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Unsigned Orthogonal Distance Fields: An Accurate Neural Implicit Representation for Diverse 3D Shapes
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Proposes unsigned orthogonal distance fields (UODFs), three per-axis unsigned distance fields regressed by MLPs that let surface points be read off directly without interpolation, improving accurate reconstruction of watertight, open, and complex shapes.
Problem
SDF and UDF neural implicit representations lose reconstruction accuracy when converting to explicit surface points and meshes, due to network fitting errors and interpolation errors in marching-cubes-style grid edge point extraction; SDF cannot handle non-watertight shapes.
Approach
Define the unsigned distance to the surface along three orthogonal axis directions (UODF_LR, UODF_FB, UODF_UD), so each sample point directly predicts its closest surface point along a ray; surface points are estimated by averaging predictions along segments, avoiding interpolation and allowing discontinuous fields fitted by MLPs with derivative and predicted-point consistency losses.
Key results
- On Thingi32, UODFs achieve CD-GEP 0.378e-5 versus 0.432e-5 for NGLOD5 and CD-Mesh 2.69e-5 vs 2.83e-5 (NGLOD5).
- On MGN10 non-watertight garments, UODFs reach CD-GEP 0.227e-5 and NC-Mesh 99.6 versus 4.95e-5 CD-GEP for the next best UDF method HSDF (NC 92.0).
- UODFs outperform MeshUDF at all tested grid resolutions (32^3 to 256^3) even though MeshUDF is given ground-truth UDF values and gradients.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add Lder (ablation) | UODFs · Nandi the Bull | CD-GEP (*105): 0.238 -> 0.228 | Helped |
| add Lder (ablation) | UODFs · Bunny | CD-GEP (*105): 0.161 -> 0.170 | Hurt |
| add Lder (ablation) | UODFs · Hilbert Cube | CD-GEP (*105): 0.00663 -> 0.00532 | Helped |
| add Lpred (ablation) | UODFs · Nandi the Bull | CD-GEP (*105): 0.297 -> 0.228 | Helped |
| add Lpred (ablation) | UODFs · Bunny | CD-GEP (*105): 0.152 -> 0.170 | Hurt |
| add Lpred (ablation) | UODFs · Hilbert Cube | CD-GEP (*105): 0.256 -> 0.00532 | Helped |
Surprising findings
- A discontinuous distance field (UODF) can be fitted well by an MLP, challenging the belief that only continuous fields suit neural fitting.
- UODFs outperform MeshUDF even when MeshUDF uses ground-truth UDF values as input.
Limitations
- Requires three separate neural networks (one per orthogonal UODF), giving a large parameter count.
- Per-shape training; fitting all three fields in a single network is left to future work.
Experimental setup
Datasets: Thingi10K Thingi32 Stanford 3D Scanning Repository ShapeNet MGN
Benchmarks: Thingi32 MGN10 Stanford Bunny Hilbert Cube T-shirt multi-resolution
Metrics: CD-GEP CD-Mesh NC-Mesh
Baselines: SIREN NGLOD3 NGLOD5 NDF HSDF GIFS MeshUDF
Builds on: marching cubes NeUDF MeshUDF NGLOD SIREN
Closest papers by meaning
- DUDF: Differentiable Unsigned Distance Fields with Hyperbolic Scaling (CVPR 2024 · similarity 0.90)
- A Lightweight UDF Learning Framework for 3D Reconstruction Based on Local Shape Functions (CVPR 2025 · similarity 0.88)
- High Resolution UDF Meshing via Iterative Networks (NeurIPS 2025 · similarity 0.88)
- Small Steps and Level Sets: Fitting Neural Surface Models with Point Guidance (CVPR 2024 · similarity 0.88)
- Few-Shot Unsupervised Implicit Neural Shape Representation Learning with Spatial Adversaries (ICML 2024 · similarity 0.88)
- Details Enhancement in Unsigned Distance Field Learning for High-fidelity 3D Surface Reconstruction (AAAI 2025 · similarity 0.88)
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