# PNeRF: Probabilistic Neural Scene Representations for Uncertain 3D Visual Mapping

arXiv: https://arxiv.org/abs/2209.11677 · HTML: https://mlsanity.com/paper/2209.11677/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 41 references that are in the map.
- First posted on arXiv 23 Sep 2022.

## Builds on (most cited first, 23 of 23)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [pixelNeRF: Neural Radiance Fields from One or Few Images](https://mlsanity.com/paper/2012.02190/) (2020)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [NeRF++: Analyzing and Improving Neural Radiance Fields](https://mlsanity.com/paper/2010.07492/) (2020)
- [Depth-supervised NeRF: Fewer Views and Faster Training for Free](https://mlsanity.com/paper/2107.02791/) (2021)
- [Local Light Field Fusion: Practical View Synthesis with Prescriptive Sampling Guidelines](https://mlsanity.com/paper/1905.00889/) (2019)
- [BARF: Bundle-Adjusting Neural Radiance Fields](https://mlsanity.com/paper/2104.06405/) (2021)
- [NICE-SLAM: Neural Implicit Scalable Encoding for SLAM](https://mlsanity.com/paper/2112.12130/) (2021)
- [iMAP: Implicit Mapping and Positioning in Real-Time](https://mlsanity.com/paper/2103.12352/) (2021)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [INeRF: Inverting Neural Radiance Fields for Pose Estimation](https://mlsanity.com/paper/2012.05877/) (2020)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [SynSin: End-to-end View Synthesis from a Single Image](https://mlsanity.com/paper/1912.08804/) (2019)
- [DONeRF: Towards Real-Time Rendering of Compact Neural Radiance Fields using Depth Oracle Networks](https://mlsanity.com/paper/2103.03231/) (2021)
- [NeX: Real-time View Synthesis with Neural Basis Expansion](https://mlsanity.com/paper/2103.05606/) (2021)
- [Self-Calibrating Neural Radiance Fields](https://mlsanity.com/paper/2108.13826/) (2021)
- [NerfingMVS: Guided Optimization of Neural Radiance Fields for Indoor Multi-view Stereo](https://mlsanity.com/paper/2109.01129/) (2021)
- [NeRF--: Neural Radiance Fields Without Known Camera Parameters](https://mlsanity.com/paper/2102.07064/) (2021)
- [Vision-Only Robot Navigation in a Neural Radiance World](https://mlsanity.com/paper/2110.00168/) (2021)
- [NeRF-Supervision: Learning Dense Object Descriptors from Neural Radiance Fields](https://mlsanity.com/paper/2203.01913/) (2022)
- [Learning Signed Distance Field for Multi-view Surface Reconstruction](https://mlsanity.com/paper/2108.09964/) (2021)
- [Mip-NeRF RGB-D: Depth Assisted Fast Neural Radiance Fields](https://mlsanity.com/paper/2205.09351/) (2022)

## Abstract (arXiv)

Recently neural scene representations have provided very impressive results for representing 3D scenes visually, however, their study and progress have mainly been limited to visualization of virtual models in computer graphics or scene reconstruction in computer vision without explicitly accounting for sensor and pose uncertainty. Using this novel scene representation in robotics applications, however, would require accounting for this uncertainty in the neural map. The aim of this paper is therefore to propose a novel method for training em probabilistic neural scene representations with uncertain training data that could enable the inclusion of these representations in robotics applications. Acquiring images using cameras or depth sensors contains inherent uncertainty, and furthermore, the camera poses used for learning a 3D model are also imperfect. If these measurements are used for training without accounting for their uncertainty, then the resulting models are non-optimal, and the resulting scene representations are likely to contain artifacts such as blur and un-even geometry. In this work, the problem of uncertainty integration to the learning process is investigated by focusing on training with uncertain information in a probabilistic manner. The proposed method involves explicitly augmenting the training likelihood with an uncertainty term such that the learnt probability distribution of the network is minimized with respect to the training uncertainty. It will be shown that this leads to more accurate image rendering quality, in addition to more precise and consistent geometry. Validation has been carried out on both synthetic and real datasets showing that the proposed approach outperforms state-of-the-art methods. The results show notably that the proposed method is capable of rendering novel high-quality views even when the training data is limited.