A Multigrid Algorithm for Maxflow and Min-Cut Problems with Applications to Multiphase Image Segmentation

In this paper, we propose a multiphase image segmentation method via solving the min-cut minimization problem under the multigrid method framework. At each level of the multigrid method for the min-cut problem, we first transfer it to the equivalent form, e.g., max-flow problem, then actually solve...

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Bibliographic Details
Published in:Journal of scientific computing Vol. 87; no. 3; p. 101
Main Authors: Tai, Xue-Cheng, Deng, Liang-Jian, Yin, Ke
Format: Journal Article
Language:English
Published: New York Springer US 01.06.2021
Springer Nature B.V
Subjects:
Algorithms
Computational Mathematics and Numerical Analysis
Image segmentation
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Multiphase
Optimization
Theoretical
Multigrid method
Multiphase image segmentation
Continuous min-cut and max-flow
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary:In this paper, we propose a multiphase image segmentation method via solving the min-cut minimization problem under the multigrid method framework. At each level of the multigrid method for the min-cut problem, we first transfer it to the equivalent form, e.g., max-flow problem, then actually solve the dual of the max-flow problem. Particularly, a classical multigrid method is used to solve the sub-minimization problems. Several outer iterations are used for the multigrid method. The proposed idea can be used for general min-cut/max-flow minimization problems. We use multiphase image segmentation as an example in this work. Extensive experiments on simulated and real images demonstrate the efficiency and effectiveness of the proposed method.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-021-01458-3