R$^2$-Seg: Training-Free OOD Medical Tumor Segmentation via Anatomical Reasoning and Statistical Rejection

Foundation models for medical image segmentation struggle under out-of-distribution (OOD) shifts, often producing fragmented false positives on OOD tumors. We introduce **R$^2$-Seg**, a **training-free** framework for robust OOD tumor segmentation that operates via a two-stage **Reason-and-Reject** process. First, the **Reason** step employs an LLM-guided anatomical reasoning planner to localize organ anchors and generate multi-scale ROIs. Second, the **Reject** step applies two-sample statistical testing to candidates generated by a frozen foundation model (BiomedParse) within these ROIs. This statistical rejection filter retains only candidates significantly different from normal tissue, effectively suppressing false positives. Our framework requires no parameter updates, making it compatible with zero-update test-time augmentation and avoiding catastrophic forgetting. On multi-center and multi-modal tumor segmentation benchmarks, **R$^2$-Seg** substantially improves Dice, specificity, and sensitivity over strong baselines and the original foundation models.