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ND-SDF: Learning Normal Deflection Fields for High-Fidelity Indoor Reconstruction
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Proposes ND-SDF, which learns a normal deflection quaternion field to model angular deviations between rendered scene normals and monocular normal priors, enabling adaptive prior usage plus deflection-guided sampling, photometric loss, and unbiased rendering for high-fidelity indoor surface reconstruction.
Problem
High-fidelity indoor 3D surface reconstruction from multi-view images: textureless regions need smoothness from priors, but monocular normal/depth priors are unreliable in complex thin structures, causing detail loss and erroneous surfaces.
Approach
A normal deflection field (quaternion predicted by an MLP and volume-rendered) rotates rendered normals toward the prior; the deflection angle then adaptively weights normal/depth prior losses, guides ray sampling and color loss, and selects regions for partial unbiased SDF-to-density conversion.
Key results
- On ScanNet, ND-SDF reports F-score 82.0 and Chamfer 0.034, versus 79.9 F-score for H2OSDF (the prior best in the table).
- On ScanNet++ (6 scenes), ND-SDF achieves F-score 0.721 and recall 0.785, above MonoSDF (Grid) at 0.675 and DebSDF (Grid) at 0.696.
- On Replica, ND-SDF reaches F-score 91.60 and Chamfer 2.57, the best on both, while DebSDF (MLP) has the highest normal consistency (93.23 vs 92.85).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add the normal deflection field and deflected normal loss (ablation) | Base reconstruction model · ScanNet++ | F-score: 0.606 -> 0.632 | Helped |
| Add adaptive deflection angle prior loss (ablation) | ModelA · ScanNet++ | F-score: 0.632 -> 0.679 | Helped |
| Add deflection-angle-guided sampling and photometric loss (ablation) | ModelB · ScanNet++ | F-score: 0.679 -> 0.681 | Helped |
| Add deflection-angle-guided unbiased rendering (ablation) | ModelC · ScanNet++ | F-score: 0.681 -> 0.686 | Helped |
| Use progressive deflection-field warm-up (ablation) | ND-SDF · ScanNet++ | F-score: 0.667 -> 0.686 | Helped |
| Apply partial unbiased rendering to deflection-indicated fine regions (ablation) | ND-SDF · ScanNet | F-score: 0.707 -> 0.746 | Helped |
| Use adaptive deflection-angle depth prior loss (ablation) | ND-SDF · ScanNet++ | F-score: 0.664 -> 0.686 | Helped |
| Add curvature loss (ablation) | ND-SDF · Indoor reconstruction | surface smoothness | No clear effect |
| Use ND-SDF instead of H2OSDF | Indoor reconstruction on ScanNet · ScanNet (4 scenes) | F-score: 79.9 -> 82.0 | Helped |
| Use ND-SDF instead of DebSDF (Grid) | Indoor reconstruction on ScanNet++ · ScanNet++ (6 scenes) | F-score: 0.696 -> 0.721 | Helped |
| Use ND-SDF instead of DebSDF (MLP) | Indoor reconstruction on Replica · Replica | F-score: 88.36 -> 91.60 | Helped |
| Use ND-SDF instead of MonoSDF (Grid) | Indoor reconstruction on Tanks and Temples · Tanks and Temples (mean) | F-score: 10.11 -> 14.46 | Helped |
Surprising findings
- Applying the unbiased SDF-to-density transform to all regions led to poor surface convergence, so it was applied only to regions flagged by the deflection angle.
- Reported ScanNet++ ablation shows the Recall-oriented model variant ModelC slightly exceeding the full model on Recall (0.740 vs 0.728).
Limitations
- Confined to reconstruction scenarios that have normal/depth priors; limited capability in areas with less view coverage.
- Ambiguous observations can make the deflection field learn incorrect structures and converge to local optima.
Experimental setup
Datasets: ScanNet Replica Tanks and Temples ScanNet++
Benchmarks: ScanNet Replica Tanks and Temples ScanNet++
Metrics: Accuracy Completeness Precision Recall Chamfer distance F-score normal consistency
Baselines: COLMAP VolSDF NeuS NeuRIS MonoSDF HelixSurf DebSDF H2O-SDF Baked-Angelo
Builds on: MonoSDF VolSDF Neuralangelo TUVR Instant-NGP
Closest papers by meaning
- NC-SDF: Enhancing Indoor Scene Reconstruction Using Neural SDFs with View-Dependent Normal Compensation (CVPR 2024 · similarity 0.90)
- NeRFPrior: Learning Neural Radiance Field as a Prior for Indoor Scene Reconstruction (CVPR 2025 · similarity 0.88)
- H2O-SDF: Two-phase Learning for 3D Indoor Reconstruction using Object Surface Fields (ICLR 2024 · similarity 0.87)
- AniSDF: Fused-Granularity Neural Surfaces with Anisotropic Encoding for High-Fidelity 3D Reconstruction (ICLR 2025 · similarity 0.85)
- Sparis: Neural Implicit Surface Reconstruction of Indoor Scenes from Sparse Views (AAAI 2025 · similarity 0.85)
- 3D Reconstruction with Generalizable Neural Fields using Scene Priors (ICLR 2024 · similarity 0.85)
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