When Variance Is Not an Error Map: Calibrated Uncertainty for Radiative Gaussian Splatting in Sparse-View CT

Abstract

Does an uncertainty map identify where a reconstruction is wrong? In sparse-view computed tomography (CT), we find a sharp gap between whole-volume evaluation and error localization inside the object. We derive clamp-aware analytic moments for factorized Gaussian-density distributions, with a variance pass through existing rendering interfaces that is $7.9\times$ faster than a 16-sample estimator. On a 15-scene benchmark, median variance--error Spearman correlation falls from $0.846$ over the whole volume to $0.108$ in foreground. The pattern recurs across representations and acquisition settings. Two analyses help explain the discrepancy: region contrast dominates global covariance, while $72$--$96\%$ of in-object squared error is shared across independently trained members. Spread is unchanged by a common error, although shared error alone does not determine ranking. Correcting the offset between the deployed reconstruction and predictive mean improves foreground correlation by only $0.0014$. The diagnosis separates two remedies. A log-normal control improves scale transfer without restoring localization; a supervised error predictor raises foreground correlation to $0.427$ on the benchmark and $0.566$ on eight held-out human subjects under simulated acquisition. A verified retrospective re-execution on eight additional subjects retains a median of $0.537$, with the same frozen predictors. The central lesson is to validate uncertainty in the region, and against the error target, for which it will be used.