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. Code are available at https://github.com/Eurekashen/R2Seg.