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Neural Signed Distance Function Inference through Splatting 3D Gaussians Pulled on Zero-Level Set
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Jointly optimizes 3D Gaussians and a neural SDF by pulling Gaussians onto the SDF zero-level set and pulling query points onto Gaussian disks, with splatting and geometry losses, for multi-view surface reconstruction.
Problem
Inferring accurate, smooth, and complete neural signed distance fields for multi-view surface reconstruction from discrete, sparse, and off-surface-drifting 3D Gaussians.
Approach
Dynamically pull 3D Gaussians onto the SDF zero-level set via neural pulling and render them by splatting, while pulling neighboring query points onto flattened Gaussian disks (not centers) with thin, tangent, and orthogonal constraints, so RGB and geometry constraints jointly train Gaussians and SDF.
Key results
- Achieves mean Chamfer Distance 0.75 on DTU, the best among compared Gaussian-based methods (2DGS 0.80, 3DGS 1.96).
- Achieves mean F-score 0.43 on Tanks and Temples, higher than 2DGS (0.32) and NeuS (0.38).
- On Mip-NeRF 360 outdoor LPIPS 0.278 is best among listed methods, while indoor PSNR 30.78 trails Mip-NeRF 360 (31.72).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Gaussian disks rather than Gaussian centers as pulling targets for query points (ablation) | Neural SDF inference with 3D Gaussian splatting · DTU | Chamfer Distance (CD): 0.85 -> 0.75 | Helped |
| Pull Gaussians onto the SDF zero-level set before splatting (ablation) | Neural SDF inference with 3D Gaussian splatting · DTU | Chamfer Distance (CD): 0.90 -> 0.75 | Helped |
| Add the thin-disk constraint (ablation) | Neural SDF inference with 3D Gaussian splatting · DTU | Chamfer Distance (CD): 0.78 -> 0.75 | Helped |
| Add the tangent constraint (ablation) | Neural SDF inference with 3D Gaussian splatting · DTU | Chamfer Distance (CD): 0.82 -> 0.75 | Helped |
| Add the orthogonal constraint (ablation) | Neural SDF inference with 3D Gaussian splatting · DTU | Chamfer Distance (CD): 0.79 -> 0.75 | Helped |
| Use marching cubes on the learned SDF rather than TSDF fusion for mesh extraction (ablation) | Neural SDF inference with 3D Gaussian splatting · DTU | Chamfer Distance (CD): 1.41 -> 0.75 | Helped |
| Use marching cubes on the learned SDF rather than screened Poisson reconstruction for mesh extraction (ablation) | Neural SDF inference with 3D Gaussian splatting · DTU | Chamfer Distance (CD): 0.79 -> 0.75 | Helped |
| Add an Eikonal term to constrain the SDF gradient length (ablation) | Neural SDF inference with 3D Gaussian splatting · DTU | reconstruction quality | Hurt |
| Use the proposed method instead of 2DGS | Neural SDF inference with 3D Gaussian splatting · DTU | Chamfer Distance (CD) mean: 0.80 -> 0.75 | Helped |
| Use the proposed method instead of NeuS | Neural SDF inference with 3D Gaussian splatting · Tanks and Temples | F-score mean: 0.38 -> 0.43 | Helped |
| Use the proposed method instead of MipNeRF 360 | Neural SDF inference with 3D Gaussian splatting · Mip-NeRF 360 indoor | PSNR: 31.72 -> 30.78 | Hurt |
| Use the proposed method instead of 2DGS | Neural SDF inference with 3D Gaussian splatting · Mip-NeRF 360 outdoor | LPIPS: 0.284 -> 0.278 | Helped |
Surprising findings
- Adding an Eikonal term to constrain gradient length significantly degrades results because Neural-Pull depends on predicted SDF values and gradient directions.
- Pulling Gaussian centers rather than disks yields an SDF that overfits every Gaussian center, causing incomplete meshes.
Limitations
- Struggles with transparent objects and strong specular reflections inherited from 3DGS.
- Produces holes in extremely sparse regions such as distant areas of unbounded scenes.
- MLP-based SDF captures low-frequency structure and misses high-frequency details.
Experimental setup
Datasets: DTU Tanks and Temples Mip-NeRF 360
Benchmarks: DTU Tanks and Temples Mip-NeRF 360
Metrics: Chamfer Distance F-score PSNR SSIM LPIPS
Baselines: NeuS 3DGS SuGaR DN-Splatter GaussianSurfels 2DGS Instant-NGP Mip-NeRF 360 BakedSDF
Builds on: 3D Gaussian Splatting Neural-Pull NeuS 2DGS
Closest papers by meaning
- GaussianUDF: Inferring Unsigned Distance Functions through 3D Gaussian Splatting (CVPR 2025 · similarity 0.93)
- GSDF: 3DGS Meets SDF for Improved Neural Rendering and Reconstruction (NeurIPS 2024 · similarity 0.93)
- GaussianPro: 3D Gaussian Splatting with Progressive Propagation (ICML 2024 · similarity 0.90)
- Sensing Surface Patches in Volume Rendering for Inferring Signed Distance Functions (AAAI 2025 · similarity 0.89)
- Evolving High-Quality Rendering and Reconstruction in a Unified Framework with Contribution-Adaptive Regularization (CVPR 2025 · similarity 0.89)
- GVKF: Gaussian Voxel Kernel Functions for Highly Efficient Surface Reconstruction in Open Scenes (NeurIPS 2024 · similarity 0.89)
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