Curve-Aware Gaussian Splatting for 3D Parametric Curve Reconstruction

2025-06-26

AI Summary

To address error accumulation in two-stage methods for reconstructing 3D parametric curves from multi-view edge maps—caused by decoupled optimization—this paper proposes CurveGaussian, an end-to-end differentiable framework. Our key contributions are: (1) a novel curve-Gaussian bidirectional coupling representation that jointly models parametric curves and edge-guided Gaussian splatting; (2) a differentiable dynamic topology optimization framework enabling linearization, merging, splitting, and pruning of curve structures; and (3) integration of differentiable rendering, multi-view geometric constraints, and adaptive topology updates. Evaluated on the ABC dataset and real-world scenes, CurveGaussian achieves significant improvements in reconstruction accuracy and robustness. It reduces model parameters by 37%, accelerates training by 2.1×, and yields cleaner outputs with stronger geometric consistency compared to prior approaches.

Technology Category

• Computer Vision: Learning & Optimization for CV
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Learning with Manifolds

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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, extbf{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.

Problem

• Reconstruct 3D parametric curves from multi-view edge maps
• Overcome error accumulation in two-stage curve reconstruction methods
• Enable differentiable rendering for parametric curve optimization

Innovation

• One-stage 3D curve optimization from 2D edges
• Bi-directional coupling for differentiable rendering
• Dynamic topology optimization for curve refinement