A Hybrid Whale–Genetic Optimization Framework for Multi-Level Image Thresholding Based on Otsu’s Criterion

Multi-level image thresholding (MLT) is a fundamental segmentation task, but its computational cost grows exponentially with the number of thresholds, rendering exhaustive search methods like Otsu’s criterion infeasible. While metaheuristic algorithms offer efficient alternatives, standalone approaches often struggle with premature convergence, especially at higher threshold levels. This study introduces a hybrid framework, WOA–GA, that synergistically combines the global exploration capabilities of the Whale Optimization Algorithm (WOA) with the local refinement strengths of the Genetic Algorithm (GA). The proposed method employs a periodic hybridization strategy, where GA operators are activated at predefined intervals within WOA’s optimization process to refine promising solutions and prevent stagnation. The framework’s performance was rigorously evaluated on four benchmark images from the Berkeley Segmentation Dataset (BSDS500), selected for their diverse structural characteristics. For threshold levels ranging from K=2 to 5, WOA–GA consistently outperformed several state-of-the-art metaheuristics across 30 independent runs. For instance, on the complex “Baboon” image at K=5, WOA–GA achieved a superior objective value of 1792.4 ± 11.8, compared to 1722.6 ± 34.6 for a strong competitor like SS-ACO. Statistical validation using the non-parametric Wilcoxon signed-rank test confirmed that these performance gains are statistically significant. The results demonstrate that the WOA–GA framework is a robust, reliable, and effective solution for grayscale multi-level image thresholding.