GPS: Geometry-aware and Peripheral-background Synergy for Cross-Domain Few-Shot Medical Image Segmentation

Few-shot medical image segmentation (FSMIS) aims to generalize to novel classes with minimal annotations, yet its effectiveness is severely hindered by the challenge of domain shift, where substantial inter-domain discrepancies (e.g., MRI to CT) often lead to significant performance degradation. Current cross-domain FSMIS methods primarily rely on volatile appearance-based features or computationally expensive graph-matching, failing to capture stable anatomical representations. In this paper, we observe a crucial yet under-explored phenomenon: while domain-specific textures vary drastically, the geometric topology of organs and their surrounding peripheral-background distributions remain remarkably consistent across divergent domains. Based on this insight, we propose a novel framework termed Geometry-aware and Peripheral-background Synergy (GPS) for cross-domain FSMIS. GPS leverages these stable invariants as "Anatomical Anchors" to steer the model beyond domain-sensitive biases. Specifically, GPS consists of three synergistic modules: (1) a Geometry-Aware Injector (GAI) that modulates feature responses based on geometric shape priors to distill domain-invariant representations; (2) a Peripheral-aware Prototype Mining (PPM) module that constructs multi-prototypes for both the target organ and its surrounding tissues; and (3) a Prototype Synergy Refinement (PSR) module that exploits foreground-background complementarity for fine-grained segmentation. Extensive experiments on three popular medical image benchmarks demonstrate that our GPS significantly outperforms state-of-the-art methods, exhibiting superior robustness and generalization across diverse domains.