# PRIMU: Uncertainty Estimation for Novel Views in Gaussian Splatting from Primitive-Based Representations of Error and Coverage

arXiv: https://arxiv.org/abs/2508.02443 · HTML: https://mlsanity.com/paper/2508.02443/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 48 references that are in the map.
- First posted on arXiv 4 Aug 2025.

## Builds on (most cited first, 29 of 29)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Mip-NeRF 360: Unbounded Anti-Aliased Neural Radiance Fields](https://mlsanity.com/paper/2111.12077/) (2021)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [Gaussian Splatting SLAM](https://mlsanity.com/paper/2312.06741/) (2023)
- [Gaussian Grouping: Segment and Edit Anything in 3D Scenes](https://mlsanity.com/paper/2312.00732/) (2023)
- [WildGaussians: 3D Gaussian Splatting in the Wild](https://mlsanity.com/paper/2407.08447/) (2024)
- [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)
- [CoR-GS: Sparse-View 3D Gaussian Splatting via Co-Regularization](https://mlsanity.com/paper/2405.12110/) (2024)
- [Bayes' Rays: Uncertainty Quantification for Neural Radiance Fields](https://mlsanity.com/paper/2309.03185/) (2023)
- [Nerfbusters: Removing Ghostly Artifacts from Casually Captured NeRFs](https://mlsanity.com/paper/2304.10532/) (2023)
- [Conditional-Flow NeRF: Accurate 3D Modelling with Reliable Uncertainty Quantification](https://mlsanity.com/paper/2203.10192/) (2022)
- [FisherRF: Active View Selection and Uncertainty Quantification for Radiance Fields using Fisher Information](https://mlsanity.com/paper/2311.17874/) (2023)
- [Density-aware NeRF Ensembles: Quantifying Predictive Uncertainty in Neural Radiance Fields](https://mlsanity.com/paper/2209.08718/) (2022)
- [Relaxing Accurate Initialization Constraint for 3D Gaussian Splatting](https://mlsanity.com/paper/2403.09413/) (2024)
- [An Uncertainty-aware Transfer Learning-based Framework for Covid-19 Diagnosis](https://mlsanity.com/paper/2007.14846/) (2020)
- [Learning Barrier Functions with Memory for Robust Safe Navigation](https://mlsanity.com/paper/2011.01899/) (2020)
- [Improving NeRF Quality by Progressive Camera Placement for Unrestricted Navigation in Complex Environments](https://mlsanity.com/paper/2309.00014/) (2023)
- [Modeling uncertainty for Gaussian Splatting](https://mlsanity.com/paper/2403.18476/) (2024)
- [Manifold Sampling for Differentiable Uncertainty in Radiance Fields](https://mlsanity.com/paper/2409.12661/) (2024)
- [Modeling Uncertainty in 3D Gaussian Splatting through Continuous Semantic Splatting](https://mlsanity.com/paper/2411.02547/) (2024)
- [Evaluating Human Perception of Novel View Synthesis: Subjective Quality Assessment of Gaussian Splatting and NeRF in Dynamic Scenes](https://mlsanity.com/paper/2501.08072/) (2025)
- [Differentiable and accelerated spherical harmonic and Wigner transforms](https://mlsanity.com/paper/2311.14670/) (2023)
- [View-Dependent Uncertainty Estimation of 3D Gaussian Splatting](https://mlsanity.com/paper/2504.07370/) (2025)
- [Instant Uncertainty Calibration of NeRFs Using a Meta-Calibrator](https://mlsanity.com/paper/2312.02350/) (2023)
- [ProvNeRF: Modeling per Point Provenance in NeRFs as a Stochastic Field](https://mlsanity.com/paper/2401.08140/) (2024)

## Built on by (most cited first, 6 of 6)

- [Predictive Photometric Uncertainty in Gaussian Splatting for Novel View Synthesis](https://mlsanity.com/paper/2603.22786/) (2026)
- [SA-ResGS: Self-Augmented Residual 3D Gaussian Splatting for Next Best View Selection](https://mlsanity.com/paper/2601.03024/) (2026)
- [GO-PRE: Goal-Oriented Next-Best-View Selection via Predictive Rendering Entropy for Active 3D Reconstruction](https://mlsanity.com/paper/2607.29037/) (2026)
- [Mind the Gap: Standard 3DGS Evaluation Primarily Measures Near-Trajectory Interpolation](https://mlsanity.com/paper/2607.01556/) (2026)
- [UGOD: Uncertainty-Guided Opacity and Dropout for Sparse-View 3D Gaussian Splatting](https://mlsanity.com/paper/2609.39089/) (2026)
- [VCURF: Virtual Camera-based Uncertainty of Radiance Fields](https://mlsanity.com/paper/2610.04076/) (2026)

## Abstract (arXiv)

We introduce Primitive-based Representations of Uncertainty (PRIMU), a post-hoc uncertainty estimation (UE) framework for Gaussian Splatting (GS). Reliable UE is essential for deploying GS in safety-critical domains such as robotics and medicine. Existing approaches typically estimate Gaussian-primitive variances and rely on the rendering process to obtain pixel-wise uncertainties. In contrast, we construct primitive-level representations of error and visibility/coverage from training views, capturing interpretable uncertainty information. These representations are obtained by projecting view-dependent training errors and coverage statistics onto the primitives. Uncertainties for novel views are inferred by rendering these primitive-level representations, producing uncertainty feature maps, which are aggregate through pixel-wise regression on holdout data. We analyze combinations of uncertainty feature maps and regression models to understand how their interactions affect prediction accuracy and generalization. PRIMU also enables an effective active view selection strategy by directly leveraging these uncertainty feature maps. Additionally, we study the effect of separating splatting into foreground and background regions. Our estimates show strong correlations with true errors, outperforming state-of-the-art methods, especially for depth UE and foreground objects. Finally, our regression models show generalization capabilities to unseen scenes, enabling UE without additional holdout data.