  Inferring unknown conic sections on the basis of noisy data is a challenging
problem with applications in computer vision. A major limitation of the
currently available methods for conic sections is that estimation methods rely
on the underlying shape of the conics (being known to be ellipse, parabola or
hyperbola). A general purpose Bayesian hierarchical model is proposed for conic
sections and corresponding estimation method based on noisy data is shown to
work even when the specific nature of the conic section is unknown. The model,
thus, provides probabilistic detection of the underlying conic section and
inference about the associated parameters of the conic section. Through
extensive simulation studies where the true conics may not be known, the
methodology is demonstrated to have practical and methodological advantages
relative to many existing techniques. In addition, the proposed method provides
probabilistic measures of uncertainty of the estimated parameters. Furthermore,
we observe high fidelity to the true conics even in challenging situations,
such as data arising from partial conics in arbitrarily rotated and
non-standard form, and where a visual inspection is unable to correctly
identify the type of conic section underlying the data.
