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Dynamic Neural Surfaces for Elastic 4D Shape Representation and Analysis
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Proposes Dynamic Spherical Neural Surfaces (D-SNS), an MLP-based continuous spatiotemporal representation of genus-0 4D surfaces that enables registration, geodesics, and Karcher mean computation without discretization.
Problem
Statistical analysis of genus-0 4D surfaces (deforming 3D surfaces over time) requires spatiotemporal registration, which is usually done on discretized meshes and yields resolution-dependent, suboptimal results.
Approach
Treat 4D surfaces as continuous functions from a sphere and time to 3D, parameterized by an MLP (D-SNS), and perform elastic registration via SRNF (spatial) and SRVF (temporal) L2 formulations directly on the neural representation.
Key results
- D-SNS reconstructs genus-0 4D surfaces with mean point-wise L2 error on the order of 1e-6 across DFAUST, CAPE, COMA, and VOCA (Table 1).
- On ten same-action pairs, geodesic distance after registration is lower than 4D Atlas on all four datasets, e.g., CAPE 0.4597 vs 0.5358 mean.
- Temporal registration error stays stable at 25 temporal samples while 4D Atlas error increases (Figure 8).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use D-SNS spatiotemporal registration instead of 4D Atlas | 4D surface registration · CAPE | geodesic distance: 0.5358 -> 0.4597 | Helped |
| Use D-SNS spatiotemporal registration instead of 4D Atlas | 4D surface registration · DFAUST | geodesic distance: 0.8891 -> 0.7944 | Helped |
| Use D-SNS spatiotemporal registration instead of 4D Atlas | 4D surface registration · COMA | geodesic distance: 0.0478 -> 0.0456 | Helped |
| Use D-SNS spatiotemporal registration instead of 4D Atlas | 4D surface registration · VOCA | geodesic distance: 0.1768 -> 0.1171 | Helped |
Limitations
- Evaluation limited to genus-0 surfaces, mainly human bodies and faces
- Requires per-sequence overfitting of a D-SNS (2-3 hours per 4D surface)
- Comparison only against a single baseline (4D Atlas)
Experimental setup
Datasets: MPI DFAUST VOCA COMA CAPE
Benchmarks: DFAUST CAPE COMA VOCA
Metrics: mean pointwise L2 representation error temporal registration error vs inverse warp geodesic distance after registration
Baselines: 4D Atlas
Builds on: Neural Surface Maps Spherical Neural Surfaces 4D Atlas SRNF elastic shape analysis SRVF curve registration
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