Research map / 3D vision / Gaussian splatting
SGCR: Spherical Gaussians for Efficient 3D Curve Reconstruction
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Proposes Spherical Gaussians, isotropic fixed-radius Gaussians optimized from 2D edge maps, and SGCR, an optimization-based fitting of rational Bézier curves to them, to reconstruct 3D feature curves from calibrated multi-view images.
Problem
Accurate 3D edge/feature curve reconstruction from multi-view images, since anisotropic 3D Gaussians fit 2D appearance but not 3D geometric structure, and prior image-based curve methods are slow or limited to straight lines.
Approach
Replace anisotropic 3DGS primitives with isotropic, fixed-radius, grayscale-colored Spherical Gaussians trained on 2D edge maps with an edge-aware loss, opacity-color consistency loss, and two-phase pruning; then fit rational Bézier curves to them via line fitting and weighted Chamfer global optimization.
Key results
- On ABC-NEF, SGCR reaches CD 0.0280, F-score 0.9260 and IoU 0.8615, outperforming RFEPS, NerVE, NEF and EMAP on all metrics.
- On ModelNet, SGCR achieves CD 0.0264 and IoU 0.8164, best CD and IoU among compared methods (NerVE has higher precision).
- Full pipeline runs in about 87s generation plus 32s curve reconstruction, reported as roughly 50x faster than NEF and EMAP.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace Spherical Gaussians with original 3D Gaussians (ablation) | SGCR · ABC-NEF | F-score: 0.926 -> 0.330 | Hurt |
| Add grid initialization (ablation) | SGCR · ABC-NEF | F-score: 0.901 -> 0.926 | Helped |
| Add edge loss Ledge (ablation) | SGCR · ABC-NEF | F-score: 0.853 -> 0.926 | Helped |
| Add opacity-color loss Loc (ablation) | SGCR · ABC-NEF | F-score: 0.859 -> 0.926 | Helped |
| Add regularization loss Lregular (ablation) | SGCR · ABC-NEF | F-score: 0.913 -> 0.926 | Helped |
| Use the two-phase training strategy (ablation) | SGCR · ABC-NEF | F-score: 0.920 -> 0.926 | Helped |
| Add line fitting (ablation) | SGCR · ABC-NEF | F-score: 0.911 -> 0.926 | Helped |
| Add global optimization (ablation) | SGCR · ABC-NEF | F-score: 0.876 -> 0.926 | Helped |
| Set Spherical Gaussian radius to r0 = 0.005 instead of r0 = 0.002 (ablation) | SGCR · ABC-NEF | F-score: 0.906 -> 0.926 | Helped |
| Set Spherical Gaussian radius to r0 = 0.005 instead of r0 = 0.01 (ablation) | SGCR · ABC-NEF | F-score: 0.881 -> 0.926 | Helped |
| Set Spherical Gaussian radius to r0 = 0.005 instead of variable (ablation) | SGCR · ABC-NEF | F-score: 0.863 -> 0.926 | Helped |
| Use SGCR instead of EMAP | 3D curve reconstruction · ABC-NEF | F-score: 0.9210 -> 0.9260 | Helped |
Surprising findings
- Vanilla 3D Gaussians trained on edge maps perform very poorly (CD 0.142, IoU 0.194), showing anisotropic Gaussians are ill-suited for edges.
- Setting the Gaussian radius as a learned variable performed worse than a fixed radius.
Limitations
- Reconstruction quality degrades with too few input views for complex scenes (10 views insufficient for complex cases).
- Radius choice is sensitive: too large causes underfitting and too small causes noise.
- Curve extraction relies on hand-set thresholds and sampling parameters.
Experimental setup
Datasets: ABC-NEF ModelNet DTU Replica
Benchmarks: ABC-NEF ModelNet DTU Replica
Metrics: Chamfer Distance Precision Recall F-score IoU training time reconstruction time
Baselines: RFEPS NerVE NEF EMAP 3D Gaussian Splatting
Builds on: 3D Gaussian Splatting PiDiNet BlenderProc
Closest papers by meaning
- VA-GS: Enhancing the Geometric Representation of Gaussian Splatting via View Alignment (NeurIPS 2025 · similarity 0.90)
- Textured Gaussians for Enhanced 3D Scene Appearance Modeling (CVPR 2025 · similarity 0.88)
- Effective Rank Analysis and Regularization for Enhanced 3D Gaussian Splatting (NeurIPS 2024 · similarity 0.88)
- GaussianPro: 3D Gaussian Splatting with Progressive Propagation (ICML 2024 · similarity 0.88)
- GaussianSpa: An "Optimizing-Sparsifying" Simplification Framework for Compact and High-Quality 3D Gaussian Splatting (CVPR 2025 · similarity 0.88)
- Spec-Gaussian: Anisotropic View-Dependent Appearance for 3D Gaussian Splatting (NeurIPS 2024 · similarity 0.88)
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