利用协方差矩阵和高阶张量计算三维点云的旋转对称性

IF 2.9 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2024-11-19 DOI:10.1016/j.aml.2024.109381

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

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引用次数: 0

摘要

我们证明，在一般条件下，具有旋转对称性的三维点云的协方差矩阵具有一个简单特征值（其相关特征向量提供了旋转轴的方向）和一个双特征值。旋转轴的方向也可以通过与点云相关的高阶张量计算出来，这在病理情况下非常有用。因此，检测旋转对称性和计算旋转轴的算法非常简单。

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

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.

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来源期刊

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.