Adaptive fuzzy entropy optimization with opposition-based archimedes search for robust multilevel image segmentation

Image segmentation plays a critical role in diverse computer vision applications. Multilevel thresholding (MLT) remains one of its most widely used unsupervised techniques due to its simplicity and interpretability. However, existing MLT methods often suffer from two major limitations: (1) the inability to adapt to local intensity variations and (2) the computational burden associated with high-dimensional threshold search. To address these challenges, this study proposes a novel segmentation framework that integrates a Proximity-Adaptive Fuzzy Entropy (PAFE) model with an Opposition-Based Learning-enhanced Archimedes Optimization Algorithm (OBL-EAOA). The PAFE model utilizes dynamically adjusted trapezoidal membership functions based on intensity proximity to candidate thresholds, allowing for a more adaptive and smooth entropy surface. Meanwhile, the OBL-EAOA enhances optimization performance through opposition-based learning and adaptive parameter control, improving exploration diversity and convergence speed. The proposed PAFE-EAOA framework is validated on two benchmark datasets, BSD500 and PASCAL VOC 2012, using five standard metrics: PSNR, SSIM, FSIM, SNR, and computation time. Compared with several state-of-the-art methods including Kapur Entropy (KE)-EAOA, Fuzzy Entropy (FE)-EAOA, Patch-Levy-Based Bees Algorithm (PLBA), Marine Predators Algorithm (MPA), Improved Grey Wolf Optimizer (IGWO), and standard Archimedes Optimization Algorithm (AOA), the proposed approach consistently achieves superior segmentation quality. Notably, it reduces computation time by up to 60 % and achieves statistically significant improvements, as confirmed by the Wilcoxon signed-rank test. These results demonstrate the framework’s robustness, scalability, and effectiveness for real-world MLT-based image segmentation.