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CoFie: Learning Compact Neural Surface Representations with Coordinate Fields
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Proposes CoFie, a generalizable local neural SDF representation that learns optimizable per-voxel coordinate frames (initialized from estimated normals/tangents) plus quadratic MLP layers, achieving better shape error than DeepSDF and DeepLS with fewer parameters.
Problem
Neural implicit surface representations based on local shapes are accurate but parameter-heavy, and fitting unaligned local surface patches with MLPs is a non-convex problem prone to local minima.
Approach
Decouple the rigid transformation of each local shape from its geometry by learning a Coordinate Field (per-voxel 6-DoF frames initialized from estimated normal and tangent directions) that maps points into an aligned local frame, and replace the last MLP layer with a quadratic layer to better capture local quadratic surface geometry.
Key results
- On novel instances of training categories, CoFie achieves mean chamfer distance 1.86e-4, about 48% lower than the best baseline DeepLS.
- On 10 unseen ShapeNet categories, CoFie reaches mean chamfer 3.18e-4 vs 7.27e-4 for DeepLS (about 56% reduction) and wins on 9 of 10 categories.
- CoFie with latent size 48 matches DeepLS with latent size 128 while using roughly 15% of the MLP parameters; on Thingi, CoFie is comparable to per-shape NGLOD.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use CoFie instead of DeepLS | Generalizable shape representation · ShapeNet unseen categories | mean chamfer distance (10^-4): 7.27 -> 3.18 | Helped |
| Add axis-aligned coordinate field initialization (ablation) | CoFie · ShapeNet training categories | shape error: 3.91 -> 3.45 | Helped |
| Initialize local frames with estimated normal and tangent directions (ablation) | CoFie · ShapeNet training categories | shape error: 3.91 -> 2.33 | Helped |
| Replace a linear output layer with a quadratic layer (ablation) | CoFie MLP · ShapeNet training categories | shape error: 0.9 reduction | Helped |
| Add a linear layer to the MLP instead of using a quadratic output layer (ablation) | CoFie MLP · ShapeNet training categories | shape error | Helped |
| Use geometry-aware coordinate-field initialization and a quadratic layer together (ablation) | CoFie · ShapeNet training categories | shape error | Helped |
| Use CoFie at the same parameter amount as prior works | CoFie · Novel instances from training and unseen categories | shape error: 48%; 56% | Helped |
Surprising findings
- Axis-aligned coordinate field initialization barely helps (3.91 to 3.45), while geometry-aware normal/tangent initialization reduces error to 2.33.
- Simply adding a linear layer to the MLP only slightly reduces shape error compared with the quadratic last layer.
Limitations
- Cannot perform shape completion since it models only observable local parts, unlike DeepSDF's global priors.
- Fixed voxel resolution breaks the local-shape analysis when a cell intersects thin structures.
- Still struggles to represent extremely detailed geometry parts.
Experimental setup
Datasets: ShapeNet Thingi
Benchmarks: ShapeNet unseen categories ShapeNet novel instances (training categories) Thingi
Metrics: chamfer-L2 distance
Baselines: DeepSDF DeepLS NGLOD 3DS2VS
Builds on: DeepSDF DeepLS NGLOD
Closest papers by meaning
- Unsigned Orthogonal Distance Fields: An Accurate Neural Implicit Representation for Diverse 3D Shapes (CVPR 2024 · similarity 0.87)
- Small Steps and Level Sets: Fitting Neural Surface Models with Point Guidance (CVPR 2024 · similarity 0.87)
- Implicit-ARAP: Efficient Handle-Guided Neural Field Deformation via Local Patch Meshing (NeurIPS 2025 · similarity 0.87)
- A Lightweight UDF Learning Framework for 3D Reconstruction Based on Local Shape Functions (CVPR 2025 · similarity 0.86)
- Grounding Continuous Representations in Geometry: Equivariant Neural Fields (ICLR 2025 · similarity 0.86)
- Flatten Anything: Unsupervised Neural Surface Parameterization (NeurIPS 2024 · similarity 0.86)
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