# Correspondence-Free Non-Rigid Point Set Registration Using Unsupervised Clustering Analysis

arXiv: https://arxiv.org/abs/2406.18817 · HTML: https://mlsanity.com/paper/2406.18817/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 56 references that are in the map.
- First posted on arXiv 27 Jun 2024.

## Builds on (most cited first, 16 of 16)

- [ShapeNet: An Information-Rich 3D Model Repository](https://mlsanity.com/paper/1512.03012/) (2015)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Nerfies: Deformable Neural Radiance Fields](https://mlsanity.com/paper/2011.12948/) (2020)
- [Neural Scene Flow Prior](https://mlsanity.com/paper/2111.01253/) (2021)
- [Lepard: Learning partial point cloud matching in rigid and deformable scenes](https://mlsanity.com/paper/2111.12591/) (2021)
- [Fast and Robust Iterative Closest Point](https://mlsanity.com/paper/2007.07627/) (2020)
- [A Survey of Non-Rigid 3D Registration](https://mlsanity.com/paper/2203.07858/) (2022)
- [Non-rigid Point Cloud Registration with Neural Deformation Pyramid](https://mlsanity.com/paper/2205.12796/) (2022)
- [Multiway Non-rigid Point Cloud Registration via Learned Functional Map Synchronization](https://mlsanity.com/paper/2111.12878/) (2021)
- [Neural Shape Deformation Priors](https://mlsanity.com/paper/2210.05616/) (2022)
- [Unsupervised Volumetric Animation](https://mlsanity.com/paper/2301.11326/) (2023)
- [Quasi-Newton Solver for Robust Non-Rigid Registration](https://mlsanity.com/paper/2004.04322/) (2020)
- [Deep Graph-based Spatial Consistency for Robust Non-rigid Point Cloud Registration](https://mlsanity.com/paper/2303.09950/) (2023)
- [Fast and Robust Non-Rigid Registration Using Accelerated Majorization-Minimization](https://mlsanity.com/paper/2206.03410/) (2022)
- [Zero-Assignment Constraint for Graph Matching with Outliers](https://mlsanity.com/paper/2003.11928/) (2020)
- [GraphReg: Dynamical Point Cloud Registration with Geometry-aware Graph Signal Processing](https://mlsanity.com/paper/2302.01109/) (2023)

## Built on by (most cited first, 10 of 10)

- [DV-Matcher: Deformation-based Non-Rigid Point Cloud Matching Guided by Pre-trained Visual Features](https://mlsanity.com/paper/2408.08568/) (2024)
- [BUFFER-X: Towards Zero-Shot Point Cloud Registration in Diverse Scenes](https://mlsanity.com/paper/2503.07940/) (2025)
- [Landmark-Free Preoperative-to-Intraoperative Registration in Laparoscopic Liver Resection](https://mlsanity.com/paper/2504.15152/) (2025)
- [Occlusion-aware Non-Rigid Point Cloud Registration via Unsupervised Neural Deformation Correntropy](https://mlsanity.com/paper/2502.10704/) (2025)
- [GERA: Geometric Embedding for Efficient Point Registration Analysis](https://mlsanity.com/paper/2410.00589/) (2024)
- [Toward Zero-Shot Point Cloud Registration Across Diverse Scales, Scenes, and Sensor Setups](https://mlsanity.com/paper/2601.02759/) (2026)
- [MeshLoom: Feed-Forward Non-Rigid Registration of Mesh Sequences](https://mlsanity.com/paper/2606.17027/) (2026)
- [PADReg: Physics-Aware Deformable Registration Guided by Contact Force for Ultrasound Sequences](https://mlsanity.com/paper/2508.08685/) (2025)
- [Structured Analytic Coherent Point Drift for Non-Rigid Point Set Registration](https://mlsanity.com/paper/2605.00934/) (2026)
- [Vis2Reg: Visibility-Aware Landmark-Free Geometric 3D--2D Registration for Liver Laparoscopy](https://mlsanity.com/paper/2607.17810/) (2026)

## Abstract (arXiv)

This paper presents a novel non-rigid point set registration method that is inspired by unsupervised clustering analysis. Unlike previous approaches that treat the source and target point sets as separate entities, we develop a holistic framework where they are formulated as clustering centroids and clustering members, separately. We then adopt Tikhonov regularization with an ℓ1-induced Laplacian kernel instead of the commonly used Gaussian kernel to ensure smooth and more robust displacement fields. Our formulation delivers closed-form solutions, theoretical guarantees, independence from dimensions, and the ability to handle large deformations. Subsequently, we introduce a clustering-improved Nystr"om method to effectively reduce the computational complexity and storage of the Gram matrix to linear, while providing a rigorous bound for the low-rank approximation. Our method achieves high accuracy results across various scenarios and surpasses competitors by a significant margin, particularly on shapes with substantial deformations. Additionally, we demonstrate the versatility of our method in challenging tasks such as shape transfer and medical registration.