CRISP: Rank-Guided Iterative Squeezing for Robust Medical Image Segmentation under Domain Shift

Distribution shift in medical imaging remains a central bottleneck for the clinical translation of medical AI. Failure to address it can lead to severe performance degradation in unseen environments and exacerbate health inequities. Existing methods for domain adaptation are inherently limited by exhausting predefined possibilities through simulated shifts or pseudo-supervision. Such strategies struggle in the open-ended and unpredictable real world, where distribution shifts are effectively infinite. To address this challenge, we introduce an empirical law called ``Rank Stability of Positive Regions'', which states that the relative rank of predicted probabilities for positive voxels remains stable under distribution shift. Guided by this principle, we propose CRISP, a parameter-free and model-agnostic framework requiring no target-domain information. CRISP is the first framework to make segmentation based on rank rather than probabilities. CRISP simulates model behavior under distribution shift via latent feature perturbation, where voxel probability rankings exhibit two stable patterns: regions that consistently retain high probabilities (destined positives according to the principle) and those that remain low-probability (can be safely classified as negatives). Based on these patterns, we construct high-precision (HP) and high-recall (HR) priors and recursively refine them under perturbation. We then design an iterative training framework, making HP and HR progressively ``squeeze'' to the final segmentation. Extensive evaluations on multi-center cardiac MRI and CT-based lung vessel segmentation demonstrate CRISP's superior robustness, significantly outperforming state-of-the-art methods with striking HD95 reductions of up to 0.14 (7.0\% improvement), 1.90 (13.1\% improvement), and 8.39 (38.9\% improvement) pixels across multi-center, demographic, and modality shifts, respectively.