# Neural Density-Distance Fields

arXiv: https://arxiv.org/abs/2207.14455 · HTML: https://mlsanity.com/paper/2207.14455/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 29 references that are in the map.
- First posted on arXiv 29 Jul 2022.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Neural Scene Flow Fields for Space-Time View Synthesis of Dynamic Scenes](https://mlsanity.com/paper/2011.13084/) (2020)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [BARF: Bundle-Adjusting Neural Radiance Fields](https://mlsanity.com/paper/2104.06405/) (2021)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [Non-Rigid Neural Radiance Fields: Reconstruction and Novel View Synthesis of a Dynamic Scene From Monocular Video](https://mlsanity.com/paper/2012.12247/) (2020)
- [SAL: Sign Agnostic Learning of Shapes from Raw Data](https://mlsanity.com/paper/1911.10414/) (2019)
- [INeRF: Inverting Neural Radiance Fields for Pose Estimation](https://mlsanity.com/paper/2012.05877/) (2020)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Learning to Optimize Non-Rigid Tracking](https://mlsanity.com/paper/2003.12230/) (2020)
- [TanhExp: A Smooth Activation Function with High Convergence Speed for Lightweight Neural Networks](https://mlsanity.com/paper/2003.09855/) (2020)
- [SplitFusion: Simultaneous Tracking and Mapping for Non-Rigid Scenes](https://mlsanity.com/paper/2007.02108/) (2020)

## Built on by (most cited first, 9 of 9)

- [RealFusion: 360deg Reconstruction of Any Object from a Single Image](https://mlsanity.com/paper/2302.10663/) (2023)
- [Delicate Textured Mesh Recovery from NeRF via Adaptive Surface Refinement](https://mlsanity.com/paper/2303.02091/) (2023)
- [NeO 360: Neural Fields for Sparse View Synthesis of Outdoor Scenes](https://mlsanity.com/paper/2308.12967/) (2023)
- [SHINOBI: Shape and Illumination using Neural Object Decomposition via BRDF Optimization In-the-wild](https://mlsanity.com/paper/2401.10171/) (2024)
- [The Sky's the Limit: Re-lightable Outdoor Scenes via a Sky-pixel Constrained Illumination Prior and Outside-In Visibility](https://mlsanity.com/paper/2311.16937/) (2023)
- [Unsigned Orthogonal Distance Fields: An Accurate Neural Implicit Representation for Diverse 3D Shapes](https://mlsanity.com/paper/2403.01414/) (2024)
- [Factored Neural Representation for Scene Understanding](https://mlsanity.com/paper/2304.10950/) (2023)
- [L0-Sampler: An L0 Model Guided Volume Sampling for NeRF](https://mlsanity.com/paper/2311.07044/) (2023)
- [DyGASR: Dynamic Generalized Exponential Splatting with Surface Alignment for Accelerated 3D Mesh Reconstruction](https://mlsanity.com/paper/2411.09156/) (2024)

## Abstract (arXiv)

The success of neural fields for 3D vision tasks is now indisputable. Following this trend, several methods aiming for visual localization (e.g., SLAM) have been proposed to estimate distance or density fields using neural fields. However, it is difficult to achieve high localization performance by only density fields-based methods such as Neural Radiance Field (NeRF) since they do not provide density gradient in most empty regions. On the other hand, distance field-based methods such as Neural Implicit Surface (NeuS) have limitations in objects' surface shapes. This paper proposes Neural Density-Distance Field (NeDDF), a novel 3D representation that reciprocally constrains the distance and density fields. We extend distance field formulation to shapes with no explicit boundary surface, such as fur or smoke, which enable explicit conversion from distance field to density field. Consistent distance and density fields realized by explicit conversion enable both robustness to initial values and high-quality registration. Furthermore, the consistency between fields allows fast convergence from sparse point clouds. Experiments show that NeDDF can achieve high localization performance while providing comparable results to NeRF on novel view synthesis. The code is available at https://github.com/ueda0319/neddf.