Few-Shot Medical Image Segmentation (FSMIS) offers a powerful solution to data scarcity but struggles to generalize across different imaging modalities. This performance collapse stems primarily from the drastic texture discrepancies between domains, which mislead models trained on source-specific intensity distributions. While existing methods attempt to align frequency or local texture features, they often fail to decouple semantic structure from domain-specific appearance. To address this, we identify a critical invariance: despite distinct imaging physics, the position and geometric shape of organs remain robustly consistent across modalities. Therefore, we propose a novel framework that harnesses Position and Shape Priors (PSP) for cross-domain FSMIS. Specifically, PSP first introduces a Position Coordinate Embedding (PCE) module to inject relative spatial coordinates for rapid organ localization. Subsequently, a Shape Prototype Modulation (SPM) module constructs domain-invariant structural prototypes via explicit shape priors, effectively filtering out texture noise. Furthermore, the Hybrid-Prototype Prediction (HPP) module adaptively calibrates the support prototype to the query feature distribution, mitigating feature misalignment. Extensive experiments on two public medical imaging datasets demonstrate that PSP significantly outperforms state-of-the-art methods.
Precise biomedical image segmentation is crucial for clinical diagnosis. Geometric cues (e.g., boundary, shape, and topology) can improve structural consistency, yet most are task-specific and lack a unified geometric foundation that generalizes across organs and modalities. We are motivated by the observation that several medical segmentation targets can be approximated as globally near-convex shapes. A convex region is one in which any two interior points can be connected by a line segment entirely contained within the region. In practice, medical targets may exhibit small local concavities or boundary irregularities; we refer to such globally convex-like shapes as near-convex. Motivated by this, we derive Hadwiger Shape Priors from Hadwiger's theorem as an interpretable global regularizer using three 2D measures: area A, perimeter P, and Euler characteristic chi, enabling transfer across organs and modalities. However, because medical datasets are shape-heterogeneous, enforcing near-convex priors uniformly can over-regularize non-convex anatomy with significant concavities, washing out concavities and fine details and degrading segmentation accuracy. To address this challenge, we propose Conflict-Aware Objective Balancing (CAOB), which integrates shape priors with segmentation in a gradient-aware manner. For each prior, CAOB removes only the gradient component that conflicts with segmentation while preserving the remaining aligned component, and adaptively regulates objective influences to prevent prior dominance. This enables stable use of shape priors on shape-heterogeneous data without erasing genuine concavities or fine structural details. We call this plug-and-play framework HadBalance.