Rotational symmetries of 3D point clouds using the covariance matrix and higher-order tensors

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F25%3A43973536" target="_blank" >RIV/49777513:23520/25:43973536 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0893965924004014" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0893965924004014</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aml.2024.109381" target="_blank" >10.1016/j.aml.2024.109381</a>

Result language
angličtina
Original language name
Rotational symmetries of 3D point clouds using the covariance matrix and higher-order tensors
Original language description
We prove that, under generic conditions, the covariance matrix of a 3D point cloud with rotational symmetry has a simple eigenvalue, whose associated eigenvector provides the direction of the axis of rotation, and a double eigenvalue. The direction of the axis of rotation can also be computed from higher order tensors related to the point cloud, which is useful in pathological cases. This leads to a very simple algorithm for detecting rotational symmetry and computing the axis of rotation.
Czech name
—
Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/GF21-08009K" target="_blank" >GF21-08009K: Generalized Symmetries and Equivalences of Geometric Data</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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