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Implicit Neural Surface Deformation with Explicit Velocity Fields
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Proposes an unsupervised end-to-end method that jointly learns time-varying neural SDFs and a smooth, divergence-free velocity field to deform between two point clouds via a modified level-set equation.
Problem
Recovering physically plausible intermediate shapes when deforming implicit neural surfaces between two point clouds, without intermediate shape supervision or pre-trained SDFs.
Approach
Model point motion with an explicit velocity network (smoothness and divergence-free regularization) and deform a time-varying implicit field directly via a modified level-set equation that embeds the Eikonal constraint, avoiding mesh rendering and separate SDF pre-training.
Key results
- On DeformingThings4D fox and bear sequences (55 intermediate shapes), the method maintains consistently low CD/HD on intermediate meshes while LipMLP and NISE show increasing errors at intermediate steps.
- Runs in about 20 minutes per pair on a GTX TITAN X, versus about 1.5 hours for NISE and about 15 hours per step for NFGP (per the paper's claim of 1/5 of NISE time).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MLSE instead of the original level-set equation (OLSE) (ablation) | Implicit Neural Surface Deformation · Intermediate shapes | signed distance field stability | Helped |
| Add a divergence-free velocity constraint (ablation) | Implicit Neural Surface Deformation · Extrinsic deformation | volume preservation | Helped |
| Add velocity-field smoothness regularization (ablation) | Implicit Neural Surface Deformation · Sparse correspondences | deformation smoothness | Helped |
| Use approximately 1% ground-truth correspondences instead of more correspondences (ablation) | Implicit Neural Surface Deformation · Intermediate shapes | deformation quality | Hurt |
| Increase ground-truth correspondence availability to more than approximately 10% (ablation) | Implicit Neural Surface Deformation · Intermediate shapes | deformation quality | Helped |
| Misalign 20% of correspondences with their 5th-nearest-neighbor correspondences (ablation) | Implicit Neural Surface Deformation · Intermediate shapes with local correspondence noise | deformation quality | Hurt |
| Randomly misalign 10% of correspondences globally (ablation) | Implicit Neural Surface Deformation · Intermediate shapes with global correspondence noise | deformation quality | Hurt |
| Disable the divergence-free constraint (ablation) | Implicit Neural Surface Deformation · Extrinsic deformation | volume preservation | Hurt |
Surprising findings
- Reports reasonable deformations even with no ground-truth correspondences, though deformations are less smooth and show artifacts.
Limitations
- Requires sparse ground-truth point correspondences.
- Struggles with large deformations and produces surface artifacts.
- Fails when large missing regions exist in input point clouds.
Experimental setup
Datasets: Faust SMAL SHREC16 DeformingThings4D
Benchmarks: DeformingThings4D Faust SMAL SHREC16
Metrics: Chamfer Distance Hausdorff Distance
Baselines: LipMLP NISE NFGP SmS
Builds on: level-set equation LipMLP NISE as-rigid-as-possible deformation
Closest papers by meaning
- 4Deform: Neural Surface Deformation for Robust Shape Interpolation (CVPR 2025 · similarity 0.91)
- Implicit-ARAP: Efficient Handle-Guided Neural Field Deformation via Local Patch Meshing (NeurIPS 2025 · similarity 0.90)
- Occlusion-aware Non-Rigid Point Cloud Registration via Unsupervised Neural Deformation Correntropy (ICLR 2025 · similarity 0.86)
- Dynamic Neural Surfaces for Elastic 4D Shape Representation and Analysis (CVPR 2025 · similarity 0.86)
- Degrees of Freedom Matter: Inferring Dynamics from Point Trajectories (CVPR 2024 · similarity 0.85)
- Diffeomorphic Mesh Deformation via Efficient Optimal Transport for Cortical Surface Reconstruction (ICLR 2024 · similarity 0.85)
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