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Implicit-ARAP: Efficient Handle-Guided Neural Field Deformation via Local Patch Meshing
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Proposes Implicit-ARAP, which optimizes an as-rigid-as-possible energy for handle-guided neural field deformation by meshing many small flat patches projected onto multiple level sets of a neural SDF.
Problem
Handle-guided deformation of neural signed distance fields with controlled, accurate surface quality, robustness, and efficiency; ARAP energies are hard to evaluate directly on implicit surfaces.
Approach
Discretize level sets of a neural SDF with randomly placed local flat patches projected via the SDF gradient and closest-point formula, then compute a cotangent-weighted ARAP loss on these patches to train an invertible (volume-preserving) MLP deformation field, with a translation field added to fit handles.
Key results
- On TFD, Implicit-ARAP achieves 0.00% volume error versus 6.66% for NFGP, with 2m48s runtime versus 14h26m for NFGP.
- On DeFAUST, Implicit-ARAP reaches 2.41% edge length error and 0.63% area error, against 8.71% and 20.02% for NFGP.
- Implicit-ARAP's SDF gradient norm is 1.016 (std 0.146) versus 1.029 (std 0.290) for NFGP, indicating better preservation of SDF properties.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Implicit-ARAP instead of NFGP | Neural field deformation · TFD and DeFAUST | Runtime: 2m:48s vs 14h:26m (TFD); 5m:36s vs 14h:26m (DeFAUST) | Helped |
| Use Implicit-ARAP instead of NSDP | Mesh deformation · DT4D | Deformation quality metrics: Volume 7.80\% -> 0.58\%; Area 5.76\% -> 2.04\%; EL 3.59\% -> 2.03\%; FA 6.603\textdegree -> 4.728\textdegree | Helped |
| Use Implicit-ARAP instead of NSDP | Mesh deformation · DT4D | Runtime: 0m:18s -> 6m:33s | Hurt |
| Add patches from nonzero level sets (ablation) | Implicit-ARAP · Neural field deformation | SDF gradient norm preservation | Helped |
| Add the ARAP loss (ablation) | Implicit-ARAP · Neural field deformation | SDF gradient norm preservation | Helped |
| Vary patch point sampling distribution (ablation) | Implicit-ARAP · Patch meshing and deformation | Deformation quality | No clear effect |
| Increase patch density above 50 (ablation) | Implicit-ARAP · TFD | Approximation error | No clear effect |
| Decrease patch radius toward zero (ablation) | Implicit-ARAP · Neural field deformation | Deformation quality | Hurt |
| Use overly large patches (ablation) | Implicit-ARAP · Neural field deformation | Deformation quality | Hurt |
| Use zero-level-set-only marching cubes discretization (ablation) | ARAP regularization for neural fields · Neural field deformation | Deformation quality | Hurt |
| Use marching cubes across all level sets (ablation) | ARAP regularization for neural fields · Neural field deformation | Optimization behavior | Hurt |
| Decrease the ARAP loss weight (ablation) | Implicit-ARAP · Neural field handle fitting | Handle accuracy | Helped |
Surprising findings
- Explicit ARAP and Elastic achieve much lower area, edge length, and angle errors than Implicit-ARAP, which the authors attribute to them being least-squares optimal for local rigidity.
- The authors note that the method is not a drop-in replacement for marching cubes, since patches do not cover the full surface.
Limitations
- No exact guarantee of preserving SDF properties under deformation.
- ARAP loss is highly dependent on the patch discretization and requires hyperparameters such as patch radius and density.
- Explicit ARAP baselines achieve better area, edge length and angle metrics than the proposed method.
Experimental setup
Datasets: Thingi10k Stanford 3D scanning repository DeFAUST DeformingThings4D (DT4D) FAUST
Benchmarks: TFD DeFAUST DT4D
Metrics: volume error area error edge length error face angle error runtime SDF gradient norm mean and std patch approximation error
Baselines: ARAP Elastic SR-ARAP NFGP NSDP Marching cubes
Builds on: As-Rigid-As-Possible deformation Neural Field Geometry Processing (NFGP) NICE Neural Shape Deformation Priors eikonal training
Closest papers by meaning
- Implicit Neural Surface Deformation with Explicit Velocity Fields (ICLR 2025 · similarity 0.90)
- 4Deform: Neural Surface Deformation for Robust Shape Interpolation (CVPR 2025 · similarity 0.89)
- Diffeomorphic Mesh Deformation via Efficient Optimal Transport for Cortical Surface Reconstruction (ICLR 2024 · similarity 0.87)
- Small Steps and Level Sets: Fitting Neural Surface Models with Point Guidance (CVPR 2024 · similarity 0.87)
- Flatten Anything: Unsupervised Neural Surface Parameterization (NeurIPS 2024 · similarity 0.87)
- CoFie: Learning Compact Neural Surface Representations with Coordinate Fields (NeurIPS 2024 · similarity 0.87)
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