Cross-domain few-shot medical image segmentation (CD-FSMIS) requires a model to generalise simultaneously to novel anatomical categories and unseen imaging domains from only a handful of annotated examples. Existing prototypical approaches inevitably entangle anatomical structure with domain-specific appearance variations, and thus lack a stable reference for reliable matching under domain shift. We observe that the geometric structure of human anatomy constitutes a reliable, domain-transferable prior that has been overlooked. Building on this insight, we propose GeoProto, a geometry-aware CD-FSMIS framework that enriches prototypical matching with explicit structural priors. The core component, Geometry-Aware Prototype Enrichment (GAPE), augments each local appearance prototype with a learned geometric offset encoding its ordinal position within the organ's interior topology. This offset is derived from an auxiliary Ordinal Shape Branch (OSB) trained under an ordinally consistent objective that enforces monotonic variation of geometric embeddings across interior strata, requiring no annotation beyond standard segmentation masks. Extensive experiments across seven datasets spanning three evaluation settings (cross-modality, cross-sequence, and cross-context) demonstrate that GeoProto achieves state-of-the-art performance.

翻译：跨域小样本医学图像分割（CD-FSMIS）要求模型仅利用少量标注示例，同时泛化至新的解剖类别与未见过的成像域。现有基于原型的方法不可避免地会将解剖结构与特定域的外观变化纠缠在一起，因此在域偏移下缺乏稳定参考以实现可靠匹配。我们观察到，人体解剖结构的几何形态构成了一种可靠且可跨域迁移的先验信息，但此前一直被忽视。基于这一洞见，我们提出几何感知跨域小样本医学图像分割框架GeoProto，通过显式结构先验增强原型匹配。其核心组件——几何感知原型增强模块（GAPE）——为每个局部外观原型附加一个学习到的几何偏移，该偏移编码了原型在器官内部拓扑中的有序位置。该偏移由一个辅助的有序形状分支（OSB）推导得出，该分支在有序一致性目标下训练，强制几何嵌入在器官内层间呈单调变化，且无需超出标准分割掩膜之外的任何标注。在七个数据集上跨越三种评估设置（跨模态、跨序列与跨上下文）的大量实验表明，GeoProto取得了最先进性能。