Multiphase image segmentation using a phase-field model

Yibao Li, Junseok Kim

Research output: Contribution to journalArticle

43 Citations (Scopus)

Abstract

In this paper, we propose a new, fast, and stable hybrid numerical method for multiphase image segmentation using a phase-field model. The proposed model is based on the Allen-Cahn equation with a multiple well potential and a data-fitting term. The model is computationally superior to the previous multiphase image segmentation via Modica-Mortola phase transition and a fitting term. We split its numerical solution algorithm into linear and a nonlinear equations. The linear equation is discretized using an implicit scheme and the resulting discrete system of equations is solved by a fast numerical method such as a multigrid method. The nonlinear equation is solved analytically due to the availability of a closed-form solution. We also propose an initialization algorithm based on the target objects for the fast image segmentation. Finally, various numerical experiments on real and synthetic images with noises are presented to demonstrate the efficiency and robustness of the proposed model and the numerical method.

Original languageEnglish
Pages (from-to)737-745
Number of pages9
JournalComputers and Mathematics with Applications
Volume62
Issue number2
DOIs
Publication statusPublished - 2011 Jul 1

Fingerprint

Phase Field Model
Image segmentation
Image Segmentation
Numerical Methods
Numerical methods
Nonlinear Equations
Nonlinear equations
Allen-Cahn Equation
Data Fitting
Potential Well
Implicit Scheme
Multigrid Method
Term
Hybrid Method
Closed-form Solution
Initialization
Discrete Systems
System of equations
Linear equation
Phase Transition

Keywords

  • Allen-Cahn equation
  • Image segmentation
  • Modica-Mortola
  • Phase-field method

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Modelling and Simulation
  • Computational Mathematics

Cite this

Multiphase image segmentation using a phase-field model. / Li, Yibao; Kim, Junseok.

In: Computers and Mathematics with Applications, Vol. 62, No. 2, 01.07.2011, p. 737-745.

Research output: Contribution to journalArticle

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