Research map / Point clouds / Shape and surface completion
Hyperbolic-Constraint Point Cloud Reconstruction from Single RGB-D Images
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Introduces hyperbolic space into NU-MCC-style single-view RGB-D point cloud reconstruction, adding a hyperbolic Chamfer distance, a regularization loss and a triplet loss with adaptive margins to model part-whole hierarchy.
Problem
Single-view point cloud reconstruction from RGB-D images struggles to capture the hierarchical, tree-like relationships between partial and complete point clouds, and existing methods rely on costly CAD models or geometric priors.
Approach
Embed partial and complete point cloud features in a Poincaré ball so parts sit near the center and wholes near the boundary, using a hyperbolic Chamfer distance, a margin-based regularization loss with adaptive margins, and a hyperbolic triplet loss on top of NU-MCC.
Key results
- On CO3D-v2, the full hyperbolic model reaches F1 0.861 and Acc 0.104 / Com 0.094, versus NU-MCC base F1 0.802 and Acc 0.121 / Com 0.146.
- Hyperbolic distance with both regularization and triplet losses outperforms the same losses in Euclidean space (F1 0.806 for Euclidean L_Z+L_T vs 0.861).
- Delta-hyperbolicity of the encoder embeddings drops from 0.326 (E_N) to 0.294 (E_N+E_h), indicating more tree-like structure.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add hyperbolic distance, regularization loss, and triplet loss | NU-MCC · CO3D-v2 | F1: 0.802 -> 0.861 | Helped |
| Add triplet loss using Euclidean distance (ablation) | NU-MCC · CO3D-v2 | F1: 0.802 -> 0.814 | Helped |
| Add regularization loss using Euclidean distance (ablation) | NU-MCC · CO3D-v2 | F1: 0.802 -> 0.786 | Hurt |
| Add regularization and triplet losses using Euclidean distance (ablation) | NU-MCC · CO3D-v2 | F1: 0.802 -> 0.806 | No clear effect |
| Add regularization loss using hyperbolic distance (ablation) | NU-MCC · CO3D-v2 | F1: 0.802 -> 0.836 | Helped |
| Add triplet loss using hyperbolic distance (ablation) | NU-MCC · CO3D-v2 | F1: 0.802 -> 0.853 | Helped |
| Add regularization and triplet losses using hyperbolic distance (ablation) | NU-MCC · CO3D-v2 | F1: 0.802 -> 0.861 | Helped |
| Add the fully enhanced hyperbolic network encoder (ablation) | Basic encoder E_N · CO3D-v2 | δ-hyperbolicity: 0.326 -> 0.294 | Helped |
| Use adaptive margins instead of preset margin values (ablation) | HcPCR regularization loss · CO3D-v2 | reconstruction performance | Helped |
| Set curvature to -0.14 (ablation) | HcPCR · CO3D-v2 | reconstruction performance: -0.14 | Helped |
Surprising findings
- Adding the regularization loss alone in Euclidean space degrades performance (F1 0.786 vs 0.802 base), which the authors attribute to Euclidean space failing to represent tree-like structure.
Limitations
- Hyperparameters (curvature -0.14, gamma0 1000, epsilon 4) were tuned empirically with limited analysis of sensitivity beyond curvature and margin ablations.
- Evaluation limited to CO3D-v2 object reconstruction; scene-level generalization not reported in the text.
Experimental setup
Datasets: CO3D-v2
Benchmarks: CO3D-v2
Metrics: Accuracy Completeness Precision Recall L1 F1
Baselines: MCC NU-MCC
Builds on: NU-MCC MCC Vision Transformer Chamfer distance
Closest papers by meaning
- SPAR3D: Stable Point-Aware Reconstruction of 3D Objects from Single Images (CVPR 2025 · similarity 0.88)
- Adaptive 3D Reconstruction via Diffusion Priors and Forward Curvature-Matching Likelihood Updates (NeurIPS 2025 · similarity 0.87)
- Hyperbolic Uncertainty-Aware Few-Shot Incremental Point Cloud Segmentation (CVPR 2025 · similarity 0.87)
- 3DMambaIPF: A State Space Model for Iterative Point Cloud Filtering via Differentiable Rendering (AAAI 2025 · similarity 0.86)
- LAM3D: Large Image-Point Clouds Alignment Model for 3D Reconstruction from Single Image (NeurIPS 2024 · similarity 0.86)
- UniPre3D: Unified Pre-training of 3D Point Cloud Models with Cross-Modal Gaussian Splatting (CVPR 2025 · similarity 0.86)
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