Research map / Point clouds / Shape and surface completion
4Deform: Neural Surface Deformation for Robust Shape Interpolation
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Proposes 4Deform, a neural implicit surface deformation method that learns a continuous velocity field with distortion and stretching losses to interpolate point cloud and mesh sequences from sparse, noisy correspondences.
Problem
Generating physically plausible intermediate shapes between non-rigidly deformed shapes given unstructured point clouds with noisy or partial correspondences and changing topology, where prior mesh and neural implicit methods fail.
Approach
Learns a continuous velocity field in Euclidean space that drives a level-set neural implicit surface via a modified level-set equation, with new distortion (deviatoric) and tangent-plane stretching losses that regularize deformation without requiring connectivity or intermediate-shape supervision.
Key results
- On 4D-DRESS pair setting, CD 0.269e-4 vs 0.279e-4 for the physics-based baseline [45] and SA_sigma 0.018 vs 0.023, i.e. on par with better area preservation.
- On SMAL isometric animals, achieves CD 0.137e-3 vs 0.173e-3 for [45] and HD 0.221e-2 vs 0.626e-2.
- Sequence setting on 4D-DRESS: CD 0.327e-4 and HD 0.038e-2, versus 0.390e-4 for the ablation without both losses; claims an order-of-magnitude lower area distortion than LIMP on large FAUST deformations.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use 4Deform instead of [45] | 4D-Dress interpolation · 4D-Dress Pairs S/S | CD (×104): 0.279 -> 0.269 | Helped |
| Use 4Deform instead of [45] | 4D-Dress interpolation · 4D-Dress Pairs S/R | HD (×102): 0.083 -> 0.101 | Hurt |
| Use 4Deform instead of [45] | SMAL interpolation · SMAL Pairs S/S | HD (×102): 0.626 -> 0.221 | Helped |
| Add distortion loss Ld (ablation) | 4Deform · 4D-Dress Pairs S/S | SAσ(×10): 0.115 -> 0.018 | Helped |
| Add distortion loss Ld (ablation) | 4Deform · 4D-Dress Seq. S/S | CD (×104): 0.348 -> 0.327 | Helped |
| Add distortion loss Ld (ablation) | 4Deform · 4D-Dress Pairs S/R | P-RMSE (×10): 0.023 -> 0.014 | Helped |
| Add stretching loss Lst (ablation) | 4Deform · 4D-Dress Pairs S/S | CD (×104): 0.284 -> 0.269 | Helped |
| Add stretching loss Lst (ablation) | 4Deform · 4D-Dress Pairs S/S | HD (×102): 0.045 -> 0.046 | Hurt |
| Add stretching loss Lst (ablation) | 4Deform · 4D-Dress Seq. S/S | CD (×104): 0.363 -> 0.327 | Helped |
| Add both distortion loss Ld and stretching loss Lst (ablation) | 4Deform · 4D-Dress Pairs S/S | SAσ(×10): 0.023 -> 0.018 | Helped |
| Add both distortion loss Ld and stretching loss Lst (ablation) | 4Deform · 4D-Dress Seq. S/S | CD (×104): 0.390 -> 0.327 | Helped |
| Add both distortion loss Ld and stretching loss Lst (ablation) | 4Deform · 4D-Dress Pairs S/R | P-RMSE (×10): 0.024 -> 0.014 | Helped |
Surprising findings
- LIMP, a mesh-based sequence method, performs very poorly on 4D-DRESS (CD 21.98e-4 in pair setting), attributed to its data demand.
Limitations
- Does not capture mechanical joints or fluid dynamics well.
- Cannot yet separate body and loose clothing deformations.
- Relies on estimated correspondences from an external matching module and per-pair training time of 8-10 minutes.
Experimental setup
Datasets: FAUST SMAL SHREC16 4D-DRESS BeHave
Benchmarks: FAUST SMAL SHREC16 4D-DRESS BeHave
Metrics: Chamfer Distance Hausdorff Distance surface area standard deviation (SA_sigma) P-RMSE
Baselines: LIMP NFGP LipMLP NISE Neural deformation field with physical constraints (Shape-pair optimization, [45
Builds on: modified level-set equation (NISE/Eulerian deformation of implicit fields) AutoDecoder (DeepSDF-style latent) unsupervised functional map shape matching LIMP
Closest papers by meaning
- Implicit Neural Surface Deformation with Explicit Velocity Fields (ICLR 2025 · similarity 0.91)
- Diffeomorphic Mesh Deformation via Efficient Optimal Transport for Cortical Surface Reconstruction (ICLR 2024 · similarity 0.89)
- Implicit-ARAP: Efficient Handle-Guided Neural Field Deformation via Local Patch Meshing (NeurIPS 2025 · similarity 0.89)
- Motion2VecSets: 4D Latent Vector Set Diffusion for Non-rigid Shape Reconstruction and Tracking (CVPR 2024 · similarity 0.87)
- Dynamic Neural Surfaces for Elastic 4D Shape Representation and Analysis (CVPR 2025 · similarity 0.87)
- Learning Bijective Surface Parameterization for Inferring Signed Distance Functions from Sparse Point Clouds with Grid Deformation (CVPR 2025 · similarity 0.87)
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