Dispersing-aggregating effect for catch fish optimization: Algorithm design, convergence analysis, and application to medical image segmentation

Abstract Multi-threshold medical image segmentation is essential for extracting diagnostically relevant regions of interest, enabling accurate disease assessment and treatment planning. To improve segmentation performance, this paper introduces an enhanced catch fish optimization algorithm with a dispersing-aggregating effect (CFOA-DAE). The proposed algorithm incorporates a dispersing-aggregating mechanism inspired by fishermen’s cooperative behaviour to enhance global search capability and employs a hybrid strategy combining Gaussian and Linnik distributions to promote exploration of undersampled regions. Furthermore, an adaptive balance control factor dynamically modulates the exploration-exploitation trade-off, optimizing search efficiency. The algorithm was evaluated on the CEC 2022 benchmark suite against 11 classical and 7 state-of-the-art heuristic algorithms, including the original CFOA, demonstrating competitive convergence and accuracy. In multi-threshold segmentation tests on eight public medical image datasets, CFOA-DAE consistently outperformed existing approaches, achieving higher average peak signal-to-noise ratio and structural similarity index, along with improved fitness and lower mean squared error in 75% of cases. Additionally, based on stochastic convergence theory and Markov chain analysis, we provide a theoretical guarantee of the algorithm’s global convergence. Both theoretical and experimental results confirm the effectiveness and robustness of CFOA-DAE for multi-threshold medical image segmentation.