Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants with no False Negatives and no False Positives

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. In: 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), 2023-6-17 - 2023-6-24, Vancouver, Canada.

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Official URL: http://dx.doi.org/10.1109/cvpr52729.2023.00129

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:	Conference or Workshop Item (Unspecified)
Uncontrolled Keywords:	point cloud, isometry
Divisions:	Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	28 Mar 2023 08:24
Last Modified:	27 Apr 2024 13:15
DOI:	10.1109/cvpr52729.2023.00129
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3169277