# CGGT: Curve-Grounded Geometry Transformer for 3D Parametric Curve Reconstruction

arXiv: https://arxiv.org/abs/2609.14521 · HTML: https://mlsanity.com/paper/2609.14521/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 38 of its 76 references that are in the map.
- First posted on arXiv 13 Sep 2026.

## Builds on (most cited first, 30 of 38)

- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [V-Net: Fully Convolutional Neural Networks for Volumetric Medical Image Segmentation](https://mlsanity.com/paper/1606.04797/) (2016)
- [DUSt3R: Geometric 3D Vision Made Easy](https://mlsanity.com/paper/2312.14132/) (2023)
- [2D Gaussian Splatting for Geometrically Accurate Radiance Fields](https://mlsanity.com/paper/2403.17888/) (2024)
- [Depth Anything 3: Recovering the Visual Space from Any Views](https://mlsanity.com/paper/2511.10647/) (2025)
- [SpatialVLA: Exploring Spatial Representations for Visual-Language-Action Model](https://mlsanity.com/paper/2501.15830/) (2025)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [Pixel Difference Networks for Efficient Edge Detection](https://mlsanity.com/paper/2108.07009/) (2021)
- [Swin3D: A Pretrained Transformer Backbone for 3D Indoor Scene Understanding](https://mlsanity.com/paper/2304.06906/) (2023)
- [EC-Net: an Edge-aware Point set Consolidation Network](https://mlsanity.com/paper/1807.06010/) (2018)
- [PIE-NET: Parametric Inference of Point Cloud Edges](https://mlsanity.com/paper/2007.04883/) (2020)
- [RoadMap: A Light-Weight Semantic Map for Visual Localization towards Autonomous Driving](https://mlsanity.com/paper/2106.02527/) (2021)
- [DiffusionEdge: Diffusion Probabilistic Model for Crisp Edge Detection](https://mlsanity.com/paper/2401.02032/) (2024)
- [HoLa: B-Rep Generation using a Holistic Latent Representation](https://mlsanity.com/paper/2504.14257/) (2025)
- [IGGT: Instance-Grounded Geometry Transformer for Semantic 3D Reconstruction](https://mlsanity.com/paper/2510.22706/) (2025)
- [DGGT: Feedforward 4D Reconstruction of Dynamic Driving Scenes using Unposed Images](https://mlsanity.com/paper/2512.03004/) (2025)
- [NerVE: Neural Volumetric Edges for Parametric Curve Extraction from Point Cloud](https://mlsanity.com/paper/2303.16465/) (2023)
- [3Doodle: Compact Abstraction of Objects with 3D Strokes](https://mlsanity.com/paper/2402.03690/) (2024)
- [Split-and-Fit: Learning B-Reps via Structure-Aware Voronoi Partitioning](https://mlsanity.com/paper/2406.05261/) (2024)
- [PCEDNet : A Lightweight Neural Network for Fast and Interactive Edge Detection in 3D Point Clouds](https://mlsanity.com/paper/2011.01630/) (2020)
- [BrepGPT: Autoregressive B-rep Generation with Voronoi Half-Patch](https://mlsanity.com/paper/2511.22171/) (2025)
- [NEAT: Distilling 3D Wireframes from Neural Attraction Fields](https://mlsanity.com/paper/2307.10206/) (2023)
- [NeurCADRecon: Neural Representation for Reconstructing CAD Surfaces by Enforcing Zero Gaussian Curvature](https://mlsanity.com/paper/2404.13420/) (2024)
- [Delving into Crispness: Guided Label Refinement for Crisp Edge Detection](https://mlsanity.com/paper/2306.15172/) (2023)
- [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)
- [Road Mapping and Localization using Sparse Semantic Visual Features](https://mlsanity.com/paper/2108.05047/) (2021)
- [Parametric Primitive Analysis of CAD Sketches with Vision Transformer](https://mlsanity.com/paper/2407.00410/) (2024)

## Abstract (arXiv)

Recovering editable 3D parametric curves from 2D images is a fundamental challenge in computer graphics, bridging pixel-based perception and vector-based CAD modeling. Existing NeRF- and 3DGS-based methods often rely on dense calibrated views, precomputed 2D edge maps, and costly per-scene optimization, limiting their applicability to casually captured real-world inputs. We propose CGGT, a Curve-Grounded Geometry Transformer that directly grounds 3D-consistent 2D curve instances in the image space from sparse, unposed multi-view images. CGGT combines a geometry-aware transformer encoder for multi-view feature learning with a curve-aware masked-attention decoder for cross-view instance association. In a single forward pass, it predicts camera parameters, dense depth maps, and instance-level 2D curve masks, which are then lifted into 3D and refined through a fast parametric optimization stage to recover compact, editable 3D curve primitives. To support structured curve learning, we introduce Wireframe-100K, a large-scale dataset comprising 100,000 CAD models with diverse topologies, realistic multi-view renderings, and accurate parametric curve annotations. Extensive experiments show that our framework achieves substantial improvements in both reconstruction accuracy and efficiency, particularly under challenging sparse-view settings and in separating persistent 3D structural edges from view-dependent image edges caused by silhouettes, textures, and appearance variations. Despite being trained solely on synthetic data, CGGT generalizes well to real-world images, demonstrating its potential for practical CAD-style wireframe reconstruction from unconstrained visual inputs.