# Curve-Aware Gaussian Splatting for 3D Parametric Curve Reconstruction

arXiv: https://arxiv.org/abs/2506.21401 · HTML: https://mlsanity.com/paper/2506.21401/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 56 references that are in the map.
- First posted on arXiv 26 Jun 2025.

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

- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [SAM 2: Segment Anything in Images and Videos](https://mlsanity.com/paper/2408.00714/) (2024)
- [Volume Rendering of Neural Implicit Surfaces](https://mlsanity.com/paper/2106.12052/) (2021)
- [The Replica Dataset: A Digital Replica of Indoor Spaces](https://mlsanity.com/paper/1906.05797/) (2019)
- [Compact 3D Gaussian Representation for Radiance Field](https://mlsanity.com/paper/2311.13681/) (2023)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [Pixel Difference Networks for Efficient Edge Detection](https://mlsanity.com/paper/2108.07009/) (2021)
- [StableNormal: Reducing Diffusion Variance for Stable and Sharp Normal](https://mlsanity.com/paper/2406.16864/) (2024)
- [Dense Extreme Inception Network: Towards a Robust CNN Model for Edge Detection](https://mlsanity.com/paper/1909.01955/) (2019)
- [PIE-NET: Parametric Inference of Point Cloud Edges](https://mlsanity.com/paper/2007.04883/) (2020)
- [GlueStick: Robust Image Matching by Sticking Points and Lines Together](https://mlsanity.com/paper/2304.02008/) (2023)
- [DeepLSD: Line Segment Detection and Refinement with Deep Image Gradients](https://mlsanity.com/paper/2212.07766/) (2022)
- [SOLD2: Self-supervised Occlusion-aware Line Description and Detection](https://mlsanity.com/paper/2104.03362/) (2021)
- [3D Line Mapping Revisited](https://mlsanity.com/paper/2303.17504/) (2023)
- [PC2WF: 3D Wireframe Reconstruction from Raw Point Clouds](https://mlsanity.com/paper/2103.02766/) (2021)
- [Holistically-Attracted Wireframe Parsing: From Supervised to Self-Supervised Learning](https://mlsanity.com/paper/2210.12971/) (2022)
- [UV-SLAM: Unconstrained Line-based SLAM Using Vanishing Points for Structural Mapping](https://mlsanity.com/paper/2112.13515/) (2021)
- [Interpolation-based Contrastive Learning for Few-Label Semi-Supervised Learning](https://mlsanity.com/paper/2202.11915/) (2022)
- [NEF: Neural Edge Fields for 3D Parametric Curve Reconstruction from Multi-view Images](https://mlsanity.com/paper/2303.07653/) (2023)
- [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)
- [Fast Continual Multi-View Clustering with Incomplete Views](https://mlsanity.com/paper/2306.02389/) (2023)
- [DealMVC: Dual Contrastive Calibration for Multi-view Clustering](https://mlsanity.com/paper/2308.09000/) (2023)
- [Structure PLP-SLAM: Efficient Sparse Mapping and Localization using Point, Line and Plane for Monocular, RGB-D and Stereo Cameras](https://mlsanity.com/paper/2207.06058/) (2022)
- [OmniEarth-Bench: Towards Holistic Evaluation of Earth's Six Spheres and Cross-Spheres Interactions with Multimodal Observational Earth Data](https://mlsanity.com/paper/2505.23522/) (2025)
- [NEAT: Distilling 3D Wireframes from Neural Attraction Fields](https://mlsanity.com/paper/2307.10206/) (2023)
- [3D Neural Edge Reconstruction](https://mlsanity.com/paper/2405.19295/) (2024)
- [Harnessing Massive Satellite Imagery with Efficient Masked Image Modeling](https://mlsanity.com/paper/2406.11933/) (2024)
- [ARM3D: Attention-based relation module for indoor 3D object detection](https://mlsanity.com/paper/2202.09715/) (2022)
- [Delving into Crispness: Guided Label Refinement for Crisp Edge Detection](https://mlsanity.com/paper/2306.15172/) (2023)

## Built on by (most cited first, 10 of 10)

- [Benchmarking PhD-Level Coding in 3D Geometric Computer Vision](https://mlsanity.com/paper/2603.30038/) (2026)
- [Sketch&Patch++: Efficient Structure-Aware 3D Gaussian Representation](https://mlsanity.com/paper/2601.05394/) (2026)
- [3DrawAgent: Teaching LLM to Draw in 3D with Early Contrastive Experience](https://mlsanity.com/paper/2604.08042/) (2026)
- [SF-Recon: Simplification-Free Lightweight Building Reconstruction via 3D Gaussian Splatting](https://mlsanity.com/paper/2511.13278/) (2025)
- [WildGHand: Learning Anti-Perturbation Gaussian Hand Avatars from Monocular In-the-Wild Videos](https://mlsanity.com/paper/2602.20556/) (2026)
- [BrepGaussian: CAD reconstruction from Multi-View Images with Gaussian Splatting](https://mlsanity.com/paper/2602.21105/) (2026)
- [FrameTwin: Curve-Anchored Gaussian Alignment from Sparse Views for Adaptive Wireframe 3D Printing](https://mlsanity.com/paper/2605.09362/) (2026)
- [HoloTetSphere: Unified TetSphere Mesh Reconstruction for Physical Simulations](https://mlsanity.com/paper/2607.08398/) (2026)
- [CGGT: Curve-Grounded Geometry Transformer for 3D Parametric Curve Reconstruction](https://mlsanity.com/paper/2609.14521/) (2026)
- [Controllable Road Marking Generation](https://mlsanity.com/paper/2610.05771/) (2026)

## Abstract (arXiv)

This paper presents an end-to-end framework for reconstructing 3D parametric curves directly from multi-view edge maps. Contrasting with existing two-stage methods that follow a sequential ``edge point cloud reconstruction and parametric curve fitting'' pipeline, our one-stage approach optimizes 3D parametric curves directly from 2D edge maps, eliminating error accumulation caused by the inherent optimization gap between disconnected stages. However, parametric curves inherently lack suitability for rendering-based multi-view optimization, necessitating a complementary representation that preserves their geometric properties while enabling differentiable rendering. We propose a novel bi-directional coupling mechanism between parametric curves and edge-oriented Gaussian components. This tight correspondence formulates a curve-aware Gaussian representation, CurveGaussian, that enables differentiable rendering of 3D curves, allowing direct optimization guided by multi-view evidence. Furthermore, we introduce a dynamically adaptive topology optimization framework during training to refine curve structures through linearization, merging, splitting, and pruning operations. Comprehensive evaluations on the ABC dataset and real-world benchmarks demonstrate our one-stage method's superiority over two-stage alternatives, particularly in producing cleaner and more robust reconstructions. Additionally, by directly optimizing parametric curves, our method significantly reduces the parameter count during training, achieving both higher efficiency and superior performance compared to existing approaches.