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DUDF: Differentiable Unsigned Distance Fields with Hyperbolic Scaling
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Learns a hyperbolic-scaled unsigned distance field (tanh-scaled) with a sine-activated MLP, solved as a heterogeneous Eikonal problem with boundary and curvature-alignment losses, to represent open surfaces differentiably.
Problem
Neural unsigned distance fields (UDFs) are non-differentiable at the zero level set, causing errors in distances, gradients and normals, and fragmented surfaces when reconstructing open surfaces.
Approach
Replace the UDF with t_S(x)=d_S(x)tanh(αd_S(x)), which is differentiable and zero on the surface and equals d_S far away; train a SIREN-style network on a heterogeneous Eikonal PDE with Dirichlet, Neumann-like and maximum-curvature alignment conditions, plus isosurface refinement.
Key results
- On DeepFashion open surfaces, the method (MC1) reaches L1 CD 9.01 and L2 CD 0.025 versus CAP-UDF 18.1 and 1.110, with training time 326 s versus 1390 s.
- On ShapeNet cars (open), training time is 317 s versus CAP-UDF 1040 s, with L1 CD 12.3 versus 10.9 for CAP-UDF (CAP-UDF is better on L1 there).
- On closed ShapeNet cars, L2 CD 0.028 with MC1 versus 0.030 for CAP-UDF, at 319 s versus 1080 s.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use DUDF instead of CAP-UDF | open-surface reconstruction · DeepFashion | L1CD (×103): 18.1 -> 9.01 | Helped |
| use DUDF instead of CAP-UDF | open-surface reconstruction · Multi-Garment | L1CD (×103): 18.5 -> 8.70 | Helped |
| use DUDF instead of CAP-UDF | open-surface reconstruction · ShapeNet cars | NC: 0.288 -> 0.387 | Helped |
| remove the Eikonal loss (ablation) | DUDF · DeepFashion | NC: 0.020 -> 0.033 | Hurt |
| remove the maximum-curvature loss (ablation) | DUDF · DeepFashion | NC: 0.020 -> 0.021 | No clear effect |
| remove both the Eikonal and maximum-curvature losses (ablation) | DUDF · DeepFashion | NC: 0.020 -> 0.035 | Hurt |
| remove the refinement loss (ablation) | DUDF · DeepFashion | NC: 0.020 -> 0.031 | Hurt |
| approximate dS instead of hyperbolically scaled tS, using sine activations (ablation) | DUDF · DeepFashion | L1CD (×103): 9.14 -> 31.2 | Hurt |
| approximate dS instead of hyperbolically scaled tS, using ReLU activations (ablation) | DUDF · DeepFashion | L1CD (×103): 9.14 -> 47.5 | Hurt |
| vary α; larger values make tS more closely approximate dS (ablation) | DUDF · DeepFashion | reconstruction error | Hurt |
| vary α; smaller values widen the quadratic strip near the isosurface (ablation) | DUDF · DeepFashion | reconstruction performance | Hurt |
Surprising findings
- On ShapeNet cars with open surfaces, CAP-UDF attains lower L1 Chamfer distance (10.9 vs 12.3) and better normal consistency than the proposed method, though the method is faster.
Limitations
- Requires ground-truth unsigned distances for supervision, and the quadratic near-surface behavior yields a wider near-zero strip that can inflate representations.
- Computing the maximum-curvature direction field is expensive, requiring three network passes and Hessian diagonalization.
- Gradient-based Marching Cubes outputs can be less smooth than sphere tracing due to sensitivity to noise.
Experimental setup
Datasets: ShapeNet cars Multi-Garment DeepFashion
Benchmarks: ShapeNet cars Multi-Garment DeepFashion
Metrics: L1 Chamfer distance L2 Chamfer distance Normal Consistency training time
Baselines: SIREN CAP-UDF DeepSDF NDF
Builds on: SIREN CAP-UDF Marching Cubes Neural Distance Fields
Closest papers by meaning
- Details Enhancement in Unsigned Distance Field Learning for High-fidelity 3D Surface Reconstruction (AAAI 2025 · similarity 0.91)
- Unsigned Orthogonal Distance Fields: An Accurate Neural Implicit Representation for Diverse 3D Shapes (CVPR 2024 · similarity 0.90)
- High Resolution UDF Meshing via Iterative Networks (NeurIPS 2025 · similarity 0.90)
- MIND: Material Interface Generation from UDFs for Non-Manifold Surface Reconstruction (NeurIPS 2025 · similarity 0.89)
- Neural Signed Distance Function Inference through Splatting 3D Gaussians Pulled on Zero-Level Set (NeurIPS 2024 · similarity 0.89)
- GaussianUDF: Inferring Unsigned Distance Functions through 3D Gaussian Splatting (CVPR 2025 · similarity 0.88)
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