Beyond morphological dilation: Revisiting conformal prediction for 3D tumor segmentation

Deep learning has achieved remarkable performance for tu mor segmentation, yet high overlap scores do not necessarily imply re liable boundary delineation or complete identification of disconnected tumor foci. While uncertainty quantification methods provide voxel-wise confidence estimates, conformal prediction (CP) offers finite-sample cov erage guarantees through calibrated prediction sets. Existing CP meth ods for image segmentation commonly rely on morphological dilation. We show that this construction becomes vacuous in the presence of dis connected segmentation errors: missed tumor components saturate the calibrated score, producing prediction sets that preserve formal coverage while becoming operationally uninformative. We characterize this failure mode through the distinction between formal and operational coverage, and propose two complementary extensions. Instance-level CP separates boundary and structural errors, whereas Geodesic CP replaces isotropic dilation with confidence-guided expansion, and we combine both in a uni fied formulation. On BraTS 2021, across 100 calibration/test splits, the unified formulation eliminates vacuity while preserving split-conformal validity. The code is available at: https://github.com/robustml-eurecom/ conformal-tumor-segmentation.git