@article{ebb0513287eb48929c58d114b156681a,
title = "Two-Phase Segmentation for Intensity Inhomogeneous Images by the Allen--Cahn Local Binary Fitting Model",
abstract = "This paper proposes a new variational model by integrating the Allen-Cahn term with a local binary fitting energy term for segmenting images with intensity inhomogeneity and noise. An inhomogeneous graph Laplacian initialization method (IGLIM) is developed to give the initial contour for two-phase image segmentation problems. To solve the Allen-Cahn equation derived from the variational model, we adopt the exponential time differencing (ETD) method for temporal discretization, and the central finite difference method for spatial discretization. The energy stability of proposed numerical schemes can be proved. Experiments on various images demonstrate the necessity and superiority of proper initialization and verify the capability of our model for two-phase segmentation of images with intensity inhomogeneity and noise.",
keywords = "Allen-Cahn equation, edge detection, energy stability, exponential time differencing method, image segmentation, inhomogeneous graph Laplacian",
author = "Chaoyu Liu and Zhonghua Qiao and Qian Zhang",
note = "Funding Information: \ast Submitted to the journal's Computational Methods in Science and Engineering section May 21, 2021; accepted for publication (in revised form) September 20, 2021; published electronically January 31, 2022. https://doi.org/10.1137/21M1421830 Funding: The work of the second author was partially supported by the Hong Kong Research Council RFS grant RFS2021-5S03 and GRF grants 15300417 and 15302919. The work of the third author was supported by the 2019 Hong Kong Scholar Program G-YZ2Y. \dagger Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong (polyucy.liu@connect.polyu.hk). \ddagger Department of Applied Mathematics \& Research Institute for Smart Energy, The Hong Kong Polytechnic University, Hong Kong (zhonghua.qiao@polyu.edu.hk). \S Corresponding author. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong (qian77.zhang@polyu.edu.hk). Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics",
year = "2022",
month = feb,
doi = "10.1137/21M1421830",
language = "English",
volume = "44",
pages = "B177--B196",
journal = "SIAM Journal on Scientific Computing",
issn = "1064-8275",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",
}