On multi-conditioned conic fitting in Geometric algebra for conics

TL;DR

This paper develops modified algorithms for conic fitting in Geometric algebra, incorporating additional geometric constraints such as center position and axis alignment, with implementation and examples.

Contribution

It introduces new conic fitting algorithms with geometric constraints in Geometric algebra, enhancing control over fitted conics.

Findings

Algorithms successfully incorporate geometric constraints.

Implementation in MATLAB demonstrates practical applicability.

Examples illustrate improved fitting accuracy with added conditions.

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 optimisation issues, together with the implementation in MATLAB. Finally, we present examples on a sample dataset and offer possible use of the algorithms.