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

arXiv: https://arxiv.org/abs/2607.13682 · HTML: https://mlsanity.com/paper/2607.13682/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 33 references that are in the map.
- First posted on arXiv 15 Jul 2026.

## Builds on (most cited first, 24 of 24)

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [The Medical Segmentation Decathlon](https://mlsanity.com/paper/2106.05735/) (2021)
- [Solving Inverse Problems in Medical Imaging with Score-Based Generative Models](https://mlsanity.com/paper/2111.08005/) (2021)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Validation, comparison, and combination of algorithms for automatic detection of pulmonary nodules in computed tomography images: the LUNA16 challenge](https://mlsanity.com/paper/1612.08012/) (2016)
- [Uncertainty Estimates and Multi-Hypotheses Networks for Optical Flow](https://mlsanity.com/paper/1802.07095/) (2018)
- [ActiveNeRF: Learning where to See with Uncertainty Estimation](https://mlsanity.com/paper/2209.08546/) (2022)
- [NAF: Neural Attenuation Fields for Sparse-View CBCT Reconstruction](https://mlsanity.com/paper/2209.14540/) (2022)
- [Image-to-Image Regression with Distribution-Free Uncertainty Quantification and Applications in Imaging](https://mlsanity.com/paper/2202.05265/) (2022)
- [Bayes' Rays: Uncertainty Quantification for Neural Radiance Fields](https://mlsanity.com/paper/2309.03185/) (2023)
- [Evaluating and Calibrating Uncertainty Prediction in Regression Tasks](https://mlsanity.com/paper/1905.11659/) (2019)
- [Stochastic Neural Radiance Fields: Quantifying Uncertainty in Implicit 3D Representations](https://mlsanity.com/paper/2109.02123/) (2021)
- [R2-Gaussian: Rectifying Radiative Gaussian Splatting for Tomographic Reconstruction](https://mlsanity.com/paper/2405.20693/) (2024)
- [Deep Bayesian Inversion](https://mlsanity.com/paper/1811.05910/) (2018)
- [Density-aware NeRF Ensembles: Quantifying Predictive Uncertainty in Neural Radiance Fields](https://mlsanity.com/paper/2209.08718/) (2022)
- [Radiative Gaussian Splatting for Efficient X-ray Novel View Synthesis](https://mlsanity.com/paper/2403.04116/) (2024)
- [UncertaINR: Uncertainty Quantification of End-to-End Implicit Neural Representations for Computed Tomography](https://mlsanity.com/paper/2202.10847/) (2022)
- [Uncertainty Quantification for Deep Unrolling-Based Computational Imaging](https://mlsanity.com/paper/2207.00698/) (2022)
- [Variational Bayes Gaussian Splatting](https://mlsanity.com/paper/2410.03592/) (2024)
- [VarSplat: Uncertainty-aware 3D Gaussian Splatting for Robust RGB-D SLAM](https://mlsanity.com/paper/2603.09673/) (2026)
- [Radioactive 3D Gaussian Ray Tracing for Tomographic Reconstruction](https://mlsanity.com/paper/2602.01057/) (2026)
- [Active View Selection with Perturbed Gaussian Ensemble for Tomographic Reconstruction](https://mlsanity.com/paper/2603.06852/) (2026)
- [Rendering-Aware Bayesian 3D Gaussian Splatting with Native Uncertainty and Adaptive Complexity Control](https://mlsanity.com/paper/2607.05522/) (2026)

## Built on by (most cited first, 1 of 1)

- [Image Fidelity is Not Field Fidelity: Joint Thermodynamic Reconstruction and Error Localization in Neural Tomography](https://mlsanity.com/paper/2609.28868/) (2026)

## Abstract (arXiv)

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× 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.