A new level set method with global alternating minimization algorithm for image segmentation

•The total variation term with edge information is introduced into convex energy, which improves ability to process weak edges and noise.•An efficient and fast alternating optimization algorithm is designed based on ADMM and FFT.•We eliminate the explicit dependence on the time step and ensure the f...

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Bibliographic Details
Published in:Applied mathematical modelling Vol. 150; p. 116396
Main Authors: Huang, Kuidong, Li, Zhixiang, Tang, Shaojie, Yang, Fuqiang, Ye, Wenguang, Zeng, Yang
Format: Journal Article
Language:English
Published: Elsevier Inc 01.02.2026
Subjects:
Convex level set
Edge information
Global minimum
Image segmentation
Image segmentation
Global minimum
Edge information
Convex level set
ISSN:0307-904X
Online Access:Get full text
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Summary:•The total variation term with edge information is introduced into convex energy, which improves ability to process weak edges and noise.•An efficient and fast alternating optimization algorithm is designed based on ADMM and FFT.•We eliminate the explicit dependence on the time step and ensure the flexibility of the solution on the time dimension.•The proposed model has a global minimum, showing superior segmentation on industrial CT data. Due to adverse factors such as varying illumination, noise, and imaging artifacts, achieving fine-grained image segmentation of objects remains a significant challenge. To address this, we propose a level set method based on global alternating minimization. Specifically, a total variation (TV) regularization term weighted by a gradient-based edge indicator function is incorporated into a convex energy functional, enhancing the model’s ability to detect weak edges. Subsequently, an efficient segmentation framework is constructed based on the Alternating Direction Method of Multipliers (ADMM), providing a closed-form solution that improves both numerical stability and convergence speed. By adopting a convex optimization scheme, the proposed model eliminates explicit time-step dependence, thereby improving adaptability and flexibility in the temporal domain. Experimental results demonstrate that the proposed method possesses a global minimization property and consistently outperforms state-of-the-art segmentation models on publicly available datasets. Notably, compared to the Segment Anything Model (SAM), the proposed method reduces the maximum CT measurement error of the ball-plate standard by 65.66 %.
ISSN:0307-904X
DOI:10.1016/j.apm.2025.116396