# Neural Visibility Field for Uncertainty-Driven Active Mapping

arXiv: https://arxiv.org/abs/2406.06948 · HTML: https://mlsanity.com/paper/2406.06948/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- Builds on 36 of its 58 references that are in the map.
- First posted on arXiv 11 Jun 2024.

## Builds on (most cited first, 30 of 36)

- [The Unreasonable Effectiveness of Deep Features as a Perceptual Metric](https://mlsanity.com/paper/1801.03924/) (2018)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DreamFusion: Text-to-3D using 2D Diffusion](https://mlsanity.com/paper/2209.14988/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [NeRF in the Wild: Neural Radiance Fields for Unconstrained Photo Collections](https://mlsanity.com/paper/2008.02268/) (2020)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [Depth-supervised NeRF: Fewer Views and Faster Training for Free](https://mlsanity.com/paper/2107.02791/) (2021)
- [BARF: Bundle-Adjusting Neural Radiance Fields](https://mlsanity.com/paper/2104.06405/) (2021)
- [RegNeRF: Regularizing Neural Radiance Fields for View Synthesis from Sparse Inputs](https://mlsanity.com/paper/2112.00724/) (2021)
- [Nerfstudio: A Modular Framework for Neural Radiance Field Development](https://mlsanity.com/paper/2302.04264/) (2023)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Zero-Shot Text-Guided Object Generation with Dream Fields](https://mlsanity.com/paper/2112.01455/) (2021)
- [iMAP: Implicit Mapping and Positioning in Real-Time](https://mlsanity.com/paper/2103.12352/) (2021)
- [Space-time Neural Irradiance Fields for Free-Viewpoint Video](https://mlsanity.com/paper/2011.12950/) (2020)
- [Neural RGB-D Surface Reconstruction](https://mlsanity.com/paper/2104.04532/) (2021)
- [FreeNeRF: Improving Few-shot Neural Rendering with Free Frequency Regularization](https://mlsanity.com/paper/2303.07418/) (2023)
- [Neural Radiance Flow for 4D View Synthesis and Video Processing](https://mlsanity.com/paper/2012.09790/) (2020)
- [Stereo Radiance Fields (SRF): Learning View Synthesis for Sparse Views of Novel Scenes](https://mlsanity.com/paper/2104.06935/) (2021)
- [ActiveNeRF: Learning where to See with Uncertainty Estimation](https://mlsanity.com/paper/2209.08546/) (2022)
- [Occupancy Anticipation for Efficient Exploration and Navigation](https://mlsanity.com/paper/2008.09285/) (2020)
- [Stochastic Neural Radiance Fields: Quantifying Uncertainty in Implicit 3D Representations](https://mlsanity.com/paper/2109.02123/) (2021)
- [Density-aware NeRF Ensembles: Quantifying Predictive Uncertainty in Neural Radiance Fields](https://mlsanity.com/paper/2209.08718/) (2022)
- [NeurAR: Neural Uncertainty for Autonomous 3D Reconstruction with Implicit Neural Representations](https://mlsanity.com/paper/2207.10985/) (2022)
- [Uncertainty Guided Policy for Active Robotic 3D Reconstruction using Neural Radiance Fields](https://mlsanity.com/paper/2209.08409/) (2022)
- [NeU-NBV: Next Best View Planning Using Uncertainty Estimation in Image-Based Neural Rendering](https://mlsanity.com/paper/2303.01284/) (2023)
- [Uncertainty-driven Planner for Exploration and Navigation](https://mlsanity.com/paper/2202.11907/) (2022)
- [ActiveRMAP: Radiance Field for Active Mapping And Planning](https://mlsanity.com/paper/2211.12656/) (2022)
- [BNV-Fusion: Dense 3D Reconstruction using Bi-level Neural Volume Fusion](https://mlsanity.com/paper/2204.01139/) (2022)
- [Active Implicit Object Reconstruction using Uncertainty-guided Next-Best-View Optimization](https://mlsanity.com/paper/2303.16739/) (2023)

