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Learning Bijective Surface Parameterization for Inferring Signed Distance Functions from Sparse Point Clouds with Grid Deformation
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Learns a bijective spherical surface parameterization (BSP) and a grid deformation optimization (GDO) network to infer SDFs end-to-end from sparse point clouds without extra priors.
Problem
Inferring continuous signed distance functions from extremely sparse point clouds, where local geometric detail is lacking and existing self-supervised or prior-based methods produce incomplete or coarse surfaces.
Approach
Learn a bijective mapping between a unit-sphere parametric domain and 3D space, sample dense local patches around each point and integrate them into a global parametric surface, then use a deformable tetrahedral grid whose vertices move along SDF-gradient-based normal directions (GDO) to fit this surface and yield an implicit field.
Key results
- On ShapeNet with 300 input points, the method achieves mean CD-L1 0.099 x10 vs 0.137 for the prior best NTPS++ and CD-L2 0.073 vs 0.089.
- On SRB, CD-L1 0.41 x100 and HD 5.66 vs 0.49 and 6.04 for SparseOcc (best prior).
- On DFAUST, achieves best CD-L2 and NC (0.914) across percentiles, though NTPS is close.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use BSP parameterized supervision rather than sparse input alone (ablation) | BSP and GDO · ShapeNet lamp | CDL1 × 10: 0.873 -> 0.077 | Helped |
| Replace BSP with LDI upsampling (ablation) | BSP and GDO · ShapeNet lamp | CDL1 × 10: 0.077 -> 0.427 | Hurt |
| Replace BSP with single-surface TPS parameterization (ablation) | BSP and GDO · ShapeNet lamp | CDL1 × 10: 0.077 -> 0.083 | Hurt |
| Replace BSP with multi-part Atlas parameterization (ablation) | BSP and GDO · ShapeNet lamp | CDL1 × 10: 0.077 -> 0.087 | Hurt |
| Use 10 local-patch samples instead of 3 (ablation) | BSP and GDO · ShapeNet lamp | CDL1 × 10: 0.086 -> 0.077 | Helped |
| Increase local-patch samples from 10 to 15 (ablation) | BSP and GDO · ShapeNet lamp | NC: 0.914 -> 0.914 | No clear effect |
| Replace GDO with TPS optimization (ablation) | BSP and GDO · ShapeNet lamp | CDL1 × 10: 0.077 -> 0.094 | Hurt |
| Remove gradient consistency and predict grid-point offsets (ablation) | BSP and GDO · ShapeNet lamp | CDL1 × 10: 0.077 -> 0.089 | Hurt |
| Remove Lpara (ablation) | BSP and GDO · ShapeNet lamp | CDL1 × 10: 0.077 -> 0.873 | Hurt |
| Remove Ldeform (ablation) | BSP and GDO · ShapeNet lamp | CDL1 × 10: 0.077 -> 0.085 | Hurt |
| Remove Lsurf (ablation) | BSP and GDO · ShapeNet lamp | CDL1 × 10: 0.077 -> 0.081 | Hurt |
| Increase input point-cloud size (ablation) | BSP and GDO · ShapeNet | reconstruction accuracy | Helped |
Limitations
- Gains on DFAUST at the 50% percentile are not uniformly best (NTPS has lower CD-L2 at 50%).
- Hyperparameter sensitivity and computation cost of patch sampling not analyzed in the main text.
Experimental setup
Datasets: ShapeNet D-FAUST SRB 3DScene KITTI
Benchmarks: ShapeNet D-FAUST SRB 3DScene KITTI
Metrics: CD L1 CD L2 Normal Consistency Hausdorff Distance
Baselines: Nspline NP NDrop Onsurf SparseOcc NTPS NTPS++ PSR SAP VIPSS
Builds on: TPS AtlasNet Point Transformer Deep Marching Tetrahedra NTPS
Closest papers by meaning
- MultiPull: Detailing Signed Distance Functions by Pulling Multi-Level Queries at Multi-Step (NeurIPS 2024 · similarity 0.89)
- Small Steps and Level Sets: Fitting Neural Surface Models with Point Guidance (CVPR 2024 · similarity 0.89)
- A Lightweight UDF Learning Framework for 3D Reconstruction Based on Local Shape Functions (CVPR 2025 · similarity 0.88)
- Inferring Neural Signed Distance Functions by Overfitting on Single Noisy Point Clouds through Finetuning Data-Driven based Priors (NeurIPS 2024 · similarity 0.87)
- Neural Signed Distance Function Inference through Splatting 3D Gaussians Pulled on Zero-Level Set (NeurIPS 2024 · similarity 0.87)
- Toward Robust Neural Reconstruction from Sparse Point Sets (CVPR 2025 · similarity 0.87)
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