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

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 algorithm incorporates a dispersing-aggregating mechanism inspired by fishermen’s cooperative behavior, which enhances global search capability. It also employs a hybrid strategy combining Gaussian and Linnik distributions is employed to promote exploration of under-sampled regions in the solution space. Furthermore, an adaptive balance control factor dynamically modulates the trade-off between exploration and exploitation, thereby optimizing search efficiency. We evaluated CFOA-DAE using the CEC 2022 benchmark suite against 11 classical heuristic algorithms, seven state-of-the-art variants, and the original CFOA. Experimental results show that CFOA-DAE achieves competitive convergence behavior and solution accuracy. In multi-threshold segmentation tests on eight public medical image datasets, the proposed method consistently outperformed existing approaches. It delivered higher average values of Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index (SSIM), and achieved improved fitness and lower Mean Squared Error (MSE) in 75 % of the cases. Based on stochastic convergence theory and Markov chain analysis, we also provide a theoretical guarantee of the global convergence of CFOA-DAE. Both theoretical and experimental results confirm the effectiveness and robustness of the proposed algorithm for multi-threshold medical image segmentation.