# POp-GS: Next Best View in 3D-Gaussian Splatting with P-Optimality

arXiv: https://arxiv.org/abs/2503.07819 · HTML: https://mlsanity.com/paper/2503.07819/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 47 references that are in the map.
- First posted on arXiv 10 Mar 2025.

## Builds on (most cited first, 25 of 25)

- [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)
- [Block-NeRF: Scalable Large Scene Neural View Synthesis](https://mlsanity.com/paper/2202.05263/) (2022)
- [Gaussian Splatting SLAM](https://mlsanity.com/paper/2312.06741/) (2023)
- [LangSplat: 3D Language Gaussian Splatting](https://mlsanity.com/paper/2312.16084/) (2023)
- [Laplace Redux -- Effortless Bayesian Deep Learning](https://mlsanity.com/paper/2106.14806/) (2021)
- [Feature 3DGS: Supercharging 3D Gaussian Splatting to Enable Distilled Feature Fields](https://mlsanity.com/paper/2312.03203/) (2023)
- [GS-SLAM: Dense Visual SLAM with 3D Gaussian Splatting](https://mlsanity.com/paper/2311.11700/) (2023)
- [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)
- [3D Gaussian as a New Era: A Survey](https://mlsanity.com/paper/2402.07181/) (2024)
- [PUP 3D-GS: Principled Uncertainty Pruning for 3D Gaussian Splatting](https://mlsanity.com/paper/2406.10219/) (2024)
- [Bayes' Rays: Uncertainty Quantification for Neural Radiance Fields](https://mlsanity.com/paper/2309.03185/) (2023)
- [A Survey on Active Simultaneous Localization and Mapping: State of the Art and New Frontiers](https://mlsanity.com/paper/2207.00254/) (2022)
- [FisherRF: Active View Selection and Uncertainty Quantification for Radiance Fields using Fisher Information](https://mlsanity.com/paper/2311.17874/) (2023)
- [LoopSplat: Loop Closure by Registering 3D Gaussian Splats](https://mlsanity.com/paper/2408.10154/) (2024)
- [Unifying Approaches in Active Learning and Active Sampling via Fisher Information and Information-Theoretic Quantities](https://mlsanity.com/paper/2208.00549/) (2022)
- [Modeling Uncertainty in 3D Gaussian Splatting through Continuous Semantic Splatting](https://mlsanity.com/paper/2411.02547/) (2024)
- [ConvBKI: Real-Time Probabilistic Semantic Mapping Network with Quantifiable Uncertainty](https://mlsanity.com/paper/2310.16020/) (2023)
- [Beyond Uncertainty: Risk-Aware Active View Acquisition for Safe Robot Navigation and 3D Scene Understanding with FisherRF](https://mlsanity.com/paper/2403.11396/) (2024)
- [Next Best Sense: Guiding Vision and Touch with FisherRF for 3D Gaussian Splatting](https://mlsanity.com/paper/2410.04680/) (2024)
- [Gaussian Process Autonomous Mapping and Exploration for Range Sensing Mobile Robots](https://mlsanity.com/paper/1605.00335/) (2016)
- [ExplORB-SLAM: Active Visual SLAM Exploiting the Pose-graph Topology](https://mlsanity.com/paper/2209.03693/) (2022)
- [A General Relationship between Optimality Criteria and Connectivity Indices for Active Graph-SLAM](https://mlsanity.com/paper/2110.01289/) (2021)

## Built on by (most cited first, 18 of 18)

- [SpeeDe3DGS: Speedy Deformable 3D Gaussian Splatting with Temporal Pruning and Motion Grouping](https://mlsanity.com/paper/2506.07917/) (2025)
- [Predictive Photometric Uncertainty in Gaussian Splatting for Novel View Synthesis](https://mlsanity.com/paper/2603.22786/) (2026)
- [Active Next-Best-View Optimization for Risk-Averse Path Planning](https://mlsanity.com/paper/2510.06481/) (2025)
- [SA-ResGS: Self-Augmented Residual 3D Gaussian Splatting for Next Best View Selection](https://mlsanity.com/paper/2601.03024/) (2026)
- [Active View Selection with Perturbed Gaussian Ensemble for Tomographic Reconstruction](https://mlsanity.com/paper/2603.06852/) (2026)
- [Hestia: Voxel-Face-Aware Hierarchical Next-Best-View Acquisition for Efficient 3D Reconstruction](https://mlsanity.com/paper/2508.01014/) (2025)
- [Informative Object-centric Next Best View for Object-aware 3D Gaussian Splatting in Cluttered Scenes](https://mlsanity.com/paper/2602.08266/) (2026)
- [Diversity-aware View Partitioning for Scalable VGGT](https://mlsanity.com/paper/2607.01885/) (2026)
- [GO-PRE: Goal-Oriented Next-Best-View Selection via Predictive Rendering Entropy for Active 3D Reconstruction](https://mlsanity.com/paper/2607.29037/) (2026)
- [OUGS: Active View Selection via Object-aware Uncertainty Estimation in 3DGS](https://mlsanity.com/paper/2511.09397/) (2025)
- [Evaluating Time Awareness and Cross-modal Active Perception of Large Models via 4D Escape Room Task](https://mlsanity.com/paper/2603.15467/) (2026)
- [Information-Regularized Constrained Inversion for Stable Avatar Editing from Sparse Supervision](https://mlsanity.com/paper/2604.02883/) (2026)
- [Scene-SAM3D: Multi-View Scene Asset Generation Without Fine-Tuning](https://mlsanity.com/paper/2607.16805/) (2026)
- [FillGS: Filling Observation Gaps in 4D Gaussian Splatting via Viewpoint-Time Selection and Generative Refinement](https://mlsanity.com/paper/2607.29284/) (2026)
- [TRACE: Ergodic Trajectory Optimization for Active Scene Reconstruction](https://mlsanity.com/paper/2608.02304/) (2026)
- [LiTe-GS: Oracle-Efficient Next Best View Selection for 3D Gaussian Splatting](https://mlsanity.com/paper/2609.30393/) (2026)
- [AGILE-GS: Anchor-Guided Fast Next-Best-View Selection for Active 3D Gaussian Splatting](https://mlsanity.com/paper/2609.34176/) (2026)
- [UGOD: Uncertainty-Guided Opacity and Dropout for Sparse-View 3D Gaussian Splatting](https://mlsanity.com/paper/2609.39089/) (2026)

## Abstract (arXiv)

In this paper, we present a novel algorithm for quantifying uncertainty and information gained within 3D Gaussian Splatting (3D-GS) through P-Optimality. While 3D-GS has proven to be a useful world model with high-quality rasterizations, it does not natively quantify uncertainty or information, posing a challenge for real-world applications such as 3D-GS SLAM. We propose to quantify information gain in 3D-GS by reformulating the problem through the lens of optimal experimental design, which is a classical solution widely used in literature. By restructuring information quantification of 3D-GS through optimal experimental design, we arrive at multiple solutions, of which T-Optimality and D-Optimality perform the best quantitatively and qualitatively as measured on two popular datasets. Additionally, we propose a block diagonal covariance approximation which provides a measure of correlation at the expense of a greater computation cost.