One Uncertainty Field, Two Scales: Gated Anatomy Refinement and Flip-Probability Diagnosis for Liver Tumors

Liver-tumor segmentation and LI-RADS assessment are typically treated as independent modules: a segmentation network produces a mask, and diagnostic features are read off the mask with fixed thresholds, so the confidence of each voxel is discarded at the interface. We show that a single voxel-level uncertainty field $u(\mathbf{x})$, the Shannon entropy of the test-time augmentation posterior of an nnU-Net, operates at two scales. Spatially, $u$ weights a liver shape prior by local uncertainty, so the prior corrects the lesion boundary only where the network is unsure; this converts a prior that is harmful alone ($-0.19$ Dice) into a $+0.030$ Dice improvement on $119$ WAW-TACE CT studies ($0.653\to 0.683$; $80$ improve; paired Wilcoxon signed-rank $p<0.0001$). Diagnostically, a mask threshold wandering through the uncertain band moves all phase means together, parameterizing a lesion-specific feature covariance $\mathbf{\Sigma }(u)$; under a three-feature linear surrogate of LI-RADS (APHE, washout, capsule) rather than the full clinical algorithm, this yields a closed-form Gaussian flip probability $P_{\mathrm{flip}}$, the probability that measurement noise crosses the LI-RADS category boundary and reclassifies the lesion. On the $89$ lesions with a complete diagnostic readout, the propagated noise matches its boundary-perturbation Monte-Carlo reference (correlation $0.812$) but under-estimates the sampled mean flip rate $1.6$-fold ($0.027$ vs. $0.042$), whereas the fixed-noise baseline over-estimates it $4.5$-fold ($0.190$) and correlates poorly ($0.289$). We further show that refinement tends to help the least-stable tier of lesions — all five of the highest-flip-risk lesions stabilized, though this tier is small — while leaving already-confident decisions essentially unchanged. These results suggest that a single voxel-level uncertainty field can bridge segmentation and LI-RADS assessment, turning voxel confidence into both a refinement signal and a lesion-level flip probability.