Probabilistic Detection and Estimation of Conic Sections from Noisy Data

TL;DR

This paper introduces a Bayesian hierarchical model for detecting and estimating conic sections from noisy data without prior knowledge of the conic type, demonstrating high accuracy and uncertainty quantification in complex scenarios.

Contribution

It presents a novel probabilistic approach that jointly detects conic types and estimates parameters, outperforming existing methods especially when the conic nature is unknown.

Findings

Effective detection of conic types in noisy data

Accurate parameter estimation with uncertainty measures

Robust performance on partial and rotated conics

Abstract

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.