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Stable-SCore: A Stable Registration-based Framework for 3D Shape Correspondence
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Stable-SCore registers a source mesh to a target by optimizing Neural Jacobian Fields under supervision from 2D semantic flows produced by a Stable Diffusion/DINO-based 2D character correspondence adapter, and introduces the CharW in-the-wild benchmark.
Problem
Dense 3D character shape correspondence under non-isometric discrepancies, where functional map methods fall short and registration methods suffer from unstable deformations and need good initial correspondences.
Approach
Replace per-vertex deformation with Neural Jacobian Fields and supervise registration with differentiable-rendered 2D semantic flow maps from a foundation-model-based 2D correspondence adapter, plus a geometry-grounded negative loss and a shear-resistant regularizer.
Key results
- Ours (Normal) achieves 2.61 mean geodesic error on CharW versus 32.6 for ULRSSM and 12.5 for Diff3F in the cross-domain setting.
- On DT4D-H hard, Stable-SCore reaches 4.12 versus 14.3 for DFR and 22.7 for Diff3F in cross-domain evaluation.
- Replacing per-vertex displacement with Neural Jacobian Fields reduces FAUST error from 2.88 to 2.32 in the ablation.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Neural Jacobian Field instead of per-vertex displacements (ablation) | Stable-SCore · FAUST (cross-domain) | mean geodesic error ×100: 2.88 -> 2.32 | Helped |
| Add shear-resistant loss (ablation) | Stable-SCore · FAUST (cross-domain) | mean geodesic error ×100: 2.32 -> 2.07 | Helped |
| Add geometry-grounded negative loss during 2D correspondence training (ablation) | Stable-SCore · FAUST (cross-domain) | mean geodesic error ×100: 2.07 -> 1.83 | Helped |
| Train the feature adapter rather than use foundation features zero-shot (ablation) | Stable-SCore · FAUST (cross-domain) | mean geodesic error ×100: 5.60 -> 1.83 | Helped |
| Use semantic flow supervision instead of 3D correspondence supervision (ablation) | Stable-SCore registration · FAUST (cross-domain) | mean geodesic error ×100: 2.19 -> 1.83 | Helped |
| Use semantic flow supervision instead of 3D correspondence supervision (ablation) | Stable-SCore registration · CharW (cross-domain, RGB) | mean geodesic error ×100: 2.65 -> 2.57 | Helped |
| Use semantic flow supervision instead of 3D correspondence supervision (ablation) | Stable-SCore registration · DT4D-H hard (cross-domain) | mean geodesic error ×100: 4.56 -> 4.12 | Helped |
| Use Stable-SCore rather than the strongest baseline | 3D shape correspondence · CharW (cross-domain) | mean geodesic error ×100: 6.52 -> 2.61 | Helped |
| Use Stable-SCore rather than the strongest baseline | 3D shape correspondence · DT4D-H hard (cross-domain) | mean geodesic error ×100: 14.3 -> 4.12 | Helped |
| Use Stable-SCore rather than the strongest baseline | 3D shape correspondence · FAUST (intra-domain) | mean geodesic error ×100: 1.48 -> 1.58 | Hurt |
| Use Stable-SCore rather than the strongest baseline | 3D shape correspondence · DT4D-H std (intra-domain) | mean geodesic error ×100: 3.47 -> 3.11 | Helped |
| Use Stable-SCore rather than the strongest baseline | 3D shape correspondence · DT4D-H hard (intra-domain) | mean geodesic error ×100: 3.95 -> 3.38 | Helped |
Surprising findings
- Functional map methods such as ULRSSM and Hybrid ULRSSM, strong on near-isometric FAUST, degrade sharply on CharW (over 30 error), indicating poor non-isometric generalization.
- Using semantic flow supervision for registration outperforms 3D correspondence supervision derived from back-projected features (1.83 vs 2.19 on FAUST).
Limitations
- Registration requires roughly aligned rotation between source and target for the 2D correspondence model.
- Runtime grows with mesh size, requiring several minutes per pair via iterative optimization.
- Method is categorized as supervised, which the authors note as a design choice that complicates comparison with unsupervised methods.
Experimental setup
Datasets: 3DBiCar SURREAL SPair-71K FAUST DT4D-H
Benchmarks: FAUST CharW DT4D-H std DT4D-H hard
Metrics: mean geodesic error (x100, normalized by sqrt of surface are
Baselines: SmoothShell Diff3f DeepShell DFR HybridGeoFMap ULRSSM Hybrid ULRSSM GeoFMap
Builds on: Neural Jacobian Fields Diff3F DiffusionNet Marigold
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