Alzheimer’s disease brain image segmentation using multi-feature fusion in 3D Rényi entropy model and quantum hybrid optimization

Alzheimer’s disease (AD) is a prevalent neurodegenerative disorder, and its early diagnosis critically depends on accurate segmentation of brain pathological images. However, conventional multi-threshold image segmentation (MIS) methods often exhibit high sensitivity to noise and insufficient exploitation of spatial structural information, particularly when applied to AD images with complex textures and dense information content. To overcome these limitations, this study introduces a novel three-dimensional (3D) Rényi entropy model that integrates grayscale intensity, non-local means (NLM), and local entropy. The resulting joint histogram simultaneously captures grayscale, spatial, and texture features, enabling a more comprehensive characterization of image uncertainty. To effectively optimize the high-dimensional threshold space, we propose a Quantum Hybrid Electric Eel Foraging Optimization (QHEEFO) algorithm. QHEEFO incorporates a quantum tunneling strategy (QTS), quantum control factors, and a logarithmic-enhanced perturbation mechanism to enhance jump capability and global search dynamics. Importantly, it mitigates the center bias effect inherent in the original EEFO algorithm, which tends to cause premature convergence around centroidal solutions. Additionally, QHEEFO integrates three synergistic strategies: a Gauss/mouse chaotic map (GCM) to diversify the initial population, a population self-learning (PSL) mechanism to promote cooperative evolution, and an elite pooling mutation (EPM) strategy to improve local refinement stability and precision. Extensive experiments on the IEEE CEC 2017 benchmark functions demonstrate that QHEEFO achieves comparable or superior optimization accuracy while reducing function evaluations by approximately 60%. Further validation on breast cancer and self-constructed AD image datasets confirms its superior segmentation performance and robustness, underscoring its potential in real-world medical image analysis applications.