On multi-conditioned conic fitting in Geometric algebra for conics

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.