# NEF: Neural Edge Fields for 3D Parametric Curve Reconstruction from Multi-view Images

arXiv: https://arxiv.org/abs/2303.07653 · HTML: https://mlsanity.com/paper/2303.07653/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 45 references that are in the map.
- First posted on arXiv 14 Mar 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction](https://mlsanity.com/paper/2106.10689/) (2021)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [Direct Voxel Grid Optimization: Super-fast Convergence for Radiance Fields Reconstruction](https://mlsanity.com/paper/2111.11215/) (2021)
- [PlenOctrees for Real-time Rendering of Neural Radiance Fields](https://mlsanity.com/paper/2103.14024/) (2021)
- [GIRAFFE: Representing Scenes as Compositional Generative Neural Feature Fields](https://mlsanity.com/paper/2011.12100/) (2020)
- [GRAF: Generative Radiance Fields for 3D-Aware Image Synthesis](https://mlsanity.com/paper/2007.02442/) (2020)
- [KiloNeRF: Speeding up Neural Radiance Fields with Thousands of Tiny MLPs](https://mlsanity.com/paper/2103.13744/) (2021)
- [UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction](https://mlsanity.com/paper/2104.10078/) (2021)
- [Baking Neural Radiance Fields for Real-Time View Synthesis](https://mlsanity.com/paper/2103.14645/) (2021)
- [CLIP-NeRF: Text-and-Image Driven Manipulation of Neural Radiance Fields](https://mlsanity.com/paper/2112.05139/) (2021)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [MobileNeRF: Exploiting the Polygon Rasterization Pipeline for Efficient Neural Field Rendering on Mobile Architectures](https://mlsanity.com/paper/2208.00277/) (2022)
- [A General and Adaptive Robust Loss Function](https://mlsanity.com/paper/1701.03077/) (2017)
- [Editing Conditional Radiance Fields](https://mlsanity.com/paper/2105.06466/) (2021)
- [NeRF-Editing: Geometry Editing of Neural Radiance Fields](https://mlsanity.com/paper/2205.04978/) (2022)
- [Pixel Difference Networks for Efficient Edge Detection](https://mlsanity.com/paper/2108.07009/) (2021)
- [NeRF: Neural Radiance Field in 3D Vision: A Comprehensive Review (Updated Post-Gaussian Splatting)](https://mlsanity.com/paper/2210.00379/) (2022)
- [EC-Net: an Edge-aware Point set Consolidation Network](https://mlsanity.com/paper/1807.06010/) (2018)
- [BlenderProc](https://mlsanity.com/paper/1911.01911/) (2019)
- [PIE-NET: Parametric Inference of Point Cloud Edges](https://mlsanity.com/paper/2007.04883/) (2020)
- [Neural Volume Rendering: NeRF And Beyond](https://mlsanity.com/paper/2101.05204/) (2020)
- [PC2WF: 3D Wireframe Reconstruction from Raw Point Clouds](https://mlsanity.com/paper/2103.02766/) (2021)

## Built on by (most cited first, 22 of 22)

- [3Doodle: Compact Abstraction of Objects with 3D Strokes](https://mlsanity.com/paper/2402.03690/) (2024)
- [Sketch and Patch: Efficient 3D Gaussian Representation for Man-Made Scenes](https://mlsanity.com/paper/2501.13045/) (2025)
- [3D Neural Edge Reconstruction](https://mlsanity.com/paper/2405.19295/) (2024)
- [EdgeGaussians -- 3D Edge Mapping via Gaussian Splatting](https://mlsanity.com/paper/2409.12886/) (2024)
- [Curve-Aware Gaussian Splatting for 3D Parametric Curve Reconstruction](https://mlsanity.com/paper/2506.21401/) (2025)
- [Diff3DS: Generating View-Consistent 3D Sketch via Differentiable Curve Rendering](https://mlsanity.com/paper/2405.15305/) (2024)
- [Parametric Primitive Analysis of CAD Sketches with Vision Transformer](https://mlsanity.com/paper/2407.00410/) (2024)
- [SketchSplat: 3D Edge Reconstruction via Differentiable Multi-view Sketch Splatting](https://mlsanity.com/paper/2503.14786/) (2025)
- [Relighting Scenes with Object Insertions in Neural Radiance Fields](https://mlsanity.com/paper/2406.14806/) (2024)
- [WIR3D: Visually-Informed and Geometry-Aware 3D Shape Abstraction](https://mlsanity.com/paper/2505.04813/) (2025)
- [MV2Cyl: Reconstructing 3D Extrusion Cylinders from Multi-View Images](https://mlsanity.com/paper/2406.10853/) (2024)
- [LineGS : 3D Line Segment Representation on 3D Gaussian Splatting](https://mlsanity.com/paper/2412.00477/) (2024)
- [EDCSSM: Edge Detection with Convolutional State Space Model](https://mlsanity.com/paper/2409.01609/) (2024)
- [Empowering Vector Graphics with Consistently Arbitrary Viewing and View-dependent Visibility](https://mlsanity.com/paper/2505.21377/) (2025)
- [Sketch&Patch++: Efficient Structure-Aware 3D Gaussian Representation](https://mlsanity.com/paper/2601.05394/) (2026)
- [LapisGS: Layered Progressive 3D Gaussian Splatting for Adaptive Streaming](https://mlsanity.com/paper/2408.14823/) (2024)
- [STAR-Edge: Structure-aware Local Spherical Curve Representation for Thin-walled Edge Extraction from Unstructured Point Clouds](https://mlsanity.com/paper/2503.00801/) (2025)
- [RoEL: Robust Event-based 3D Line Reconstruction](https://mlsanity.com/paper/2602.18258/) (2026)
- [BrepGaussian: CAD reconstruction from Multi-View Images with Gaussian Splatting](https://mlsanity.com/paper/2602.21105/) (2026)
- [Random Walk on Point Clouds for Feature Detection](https://mlsanity.com/paper/2604.20474/) (2026)
- [One Shot Learning for Edge Detection on Point Clouds](https://mlsanity.com/paper/2604.22354/) (2026)
- [FrameTwin: Curve-Anchored Gaussian Alignment from Sparse Views for Adaptive Wireframe 3D Printing](https://mlsanity.com/paper/2605.09362/) (2026)

## Abstract (arXiv)

We study the problem of reconstructing 3D feature curves of an object from a set of calibrated multi-view images. To do so, we learn a neural implicit field representing the density distribution of 3D edges which we refer to as Neural Edge Field (NEF). Inspired by NeRF, NEF is optimized with a view-based rendering loss where a 2D edge map is rendered at a given view and is compared to the ground-truth edge map extracted from the image of that view. The rendering-based differentiable optimization of NEF fully exploits 2D edge detection, without needing a supervision of 3D edges, a 3D geometric operator or cross-view edge correspondence. Several technical designs are devised to ensure learning a range-limited and view-independent NEF for robust edge extraction. The final parametric 3D curves are extracted from NEF with an iterative optimization method. On our benchmark with synthetic data, we demonstrate that NEF outperforms existing state-of-the-art methods on all metrics. Project page: https://yunfan1202.github.io/NEF/.