Publication result detail

On Multi-conditioned Conic Fitting in Geometric Algebra for Conics

LOUČKA, P.; VAŠÍK, P.

Original Title

On Multi-conditioned Conic Fitting in Geometric Algebra for Conics

English Title

On Multi-conditioned Conic Fitting in Geometric Algebra for Conics

Type

WoS Article

Original Abstract

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.

English abstract

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.

Keywords

Conic fit; Geometric algebra; Clifford algebra; Centre position; Axial alignment

Key words in English

Conic fit; Geometric algebra; Clifford algebra; Centre position; Axial alignment

Authors

LOUČKA, P.; VAŠÍK, P.

RIV year

2024

Released

01.07.2023

Publisher

SPRINGER BASEL AG

Location

BASEL

ISBN

0188-7009

Periodical

Advances in Applied Clifford Algebras

Volume

33

Number

3

State

Swiss Confederation

Pages count

30

URL

https://link.springer.com/article/10.1007/s00006-023-01277-9

BibTex

@article{BUT183753,
  author="Pavel {Loučka} and Petr {Vašík}",
  title="On Multi-conditioned Conic Fitting in Geometric Algebra for Conics",
  journal="Advances in Applied Clifford Algebras",
  year="2023",
  volume="33",
  number="3",
  pages="30",
  doi="10.1007/s00006-023-01277-9",
  issn="0188-7009",
  url="https://link.springer.com/article/10.1007/s00006-023-01277-9"
}