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Feature-Preserving Mesh Decimation for Normal Integration
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Replaces the dense pixel grid in normal integration with a sparse anisotropic triangle mesh obtained by a screen-space quadric-based decimation combined with generalized Delaunay edge flips and vertex relocation.
Problem
Normal integration of high-resolution normal maps scales poorly because the pixel-grid linear system grows quadratically, and prior isotropic mesh-based integration struggles to represent ridges and furrows.
Approach
Derives Garland-Heckbert quadric error metrics directly from normal maps in screen space and combines them with a generalized (anisotropic) Delaunay criterion, so mesh edges and vertices align to ridges and furrows while flat regions are decimated.
Key results
- On DiLiGenT-MV at the high setting, the method reaches RMSE within sub-millimetre range of the pixel-based method [2] (e.g., BUDDHA 6.61 mm vs 6.74 reference-pixel-based table value 6.74 vs isotropic 7.33 at low) and outperforms isotropic remeshing [14] at equal vertex counts.
- Ablation on a 1k-vertex mesh: full method achieves 1.55 mm RMSE / 5.74 degrees MAE vs 1.64 mm / 6.18 degrees for decimation only.
- For resolutions beyond 10MP, mesh-based methods are up to 100 times faster than traditional pixel-based integration, and the overhead pays off already at about 1MP.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use anisotropic decimation instead of isotropic remeshing at the high setting | Mesh-based normal integration · DiLiGenT-MV | RMSE (mm): BEAR 3.37 -> 3.04; BUDDHA 7.33 -> 6.61; COW 2.96 -> 2.74; POT2 5.65 -> 5.29; READING 6.83 -> 6.50 | Helped |
| Add vertex alignment to decimation (ablation) | Proposed method · DiLiGenT-MV, 1k vertices | RMSE (mm): 1.64 -> 1.59 | Helped |
| Add vertex alignment to decimation (ablation) | Proposed method · DiLiGenT-MV, 1k vertices | MAE (°): 6.18° -> 6.03° | Helped |
| Add edge alignment to decimation (ablation) | Proposed method · DiLiGenT-MV, 1k vertices | RMSE (mm): 1.64 -> 1.72 | Hurt |
| Add edge alignment to decimation (ablation) | Proposed method · DiLiGenT-MV, 1k vertices | MAE (°): 6.18° -> 5.90° | Helped |
| Use both vertex and edge alignment with decimation (ablation) | Proposed method · DiLiGenT-MV, 1k vertices | RMSE (mm): 1.64 -> 1.55 | Helped |
| Use both vertex and edge alignment with decimation (ablation) | Proposed method · DiLiGenT-MV, 1k vertices | MAE (°): 6.18° -> 5.74° | Helped |
| Increase the decimation threshold | Proposed method · LUCES | RMSE (mm) | Mixed |
Limitations
- Designed for continuous surfaces; discontinuities not handled
- Single-view normal integration suffers from inherent scale ambiguity
- Compression at moderate ratios yields only results comparable to pixel-based methods; slightly higher runtime than isotropic remeshing
Experimental setup
Datasets: DiLiGenT-MV LUCES RGBN PS datasets (Boss et al.) synthetic rendered normal maps from 3D scans
Benchmarks: DiLiGenT-MV LUCES RGBN synthetic high-resolution normal maps
Metrics: RMSE (mm) mean angular error (degrees) runtime (s)
Baselines: Isotropic remeshing [14] pixel-based normal integration [2] pixel-based integration [13]
Builds on: quadric error metrics (Garland and Heckbert) optimal Delaunay triangulation isotropic screen-space mesh-based normal integration normal-based functional for normal integration
Closest papers by meaning
- Discontinuity-preserving Normal Integration with Auxiliary Edges (CVPR 2024 · similarity 0.88)
- QUADify: Extracting Meshes with Pixel-level Details and Materials from Images (CVPR 2024 · similarity 0.85)
- Normal-GS: 3D Gaussian Splatting with Normal-Involved Rendering (NeurIPS 2024 · similarity 0.85)
- SuperNormal: Neural Surface Reconstruction via Multi-View Normal Integration (CVPR 2024 · similarity 0.84)
- PMNI: Pose-free Multi-view Normal Integration for Reflective and Textureless Surface Reconstruction (CVPR 2025 · similarity 0.84)
- GeoSVR: Taming Sparse Voxels for Geometrically Accurate Surface Reconstruction (NeurIPS 2025 · similarity 0.84)
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