Research map / 3D vision / Depth and stereo
Degrees of Freedom Matter: Inferring Dynamics from Point Trajectories
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Proposes DOMA, a compact spatiotemporal implicit motion field (SIREN with time input and affine output) that predicts dense long-range 3D point motion from sparse point trajectories, with a smoothness regularizer.
Problem
Inferring dense long-range motion of generic 3D scenes from observed point trajectories, without data-driven or scene-specific priors, while keeping models compact and temporally consistent.
Approach
Extends the per-frame dynamic point field to a single SIREN taking (x, t) as input and outputting an affine map plus translation; extra output degrees of freedom (scaling, shearing) raise representational power via the Jacobian without adding hidden layers, and a Charbonnier-based piece-wise smoothness loss curbs overfitting.
Key results
- On DeformingThings4D, Ours-Affinity achieves EPE 78.1e-4 and LCD 1.266e-4, outperforming BoneCloud (136.1 EPE) and MLP baselines.
- On Resynth guided mesh alignment, DOMA-Affinity matches frame-wise DPF accuracy (LCD 1.142 vs 1.149) with better temporal smoothness (STD(E) 11.9 vs 11.6 and STD(V) 22.8 vs 24.6 in Table 3), and checkpoint size of about 211KB vs 7800KB for DPF.
- On synthetic sequences, Affinity-H reaches EPE 5.4e-4 on rotation and 8.5e-4 on shearing, showing extra DOFs and matching regularization matter.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace the translation field with an affine field (ablation) | DOMA for novel point motion prediction · DeformingThings4D sequences | LCD: 1.401 -> 1.266 | Helped |
| Use an SE(3) output transform instead of translation-only (ablation) | DOMA · DeformingThings4D sequences | EPE: 78.5 -> 76.7 | Helped |
| Add scaling to the SE(3) output transform (ablation) | DOMA · DeformingThings4D sequences | EPE: 76.7 -> 76.2 | Helped |
| Use an affine field instead of translation-only (ablation) | DOMA for guided mesh alignment · Resynth sequences | LCD: 1.230 -> 1.142 | Helped |
| Add motion smoothness regularization (ablation) | DOMA-Affinity for guided mesh alignment · Resynth sequences | LCD: 1.142 -> 1.127 | Helped |
| Add AIAP and motion smoothness regularization together (ablation) | DOMA-Affinity for guided mesh alignment · Resynth sequences | LCD: 1.142 -> 1.187 | Hurt |
| Add motion smoothness regularization (ablation) | DOMA for novel point motion prediction · Synthetic sequences | EPE: 622.1 -> 8.5 | Mixed |
| Use motion smoothness regularization without Charbonnier (ablation) | DOMA variants · Synthetic sequences | EPE | Mixed |
| Use elasticity regularization (ablation) | DOMA-Affinity · Synthetic sequences | EPE: 1486.0 -> 19.2 | Mixed |
| Replace per-frame DPF with a single spatiotemporal model (ablation) | DOMA-Trans · Resynth sequences | STD(V): 24.6 -> 22.9 | Helped |
| Use an affine field rather than a translation field (ablation) | DOMA for guided mesh alignment · Resynth sequences | STD(V): 22.9 -> 22.8 | No clear effect |
Surprising findings
- Adding elastic regularization (-E) from Nerfies helps rigid motion but performs worse on scaling and shearing, indicating regularizer choice must match motion type.
- DOMA-Trans gives worse alignment accuracy than frame-wise DPF, so compressing the sequence into a single network costs representational power unless extra DOFs are added.
Limitations
- Loss weights for the four-term guided mesh alignment objective are hard to balance and can degrade performance considerably.
- Requires known point correspondences between frames; extra DOFs may make correspondence extraction harder.
- Model is deterministic and does not capture motion uncertainty.
Experimental setup
Datasets: DeformingThings4D Resynth synthetic elemental motion sequences
Benchmarks: DeformingThings4D Resynth synthetic elemental motion sequences
Metrics: end point error (EPE) Chamfer distance Chamfer normal distance temporal edge-length std (STD(E)) velocity std (STD(V)) checkpoint size
Baselines: MLP-ReLU MLP-ReLU PE.6 DCT-NeRF BANMO BoneCloud DPF
Builds on: Dynamic Point Field SIREN AIAP loss Nerfies elastic regularization
Closest papers by meaning
- Motion4D: Learning 3D-Consistent Motion and Semantics for 4D Scene Understanding (NeurIPS 2025 · similarity 0.86)
- 4D3R: Motion-Aware Neural Reconstruction and Rendering of Dynamic Scenes from Monocular Videos (NeurIPS 2025 · similarity 0.86)
- PointZero: 3D Point Track Completion for Learning Transferable 3D Dynamics (NeurIPS 2026 · similarity 0.86)
- Motion2VecSets: 4D Latent Vector Set Diffusion for Non-rigid Shape Reconstruction and Tracking (CVPR 2024 · similarity 0.86)
- Joint Optimization of Neural Radiance Fields and Continuous Camera Motion from a Monocular Video (CVPR 2025 · similarity 0.85)
- FreeGave: 3D Physics Learning from Dynamic Videos by Gaussian Velocity (CVPR 2025 · similarity 0.85)
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