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Partial point cloud registration is a challenging problem in robotics, especially when the robot undergoes a large transformation, causing a significant initial pose error and a low overlap between measurements. This letter proposes exploiting equivariant learning from 3D point clouds to improve registration robustness. We propose SE3ET, an SE(3)-equivariant registration framework that employs equivariant point convolution and equivariant transformer designs to learn expressive and robust geometric features. We tested the proposed registration method on indoor and outdoor benchmarks where the point clouds are under arbitrary transformations and lowoverlapping ratios.We also provide generalization tests and run-time performance.
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This content will become publicly available on June 1, 2026
Partial transport for point-cloud registration
Abstract Point cloud registration is an important task in fields like robotics, computer graphics, and medical imaging, involving the determination of spatial relationships between point sets in 3D space. Real-world challenges, such as non-rigid movements and partial visibility, including occlusions and sensor noise, make non-rigid registration particularly difficult. Traditional methods are often computationally intensive, exhibit unstable performance, and lack strong theoretical guarantees. Recently, the optimal transport problem, including its unbalanced variations like the optimal partial transport problem, has emerged as a powerful tool for point-cloud registration. These methods treat point clouds as empirical measures and provide a mathematically rigorous framework to quantify the correspondence between transformed source and target points. In this paper, we address the non-rigid registration problem using optimal transport theory and introduce a set of non-rigid registration methods based on the optimal partial transportation problem. Additionally, by leveraging efficient solutions to the one-dimensional optimal partial transport problem and extending them via slicing, we achieve significant computational efficiency, resulting in fast and robust registration algorithms. We validate our methods by comparing baselines on various 3D and 2D non-rigid registration problems with noisy point clouds.
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- Award ID(s):
- 2339898
- PAR ID:
- 10656697
- Publisher / Repository:
- Birkhäuser
- Date Published:
- Journal Name:
- Sampling Theory, Signal Processing, and Data Analysis
- Volume:
- 23
- Issue:
- 1
- ISSN:
- 2730-5716
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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