On an effective multigrid solver for solving a class of variational problems with application to image segmentation

Roberts, Michael1,2; Chen, Ke1,2; Li, Jingzhi3; Irion, Klaus L.4

2019-10-11

10.1080/00207160.2019.1674290

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS   影响因子和分区

0020-7160

1029-0265

In this paper we reformulate a class of non-linear variational models for global and selective image segmentation and obtain convergent multigrid solutions. In contrast, non-linear multigrid schemes do not converge for these problems with strong non-linearity and non-smoothness (jumps). Our new approach is to reformulate the non-linear models, using splitting techniques, to generate linear models in a higher dimension which are easier to solve and amenable to the linear multigrid framework. Although splitting techniques are well studied in isolation, direct application of a splitting idea is not sufficient and it is the combination of two splitting approaches and linear multigrid theory approaches which results in a highly effective multigrid algorithm. Numerical results demonstrate the fast convergence of the new multigrid methods.

Iterative methods multigrid Euler-Lagrange equations segmentation models

SCI ; EI

英语

其他

Engineering and Physical Sciences Research Council (UK EPSRC)[EP/N014499/1]

Mathematics

Mathematics, Applied

WOS:000492260200001

TAYLOR & FRANCIS LTD

20194407600722

Convergence of numerical methods ; Iterative methods ; Equations of motion

Calculus:921.2 ; Numerical Methods:921.6

ENGINEERING

Web of Science

1.Univ Liverpool, Ctr Math Imaging Tech, Liverpool, Merseyside, England
2.Univ Liverpool, Dept Math Sci, Liverpool, Merseyside, England
3.Southern Univ Sci & Technol, Dept Math, Shenzhen, Peoples R China
4.Manchester Univ NHS Fdn Trust, Dept Radiol, Manchester, Lancs, England

Roberts, Michael,Chen, Ke,Li, Jingzhi,et al. On an effective multigrid solver for solving a class of variational problems with application to image segmentation[J]. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,2019,97:2015-2035.

Roberts, Michael,Chen, Ke,Li, Jingzhi,&Irion, Klaus L..(2019).On an effective multigrid solver for solving a class of variational problems with application to image segmentation.INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS,97,2015-2035.

Roberts, Michael,et al."On an effective multigrid solver for solving a class of variational problems with application to image segmentation".INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 97(2019):2015-2035.