Research map / 3D vision / Depth and stereo
Discontinuity-preserving Normal Integration with Auxiliary Edges
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Proposes discontinuity-preserving normal integration by discretizing the domain into per-pixel quadrilaterals bridged by auxiliary edges, optimizing sparse jump magnitudes via IRLS, gradient filtering, and a two-pass lambda schedule.
Problem
Recovering an accurate depth map from a normal map whose underlying surface has depth discontinuities (e.g., self-occlusion), where standard Poisson integration introduces global distortions and prior discontinuity-aware methods miss small jumps.
Approach
Model surface jumps explicitly as gradient edits on auxiliary edges bridging per-pixel quadrilaterals, and optimize sparse jump magnitudes with alternating weighted least squares, reweighting and explicit gradient filtering for strong l0-style sparsity.
Key results
- On DiLiGenT, the method achieves lower mean absolute depth error than BiNI on most objects, e.g., Bear 0.45 vs 0.49, Harvest 2.44 vs 3.30, Reading 0.15 vs 0.32.
- Compared with Poisson, depth errors drop substantially on several objects (e.g., Buddha 0.67 vs 3.71, Reading 0.15 vs 6.62).
- Prototype takes about 120 seconds for a 512x512 normal map on a Titan RTX GPU.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use auxiliary edges with explicit jump modeling and sparsity regularization instead of BiNI | normal integration · DiLiGenT Bear | mean absolute depth error: 0.49 -> 0.45 | Helped |
| use auxiliary edges with explicit jump modeling and sparsity regularization instead of BiNI | normal integration · DiLiGenT Buddha | mean absolute depth error: 0.76 -> 0.67 | Helped |
| use auxiliary edges with explicit jump modeling and sparsity regularization instead of BiNI | normal integration · DiLiGenT Cat | mean absolute depth error: 0.11 -> 0.24 | Hurt |
| use auxiliary edges with explicit jump modeling and sparsity regularization instead of BiNI | normal integration · DiLiGenT Cow | mean absolute depth error: 0.07 -> 0.06 | Helped |
| use auxiliary edges with explicit jump modeling and sparsity regularization instead of BiNI | normal integration · DiLiGenT Harvest | mean absolute depth error: 3.30 -> 2.44 | Helped |
| use auxiliary edges with explicit jump modeling and sparsity regularization instead of BiNI | normal integration · DiLiGenT Pot1 | mean absolute depth error: 0.63 -> 0.57 | Helped |
| use auxiliary edges with explicit jump modeling and sparsity regularization instead of BiNI | normal integration · DiLiGenT Pot2 | mean absolute depth error: 0.24 -> 0.19 | Helped |
| use auxiliary edges with explicit jump modeling and sparsity regularization instead of BiNI | normal integration · DiLiGenT Reading | mean absolute depth error: 0.32 -> 0.15 | Helped |
| use auxiliary edges with explicit jump modeling and sparsity regularization instead of BiNI | normal integration · DiLiGenT Goblet | mean absolute depth error: 8.65 -> 9.02 | Hurt |
| add iterative reweighting (ablation) | auxiliary-edge discontinuity optimization · complex shapes | discontinuity reconstruction | Helped |
| add gradient filtering of auxiliary-edge gradients (ablation) | auxiliary-edge discontinuity optimization · discontinuity reconstruction | sparsity | Helped |
| add the two-pass update (ablation) | auxiliary-edge discontinuity optimization · complex shapes | discontinuity reconstruction | Helped |
Surprising findings
- On the Goblet object, BiNI (8.65) outperforms the proposed method (9.02) in mean absolute depth error.
Limitations
- Fails on noisy human hand scans where finger discontinuities are not recovered.
- Global offset/scale ambiguity when discontinuities cut the integration domain into surface islands.
- Runtime of about 120 s per 512x512 map in an unoptimized prototype.
Experimental setup
Datasets: DiLiGenT RenderPeople human body models (27 models, rendered)
Benchmarks: DiLiGenT human body dataset (RenderPeople)
Metrics: mean absolute depth error
Baselines: Poisson solver BiNI
Builds on: Poisson normal integration BiNI iteratively reweighted least squares discrete geometry processing
Closest papers by meaning
- Feature-Preserving Mesh Decimation for Normal Integration (CVPR 2025 · similarity 0.88)
- FNIN: A Fourier Neural Operator-based Numerical Integration Network for Surface-from-gradients (AAAI 2025 · similarity 0.84)
- Flatten Anything: Unsupervised Neural Surface Parameterization (NeurIPS 2024 · similarity 0.83)
- PMNI: Pose-free Multi-view Normal Integration for Reflective and Textureless Surface Reconstruction (CVPR 2025 · similarity 0.83)
- SuperNormal: Neural Surface Reconstruction via Multi-View Normal Integration (CVPR 2024 · similarity 0.82)
- GeoSVR: Taming Sparse Voxels for Geometrically Accurate Surface Reconstruction (NeurIPS 2025 · similarity 0.82)
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