A Bayesian approach to type-specific conic fitting

TL;DR

This paper introduces a Bayesian method for conic fitting that minimizes bias and improves reliability by optimal normalization, reweighting, and prior conditioning, providing accurate error estimates and confidence intervals.

Contribution

It presents a Bayesian approach to conic fitting that enhances accuracy and reduces bias through normalization, reweighting, and prior conditioning, advancing existing methods.

Findings

Optimal normalization minimizes bias.

Iteration with reweighting improves reliability.

Error estimates enable bias correction and confidence intervals.

Abstract

A perturbative approach is used to quantify the effect of noise in data points on fitted parameters in a general homogeneous linear model, and the results applied to the case of conic sections. There is an optimal choice of normalisation that minimises bias, and iteration with the correct reweighting significantly improves statistical reliability. By conditioning on an appropriate prior, an unbiased type-specific fit can be obtained. Error estimates for the conic coefficients may also be used to obtain both bias corrections and confidence intervals for other curve parameters.