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On Multi-conditioned Conic Fitting in Geometric Algebra for Conics

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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.

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Notes

  1. For the sake of easy referencing, let us denote the original conic fitting algorithm as Algorithm Q.

  2. Let us note that the comparison of the original Algorithm Q with other conic fitting algorithms without additional geometric conditions can be found in [10].

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Acknowledgements

The research was supported by a grant no. FSI-S-23-8161.

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  1. Technická 2896/2, 616 69, Brno, Czech Republic

    Pavel Loučka & Petr Vašík

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  1. Pavel Loučka
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  2. Petr Vašík
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Correspondence to Petr Vašík.

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Loučka, P., Vašík, P. On Multi-conditioned Conic Fitting in Geometric Algebra for Conics. Adv. Appl. Clifford Algebras 33, 31 (2023). https://doi.org/10.1007/s00006-023-01277-9

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  • DOI: https://doi.org/10.1007/s00006-023-01277-9

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