Curve-Aware Gaussian Splatting for
3D Parametric Curve Reconstruction

Zhirui Gao Renjiao Yi Yaqiao Dai Xuening Zhu Wei Chen Chenyang Zhu Kai Xu
National University of Defense Technology
ICCV 2025
Paper arXiv Video Code

CurveGaussian enables compact 3D parametric curve reconstruction from multi-view 2D edge maps!

CurveGaussian is a novel bi-directional coupling framework between parametric curves and edge-oriented Gaussian components, enabling direct optimization of parametric curves through differentiable Gaussian splatting.

Abstract

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.

Pipeline

Scenethesis Demo

We propose a curve-aware Gaussian representation that optimizes parametric curves through a one-stage optimization in a self-supervised manner by re-rendering losses. The method employs many adaptive strategies, including curve linearization, merging, splitting, and pruning, to dynamically adjust the curves during training.

Experimnets on Replica dataset

Qualitative comparisons to state-of-the-art 3D parametric curve reoncstruction approaches: LIMAP, NEF, EdgeGS, and EMAP. Distinct colors represent different curves/lines. Our method achieves more complete and accurate edge reconstruction of objects while maintaining parametric compactness.

Feature Reconstruction
Edge Detection
3D Curve Mapping

Experimnets on ABC-NEF dataset

Our approach seamlessly scales to scene-level applications.

Feature Reconstruction
Edge Detection
3D Curve Mapping

Additional Results on real-life objects

Our method achieves clean and accurate parametric curve reconstruction through a one-stage optimization utilizing the proposed curve-aware Gaussian

BibTeX


     @misc{gao2025curveawaregaussiansplatting3d,
      title={Curve-Aware Gaussian Splatting for 3D Parametric Curve Reconstruction}, 
      author={Zhirui Gao and Renjiao Yi and Yaqiao Dai and Xuening Zhu and Wei Chen and Chenyang Zhu and Kai Xu},
      year={2025},
      eprint={2506.21401},
      archivePrefix={arXiv},
      primaryClass={cs.CV},
      url={https://arxiv.org/abs/2506.21401}, 
}