# NerVE: Neural Volumetric Edges for Parametric Curve Extraction from Point Cloud

arXiv: https://arxiv.org/abs/2303.16465 · HTML: https://mlsanity.com/paper/2303.16465/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 42 references that are in the map.
- First posted on arXiv 29 Mar 2023.

## Builds on (most cited first, 17 of 17)

- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [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)
- [Learning Implicit Fields for Generative Shape Modeling](https://mlsanity.com/paper/1812.02822/) (2018)
- [A Point Set Generation Network for 3D Object Reconstruction from a Single Image](https://mlsanity.com/paper/1612.00603/) (2016)
- [Pixel2Mesh: Generating 3D Mesh Models from Single RGB Images](https://mlsanity.com/paper/1804.01654/) (2018)
- [3D-R2N2: A Unified Approach for Single and Multi-view 3D Object Reconstruction](https://mlsanity.com/paper/1604.00449/) (2016)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [EC-Net: an Edge-aware Point set Consolidation Network](https://mlsanity.com/paper/1807.06010/) (2018)
- [Neural Dual Contouring](https://mlsanity.com/paper/2202.01999/) (2022)
- [PIE-NET: Parametric Inference of Point Cloud Edges](https://mlsanity.com/paper/2007.04883/) (2020)
- [Neural Marching Cubes](https://mlsanity.com/paper/2106.11272/) (2021)
- [PC2WF: 3D Wireframe Reconstruction from Raw Point Clouds](https://mlsanity.com/paper/2103.02766/) (2021)
- [ComplexGen: CAD Reconstruction by B-Rep Chain Complex Generation](https://mlsanity.com/paper/2205.14573/) (2022)
- [PCEDNet : A Lightweight Neural Network for Fast and Interactive Edge Detection in 3D Point Clouds](https://mlsanity.com/paper/2011.01630/) (2020)
- [3D Parametric Wireframe Extraction Based on Distance Fields](https://mlsanity.com/paper/2107.06165/) (2021)

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

- [CAD-Recode: Reverse Engineering CAD Code from Point Clouds](https://mlsanity.com/paper/2412.14042/) (2024)
- [CAD-Assistant: Tool-Augmented VLLMs as Generic CAD Task Solvers](https://mlsanity.com/paper/2412.13810/) (2024)
- [TransCAD: A Hierarchical Transformer for CAD Sequence Inference from Point Clouds](https://mlsanity.com/paper/2407.12702/) (2024)
- [SHARP Challenge 2023: Solving CAD History and pArameters Recovery from Point clouds and 3D scans. Overview, Datasets, Metrics, and Baselines](https://mlsanity.com/paper/2308.15966/) (2023)
- [Split-and-Fit: Learning B-Reps via Structure-Aware Voronoi Partitioning](https://mlsanity.com/paper/2406.05261/) (2024)
- [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)
- [Auto-Regressive Surface Cutting](https://mlsanity.com/paper/2506.18017/) (2025)
- [Parametric Primitive Analysis of CAD Sketches with Vision Transformer](https://mlsanity.com/paper/2407.00410/) (2024)
- [CLR-Wire: Towards Continuous Latent Representations for 3D Curve Wireframe Generation](https://mlsanity.com/paper/2504.19174/) (2025)
- [SketchSplat: 3D Edge Reconstruction via Differentiable Multi-view Sketch Splatting](https://mlsanity.com/paper/2503.14786/) (2025)
- [PBWR: Parametric Building Wireframe Reconstruction from Aerial LiDAR Point Clouds](https://mlsanity.com/paper/2311.12062/) (2023)
- [PI3DETR: Parametric Instance Detection of 3D Point Cloud Edges With a Geometry-Aware 3DETR](https://mlsanity.com/paper/2509.03262/) (2025)
- [STAR-Edge: Structure-aware Local Spherical Curve Representation for Thin-walled Edge Extraction from Unstructured Point Clouds](https://mlsanity.com/paper/2503.00801/) (2025)
- [SharpNet: Enhancing MLPs to Represent Functions with Controlled Non-differentiability](https://mlsanity.com/paper/2601.19683/) (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)
- [EdgeFormer: local patch-based edge detection transformer on point clouds](https://mlsanity.com/paper/2604.21387/) (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)
- [CGGT: Curve-Grounded Geometry Transformer for 3D Parametric Curve Reconstruction](https://mlsanity.com/paper/2609.14521/) (2026)

## Abstract (arXiv)

Extracting parametric edge curves from point clouds is a fundamental problem in 3D vision and geometry processing. Existing approaches mainly rely on keypoint detection, a challenging procedure that tends to generate noisy output, making the subsequent edge extraction error-prone. To address this issue, we propose to directly detect structured edges to circumvent the limitations of the previous point-wise methods. We achieve this goal by presenting NerVE, a novel neural volumetric edge representation that can be easily learned through a volumetric learning framework. NerVE can be seamlessly converted to a versatile piece-wise linear (PWL) curve representation, enabling a unified strategy for learning all types of free-form curves. Furthermore, as NerVE encodes rich structural information, we show that edge extraction based on NerVE can be reduced to a simple graph search problem. After converting NerVE to the PWL representation, parametric curves can be obtained via off-the-shelf spline fitting algorithms. We evaluate our method on the challenging ABC dataset. We show that a simple network based on NerVE can already outperform the previous state-of-the-art methods by a great margin. Project page: https://dongdu3.github.io/projects/2023/NerVE/.