An unconditionally stable hybrid method for image segmentation

Yibao Li, Junseok Kim

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

In this paper, we propose a new unconditionally stable hybrid numerical method for minimizing the piecewise constant Mumford-Shah functional of image segmentation. The model is based on the Allen-Cahn equation and an operator splitting technique is used to solve the model numerically. We split the governing equation into two linear equations and one nonlinear equation. One of the linear equations and the nonlinear equation are solved analytically due to the availability of closed-form solutions. The other linear equation is discretized using an implicit scheme and the resulting discrete system of equations is solved by a fast numerical algorithm such as a multigrid method. We prove the unconditional stability of the proposed scheme. Since we incorporate closed-form solutions and an unconditionally stable scheme in the solution algorithm, our proposed scheme is accurate and robust. Various numerical results on real and synthetic images with noises are presented to demonstrate the efficiency, robustness, and accuracy of the proposed method.

Original languageEnglish
Pages (from-to)32-43
Number of pages12
JournalApplied Numerical Mathematics
Volume82
DOIs
Publication statusPublished - 2014 Jan 1

Fingerprint

Unconditionally Stable
Hybrid Method
Linear equations
Image segmentation
Image Segmentation
Linear equation
Closed-form Solution
Nonlinear equations
Nonlinear Equations
Mumford-Shah Functional
Allen-Cahn Equation
Unconditional Stability
Operator Splitting
Implicit Scheme
Multigrid Method
Discrete Systems
Numerical Algorithms
Fast Algorithm
System of equations
Governing equation

Keywords

  • Allen-Cahn equation
  • Chan-Vese model
  • Image segmentation
  • Mumford-Shah functional
  • Phase-field method

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

An unconditionally stable hybrid method for image segmentation. / Li, Yibao; Kim, Junseok.

In: Applied Numerical Mathematics, Vol. 82, 01.01.2014, p. 32-43.

Research output: Contribution to journalArticle

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