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Correspondence-Free Non-Rigid Point Set Registration Using Unsupervised Clustering Analysis
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Formulates non-rigid point set registration as unsupervised clustering (source as centroids, target as members), using a Tikhonov-regularized Laplacian (l1) kernel with closed-form updates and a clustering-improved Nyström approximation.
Problem
Non-rigid point set registration without correspondences, especially for shapes under large deformations.
Approach
Treats the source point set as clustering centroids and the target as clustering members in a holistic clustering objective, replaces the Gaussian kernel with an l1-induced Laplacian kernel in Tikhonov regularization for robust smooth displacement fields, and uses Elkan k-means to select landmarks for an improved Nyström approximation with a proven error bound.
Key results
- On the FAUST human scan dataset, the method achieves average RMSE 0.0092 versus 0.0143 for the next best (NSFP) and 0.0129 for Nerfies.
- On TOSCA animal deformation, average RMSE 1.5247 versus 2.0710 for NSFP.
- On the 2D IMM hand dataset, it achieves RMSE of 0.0383 to 0.0879 across four subjects, beating MR-RPM, BCPD, GMM and ZAC.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed clustering-based registration instead of GMM | 2D non-rigid point set registration · IMM hand, Subject 1 | RMSE: 0.0571 -> 0.0383 | Helped |
| Use the proposed clustering-based registration instead of GMM | 2D non-rigid point set registration · IMM hand, Subject 2 | RMSE: 0.0547 -> 0.0481 | Helped |
| Use the proposed clustering-based registration instead of GMM | 2D non-rigid point set registration · IMM hand, Subject 3 | RMSE: 0.0734 -> 0.0537 | Helped |
| Use the proposed clustering-based registration instead of GMM | 2D non-rigid point set registration · IMM hand, Subject 4 | RMSE: 0.0917 -> 0.0879 | Helped |
| Use the proposed method instead of Nerfies | 3D non-rigid point cloud registration · FAUST, average across intra- and inter-subject settings | RMSE: 0.0129 -> 0.0092 | Helped |
| Use the proposed method instead of NSFP | 3D non-rigid point cloud registration · TOSCA, average across animal classes | RMSE: 2.0710 -> 1.5247 | Helped |
| Replace the Gaussian kernel with the Laplacian kernel (ablation) | Proposed registration method · Bunny registration under varying noise | RMSE | Helped |
| Replace random Nyström sampling with clustering-improved Nyström approximation (ablation) | Proposed registration method · FAUST model-pair tests | registration error | Helped |
| Replace random Nyström sampling with clustering-improved Nyström approximation (ablation) | Proposed registration method · FAUST model-pair tests | matrix approximation error | Helped |
| Replace the Gaussian kernel with the Laplacian kernel (ablation) | Proposed registration method · Bunny registration | iterations to convergence | Helped |
Surprising findings
- The ZAC baseline performs far worse than the others on the 2D hand dataset (RMSE around 0.45-0.49).
Limitations
- Implemented in MATLAB on a CPU-only desktop; scalability to very large point sets is not demonstrated.
- Comparisons rely on baselines' public implementations with parameters tuned by the authors.
Experimental setup
Datasets: IMM hand dataset FAUST TOSCA ShapeNet Stanford Bunny CT lung volumes MRA brain vessels
Benchmarks: IMM hand dataset FAUST TOSCA
Metrics: RMSE running time
Baselines: MR-RPM BCPD GMM ZAC GBCPD Fast RNRR AMM NRR Sinkhorn Nerfies NDP NSFP
Builds on: Coherent Point Drift BCPD Elkan k-means fuzzy clustering Nyström method
Closest papers by meaning
- Non-Rigid Point Set Registration with Robust Transformation Estimation under Manifold Regularization (AAAI 2017 · similarity 0.90)
- Context-Aware Gaussian Fields for Non-Rigid Point Set Registration (CVPR 2016 · similarity 0.87)
- Group-Wise Point-Set Registration Based on Renyi's Second Order Entropy (CVPR 2017 · similarity 0.87)
- Non-Rigid Shape Registration via Deep Functional Maps Prior (NeurIPS 2023 · similarity 0.86)
- Occlusion-aware Non-Rigid Point Cloud Registration via Unsupervised Neural Deformation Correntropy (ICLR 2025 · similarity 0.86)
- Scalable 3D Registration via Truncated Entry-wise Absolute Residuals (CVPR 2024 · similarity 0.84)
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