Widdowson, Daniel and Kurlin, Vitaliy 
ORCID: 0000-0001-5328-5351
(2023)
Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and
Continuous Isometry Invariants with no False Negatives and no False Positives.
[Preprint]
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Abstract
Rigid structures such as cars or any other solid objects are often represented by finite clouds of unlabeled points. The most natural equivalence on these point clouds is rigid motion or isometry maintaining all inter-point distances. Rigid patterns of point clouds can be reliably compared only by complete isometry invariants that can also be called equivariant descriptors without false negatives (isometric clouds having different descriptions) and without false positives (non-isometric clouds with the same description). Noise and motion in data motivate a search for invariants that are continuous under perturbations of points in a suitable metric. We propose the first continuous and complete invariant of unlabeled clouds in any Euclidean space. For a fixed dimension, the new metric for this invariant is computable in a polynomial time in the number of points.
| Item Type: | Preprint |
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| Additional Information: | This conference version is for CVPR (Computer Vision and Pattern Recognition), https://cvpr2023.thecvf.com. The latest file is http://kurlin.org/projects/cloud-isometry-spaces/distance-based-invariants.pdf. The extended versions of sections 3-4 with all proofs and big examples are at arXiv:2303.14161 for metric spaces, arXiv:2303.13486 for Euclidean spaces. arXiv admin note: substantial text overlap with arXiv:2303.13486, arXiv:2303.14161 |
| Uncontrolled Keywords: | cs.CV, cs.CV, cs.CG, math.MG, 51N20, 51K05, 51F20, 51F30, 68U05, I.5.1; I.5.2 |
| Divisions: | Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science |
| Depositing User: | Symplectic Admin |
| Date Deposited: | 04 Oct 2023 08:09 |
| Last Modified: | 14 Mar 2024 17:32 |
| DOI: | 10.48550/arxiv.2303.15385 |
| Related URLs: | |
| URI: | https://livrepository.liverpool.ac.uk/id/eprint/3173400 |
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