Medical images contain topological patterns, such as connected components and loops, at scales ranging from small lesions to organ boundaries. Although hierarchical Vision Transformers have advanced medical image analysis, they do not explicitly incorporate topology throughout their multiscale representations.

We propose Topology-Reinforced Swin Transformer (TRiST), a framework that integrates topological information into feature construction, refinement, and attention. First, a Hierarchical Multi-Scale Topology Representation algorithm computes 2D persistent homology (H0 and H1) independently at four native Swin stages, producing descriptors aligned with each stage's token grid rather than downsampling fine-scale topology.

Second, a Band-Aware H0/H1 Residual Refinement module uses gated residual networks to process short-, medium-, and long-persistence information separately. Third, a Persistence-Band Progressive Attention Bias converts stage-specific descriptors into learned key-saliency scores that directly modify shifted-window attention logits.

We instantiate TRiST as Topo-SwinV2-B for classification and Topo-Swin-UNet for segmentation, preserving the underlying Swin-based backbones. Experiments on five medical image datasets show consistent improvements over Swin-based baselines and competitive performance relative to existing topology-augmented methods.