## Built on by (most cited first, 26 of 26)

- [Toward Real-world BEV Perception: Depth Uncertainty Estimation via Gaussian Splatting](https://mlsanity.com/paper/2504.01957/) (2025)
- [Peering into the Unknown: Active View Selection with Neural Uncertainty Maps for 3D Reconstruction](https://mlsanity.com/paper/2506.14856/) (2025)
- [Uncertainty-driven 3D Gaussian Splatting Active Mapping via Anisotropic Visibility Field](https://mlsanity.com/paper/2605.30342/) (2026)
- [Frequency-based View Selection in Gaussian Splatting Reconstruction](https://mlsanity.com/paper/2409.16470/) (2024)
- [Auto3R: Automated 3D Reconstruction and Scanning via Data-driven Uncertainty Quantification](https://mlsanity.com/paper/2512.04528/) (2025)
- [Towards a Science Exocortex](https://mlsanity.com/paper/2406.17809/) (2024)
- [Uni-SLAM: Uncertainty-Aware Neural Implicit SLAM for Real-Time Dense Indoor Scene Reconstruction](https://mlsanity.com/paper/2412.00242/) (2024)
- [WarpRF: Multi-View Consistency for Training-Free Uncertainty Quantification and Applications in Radiance Fields](https://mlsanity.com/paper/2506.22433/) (2025)
- [Confidence-Based Mesh Extraction from 3D Gaussians](https://mlsanity.com/paper/2603.24725/) (2026)
- [ObjSplat: Geometry-Aware Gaussian Surfels for Active Object Reconstruction](https://mlsanity.com/paper/2601.06997/) (2026)
- [The Semantic Lifecycle in Embodied AI: Acquisition, Representation and Storage via Foundation Models](https://mlsanity.com/paper/2601.08876/) (2026)
- [Active View Selection with Perturbed Gaussian Ensemble for Tomographic Reconstruction](https://mlsanity.com/paper/2603.06852/) (2026)
- [OA-NBV: Occlusion-Aware Next-Best-View Planning for Human-Centered Active Perception on Mobile Robots](https://mlsanity.com/paper/2603.11072/) (2026)
- [Coverage Optimization for Camera View Selection](https://mlsanity.com/paper/2604.05259/) (2026)
- [Camera Calibration via Circular Patterns: A Comprehensive Framework with Detection Uncertainty and Unbiased Projection Model](https://mlsanity.com/paper/2506.16842/) (2025)
- [Data Augmentation for NeRFs in the Low Data Limit](https://mlsanity.com/paper/2503.02092/) (2025)
- [Geometry-Aware Scene Configurations for Novel View Synthesis](https://mlsanity.com/paper/2510.09880/) (2025)
- [OUGS: Active View Selection via Object-aware Uncertainty Estimation in 3DGS](https://mlsanity.com/paper/2511.09397/) (2025)
- [SonoSelect: Efficient Ultrasound Perception via Active Probe Exploration](https://mlsanity.com/paper/2604.05933/) (2026)
- [MU-GeNeRF: Multi-view Uncertainty-guided Generalizable Neural Radiance Fields for Distractor-aware Scene](https://mlsanity.com/paper/2604.17965/) (2026)
- [PInVerify: An Offline Embodied Benchmark for Active Instance Verification](https://mlsanity.com/paper/2605.30639/) (2026)
- [TRACE: Ergodic Trajectory Optimization for Active Scene Reconstruction](https://mlsanity.com/paper/2608.02304/) (2026)
- [DA-NBV: A Direction-Aware Next-Best-View Planner for Efficient 3D Reconstruction of Ships at Sea](https://mlsanity.com/paper/2608.08025/) (2026)
- [Filling the Unseen: Scene Extrapolation via 3D Gaussian Splatting](https://mlsanity.com/paper/2609.13262/) (2026)
- [Matisse: Evidence-Space Reasoning for Active 3D Reconstruction](https://mlsanity.com/paper/2609.38746/) (2026)
- [VCURF: Virtual Camera-based Uncertainty of Radiance Fields](https://mlsanity.com/paper/2610.04076/) (2026)

## Abstract (arXiv)

This paper presents Neural Visibility Field (NVF), a novel uncertainty quantification method for Neural Radiance Fields (NeRF) applied to active mapping. Our key insight is that regions not visible in the training views lead to inherently unreliable color predictions by NeRF at this region, resulting in increased uncertainty in the synthesized views. To address this, we propose to use Bayesian Networks to composite position-based field uncertainty into ray-based uncertainty in camera observations. Consequently, NVF naturally assigns higher uncertainty to unobserved regions, aiding robots to select the most informative next viewpoints. Extensive evaluations show that NVF excels not only in uncertainty quantification but also in scene reconstruction for active mapping, outperforming existing methods.