# 3D Density-Gradient based Edge Detection on Neural Radiance Fields (NeRFs) for Geometric Reconstruction

arXiv: https://arxiv.org/abs/2309.14800 · HTML: https://mlsanity.com/paper/2309.14800/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 24 references that are in the map.
- First posted on arXiv 26 Sep 2023.

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

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [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)
- [Plenoxels: Radiance Fields without Neural Networks](https://mlsanity.com/paper/2112.05131/) (2021)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Scene Representation Networks: Continuous 3D-Structure-Aware Neural Scene Representations](https://mlsanity.com/paper/1906.01618/) (2019)
- [Block-NeRF: Scalable Large Scene Neural View Synthesis](https://mlsanity.com/paper/2202.05263/) (2022)
- [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)
- [FastNeRF: High-Fidelity Neural Rendering at 200FPS](https://mlsanity.com/paper/2103.10380/) (2021)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [Dynamic View Synthesis from Dynamic Monocular Video](https://mlsanity.com/paper/2105.06468/) (2021)
- [Mega-NeRF: Scalable Construction of Large-Scale NeRFs for Virtual Fly-Throughs](https://mlsanity.com/paper/2112.10703/) (2021)
- [Improving neural implicit surfaces geometry with patch warping](https://mlsanity.com/paper/2112.09648/) (2021)
- [GARF: Gaussian Activated Radiance Fields for High Fidelity Reconstruction and Pose Estimation](https://mlsanity.com/paper/2204.05735/) (2022)
- [AdaNeRF: Adaptive Sampling for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2207.10312/) (2022)
- [A Comparative Neural Radiance Field (NeRF) 3D Analysis of Camera Poses from HoloLens Trajectories and Structure from Motion](https://mlsanity.com/paper/2304.10664/) (2023)

## Built on by (most cited first, 4 of 4)

- [Density Uncertainty Quantification with NeRF-Ensembles: Impact of Data and Scene Constraints](https://mlsanity.com/paper/2312.14664/) (2023)
- [HoloGS: Instant Depth-based 3D Gaussian Splatting with Microsoft HoloLens 2](https://mlsanity.com/paper/2405.02005/) (2024)
- [FeatureGS: Eigenvalue-Feature Optimization in 3D Gaussian Splatting for Geometrically Accurate and Artifact-Reduced Reconstruction](https://mlsanity.com/paper/2501.17655/) (2025)
- [EntON: Eigenentropy-Optimized Neighborhood Densification in 3D Gaussian Splatting](https://mlsanity.com/paper/2603.06216/) (2026)

## Abstract (arXiv)

Generating geometric 3D reconstructions from Neural Radiance Fields (NeRFs) is of great interest. However, accurate and complete reconstructions based on the density values are challenging. The network output depends on input data, NeRF network configuration and hyperparameter. As a result, the direct usage of density values, e.g. via filtering with global density thresholds, usually requires empirical investigations. Under the assumption that the density increases from non-object to object area, the utilization of density gradients from relative values is evident. As the density represents a position-dependent parameter it can be handled anisotropically, therefore processing of the voxelized 3D density field is justified. In this regard, we address geometric 3D reconstructions based on density gradients, whereas the gradients result from 3D edge detection filters of the first and second derivatives, namely Sobel, Canny and Laplacian of Gaussian. The gradients rely on relative neighboring density values in all directions, thus are independent from absolute magnitudes. Consequently, gradient filters are able to extract edges along a wide density range, almost independent from assumptions and empirical investigations. Our approach demonstrates the capability to achieve geometric 3D reconstructions with high geometric accuracy on object surfaces and remarkable object completeness. Notably, Canny filter effectively eliminates gaps, delivers a uniform point density, and strikes a favorable balance between correctness and completeness across the scenes.