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On Multi-conditioned Conic Fitting in Geometric Algebra for Conics

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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Advances in Applied Clifford Algebras Springer Journals

On Multi-conditioned Conic Fitting in Geometric Algebra for Conics

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References (14)

Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
ISSN
0188-7009
eISSN
1661-4909
DOI
10.1007/s00006-023-01277-9
Publisher site
See Article on Publisher Site

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.

Journal

Advances in Applied Clifford AlgebrasSpringer Journals

Published: Jul 1, 2023

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

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