Two-phase image segmentation by the Allen-Cahn equation and a nonlocal edge detection operator

2021/04/19 by Zhonghua Qiao, Qian Zhang, Qiao, Zhonghua +1 · 1 citation
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Composite Material Mechanics #FOS: Mathematics #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.2104.08992

openalex publication_date 2021/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Based on a nonlocal Laplacian operator, a novel edge detection method of the grayscale image is proposed in this paper. This operator utilizes the information of neighbor pixels for a given pixel to obtain effective and delicate edge detection. The nonlocal edge detection method is used as an initialization for solving the Allen-Cahn equation to achieve two-phase segmentation of the grayscale image. Efficient exponential time differencing (ETD) solvers are employed in the time integration, and finite difference method is adopted in space discretization. The maximum bound principle and energy stability of the proposed numerical schemes are proved. The capability of our segmentation method has been verified in numerical experiments for different types of grayscale images.

Citations

• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Theory of edge detection
• Optimal approximations by piecewise smooth functions and associated variational problems
• Approximation of functional depending on jumps by elliptic functional via t‐convergence
• Diffuse Interface Models on Graphs for Classification of High Dimensional Data
• Maximum Principle Preserving Exponential Time Differencing Schemes for the Nonlocal Allen--Cahn Equation

Cited by

• A novel phase-field model for N-phase problems: modeling, asymptotic analysis and numerical simulations

Related

• Two-phase segmentation for intensity inhomogeneous images by the Allen-Cahn Local Binary Fitting Model
• Multi-phase image segmentation by the Allen--Cahn Chan--Vese model
• Edge Detection Methods Based on Differential Phase Congruency of Monogenic Image
• Edge Detection Based on Global and Local Parameters of the Image
• Effective two-stage image segmentation: a new non-Lipschitz decomposition approach with convergent algorithm