A New Level Set Method with Global Alternating Minimization Algorithm for Image Segmentation

Due to adverse factors such as varying illumination, noise, and imaging artifacts, achieving finegrained 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 %.