几何代数中二次曲线的多条件拟合

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2023-05-13 DOI:10.1007/s00006-023-01277-9

Pavel Loučka, Petr Vašík

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引用次数: 0

摘要

通过在优化问题中加入附加条件，我们介绍了几何代数中圆锥拟合的几种修改。这些额外条件中的每一个都确保了拟合圆锥曲线的额外几何特性，特别是坐标系原点的中心点位置、与坐标轴的轴向对齐，或者最终两者的组合。所有导出的算法都伴随着对底层代数和计算优化问题的讨论。最后，我们给出了在样本数据集上使用的示例，并提供了算法的可能应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On Multi-conditioned Conic Fitting in Geometric Algebra for Conics

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On Multi-conditioned Conic Fitting in Geometric Algebra for Conics

We introduce several modifications of conic fitting in Geometric algebra for conics by incorporating additional conditions into the optimisation problem. Each of these extra conditions ensure additional geometric properties of a fitted conic, in particular, centre point position at the origin of coordinate system, axial alignment with coordinate axes, or, eventually, combination of both. All derived algorithms are accompanied by a discussion of the underlying algebra and computational optimisation issues. Finally, we present examples of use on a sample dataset and offer possible applications of the algorithms.

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来源期刊

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.