Publication detail

On Multi-conditioned Conic Fitting in Geometric Algebra for Conics

LOUČKA, P. VAŠÍK, P.

English title

On Multi-conditioned Conic Fitting in Geometric Algebra for Conics

Type

journal article in Web of Science

Language

en

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 in English

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

Released

01.07.2023

Publisher

SPRINGER BASEL AG

Location

BASEL

ISSN

0188-7009

Volume

33

Number

3

Pages count

30

BIBTEX


@article{BUT183753,
  author="Pavel {Loučka} and Petr {Vašík},
  title="On Multi-conditioned Conic Fitting in Geometric Algebra for Conics",
  year="2023",
  volume="33",
  number="3",
  month="July",
  publisher="SPRINGER BASEL AG",
  address="BASEL",
  issn="0188-7009"
}