mlsanityData to 14 Oct 2026

Correspondence Free Multivector Cloud Registration using Conformal Geometric Algebra

arXiv 2406.11732 ↗First posted 17 Jun 2024cs.CVcited by 0

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Abstract (arXiv)

We present, for the first time, a novel theoretical approach to address the problem of correspondence free multivector cloud registration in conformal geometric algebra. Such formalism achieves several favorable properties. Primarily, it forms an orthogonal automorphism that extends beyond the typical vector space to the entire conformal geometric algebra while respecting the multivector grading. Concretely, the registration can be viewed as an orthogonal transformation (it i.e., scale, translation, rotation) belonging to SO(4,1) - group of special orthogonal transformations in conformal geometric algebra. We will show that such formalism is able to: (i) perform the registration without directly accessing the input multivectors. Instead, we use primitives or geometric objects provided by the conformal model - the multivectors, (ii) the geometric objects are obtained by solving a multilinear eigenvalue problem to find sets of eigenmultivectors. In this way, we can explicitly avoid solving the correspondences in the registration process. Most importantly, this offers rotation and translation equivariant properties between the input multivectors and the eigenmultivectors. Experimental evaluation is conducted in datasets commonly used in point cloud registration, to testify the usefulness of the approach with emphasis to ambiguities arising from high levels of noise. The code is available at https://github.com/Numerical-Geometric-Algebra/RegistrationGA . This work was submitted to the International Journal of Computer Vision and is currently under review.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 27 of its 60 references that are in the map. First posted on arXiv 17 Jun 2024.

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27 of 60 references.

References · 27

  1. 2016PointNet: Deep Learning on Point Sets for 3D Classification and Segmentationcited by 5,248
  2. 20163DMatch: Learning Local Geometric Descriptors from RGB-D Reconstructionscited by 336
  3. 2019Deep Closest Point: Learning Representations for Point Cloud Registrationcited by 321
  4. 2020PREDATOR: Registration of 3D Point Clouds with Low Overlapcited by 290
  5. 2020TEASER: Fast and Certifiable Point Cloud Registrationcited by 274
  6. 2019PointNetLK: Robust & Efficient Point Cloud Registration using PointNetcited by 233
  7. 2020Deep Global Registrationcited by 229
  8. 2020RPM-Net: Robust Point Matching using Learned Featurescited by 182
  9. 2020D3Feat: Joint Learning of Dense Detection and Description of 3D Local Featurescited by 177
  10. 2016Go-ICP: A Globally Optimal Solution to 3D ICP Point-Set Registrationcited by 159
  11. 2018PPF-FoldNet: Unsupervised Learning of Rotation Invariant 3D Local Descriptorscited by 141
  12. 2017Graph-Cut RANSACcited by 133
15 more
  1. 2020Feature-metric Registration: A Fast Semi-supervised Approach for Robust Point Cloud Registration without Correspondencescited by 109
  2. 2021Robust Point Cloud Registration Framework Based on Deep Graph Matchingcited by 97
  3. 2019Graduated Non-Convexity for Robust Spatial Perception: From Non-Minimal Solvers to Global Outlier Rejectioncited by 94
  4. 2020DeepGMR: Learning Latent Gaussian Mixture Models for Registrationcited by 91
  5. 2021Lepard: Learning partial point cloud matching in rigid and deformable scenescited by 85
  6. 2019DeepICP: An End-to-End Deep Neural Network for 3D Point Cloud Registrationcited by 77
  7. 2021You Only Hypothesize Once: Point Cloud Registration with Rotation-equivariant Descriptorscited by 68
  8. 2017Guaranteed Outlier Removal for Point Cloud Registration with Correspondencescited by 62
  9. 2021HRegNet: A Hierarchical Network for Large-scale Outdoor LiDAR Point Cloud Registrationcited by 48
  10. 2018IMLS-SLAM: scan-to-model matching based on 3D datacited by 40
  11. 2017SegICP: Integrated Deep Semantic Segmentation and Pose Estimationcited by 29
  12. 2019SDRSAC: Semidefinite-Based Randomized Approach for Robust Point Cloud Registration without Correspondencescited by 26
  13. 2022MatchNorm: Learning-based Point Cloud Registration for 6D Object Pose Estimation in the Real Worldcited by 13
  14. 2019A Performance Evaluation of Correspondence Grouping Methods for 3D Rigid Data Matchingcited by 10
  15. 2020Unsupervised Partial Point Set Registration via Joint Shape Completion and Registrationcited by 6

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