Work

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

Year: 2024

Type: article

Abstract: 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.

Source: Applied Mathematics Letters

DOI: 10.1016/j.aml.2024.109381

Authors: Juan Gerardo Alcázar, Michal Bizzarri, Miroslav Lávička, Jan Vršek

Institutions: Universidad de Alcalá, University of West Bohemia in Pilsen

Language: English

Topic: Topological and Geometric Data Analysis

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,690

Funder: Grantová Agentura České Republiky