONLINEAR STUDIES, 2013, 13 (03) : 663 - 698
[9] Differentiability of the Energy Functional of a Class of Quasi-linear Elliptic
Pan, Xiaoli
Mu, Lihua
Chen, Hui
GREEN POWER, MATERIALS AND MANUFACTURING TECHNOLOGY AND APPLICATIONS III, PTS 1 AND 2, 2014, 484-485 : 1033 - 1037
[10] Morse theory methods for a class of quasi-linear elliptic systems of higher order
Guangcun Lu
Calculus of Variations and Partial Differential Equations, 2019, 58

← 1 2 3 4 5 →