FD-HCL: A Fractal-Dimension-Guided Hierarchical Contrastive Learning Dual-Student Framework for Semi-Supervised Medical Segmentation

Semi-supervised learning (SSL) is critical for medical image segmentation but often struggles with network dependency and pseudo-label error accumulation. To address these issues, we propose a fractal-dimension-guided hierarchical contrastive learning dual-student framework(FD-HCL). We extend the Mean Teacher architecture with a dual-student design and introduce an independence-aware exponential moving average (I-EMA) update mechanism to mitigate model coupling. For enhanced feature learning, we devise a hierarchical contrastive learning (HCL) mechanism guided by voxel uncertainty, spanning global, high-confidence, and low-confidence regions. We further improve structural integrity by incorporating a fractal-dimension (FD)-weighted consistency loss and integrating a novel uncertainty-aware bidirectional copy–paste (UB-CP) augmentation. Extensive experiments on the LA and BraTS 2019 datasets demonstrate the state-of-the-art performance of our framework across 10% and 20% labeled data settings. On the LA dataset with 10% labeled data, our method achieved a Dice score that outperformed the best existing approach by 0.68%. Similarly, under the 10% labeling setting on the BraTS 2019 dataset, we surpassed the state-of-the-art Dice score by 0.55%.