Energy curve based multilevel thresholding with artificial hummingbird algorithm and minimum cross entropy

Multilevel thresholding is an important technique in color image segmentation, yet traditional methods such as OTSU’s often struggle to preserve meaningful structures in complex images. To address this limitation, we propose a hybrid segmentation framework that integrates the Artificial Hummingbird Algorithm (AHA) with the Minimum Cross Entropy Measure (MCEM) as the objective function. Instead of relying on the global histogram, the method employs an intensity level energy curve to capture spatial intensity variation and fine edge information. AHA incorporates guided, territorial, and migration foraging strategies, enabling an effective balance between exploration and exploitation during threshold optimization. The proposed approach is evaluated across multiple threshold levels and benchmarked against OTSU’s and MCEM based methods enhanced through four metaheuristics: Aquila Optimizer (AO), Equilibrium Optimizer (EO), Particle Swarm Optimization (PSO), and Whale Optimization Algorithm (WOA). Performance is assessed using seven quantitative metrics: PSNR, SSIM, FSIM, QILV, Correlation coefficient, Edge Preservation Index (EPI), and Mutual Information Factor (MIF). Experimental results on satellite images demonstrate that the proposed method delivers improved segmentation quality, robustness, and structural fidelity, showing strong potential for environmental monitoring, remote sensing, and disaster analysis applications.