RIR: Relative Intensity Relations for Single-Source Generalization under Unseen Pathology Shifts

Medical domain generalization typically addresses shifts in acquisition conditions, institutions, or patient cohorts, yet costly annotation and fragmented clinical datasets may leave deployment conditions beyond the pathology coverage available during source training. We study brain tumor segmentation under such external shifts and ask which source-derived evidence remains useful when absolute intensity, morphology, and ordinal intensity position may change across tumor categories. We propose Relative Intensity Relation (RIR), a source-only framework that distinguishes absolute intensity from image-internal contrast organization. RIR derives within-volume intensity rank and local intensity ordering from each input, reducing direct dependence on absolute intensity scale while encoding image-internal relations. Because these relations are recomputed from each input, RIR does not transfer a fixed source intensity or morphology template across cohorts. Source segmentation supervision grounds these rank-derived cues into tumor consistency, tumor-background separation, and boundary evidence, which is integrated with the original image representation through a bounded residual correction. The framework further selects its deployment checkpoint and decision threshold using held-out source validation only, without target-domain feedback. Across five source-supervision sizes, RIR achieves the highest mean two-cohort external macro Dice among the compared methods and the highest mean sensitivity on both BraTS-Africa cohorts at all five sizes. The broader comparison also shows substantial degradation beyond the source glioma category across multiple DG strategies. A representation-level diagnostic further shows smaller source-to-target displacement of source-defined tumor scores in the pre-grounding RIR space than in absolute FLAIR. Together, these results support the utility of the complete RIR framework and provide evidence that rank-derived relational structure remains useful under pathology-associated external shifts.