Estimation of Curvature from Sampled Noisy Data

Abstract

Estimation of curvature from noisy sampled data is a fundamental problem in digital arc segmentation. The facet approach to curvature estimation involves least square fitting the observed data points to a parametric cubic polynomial and the calculation of the curvature analytically from the fitted parametric coefficients. Due to the fitting, there exists systematic error or bias between curvature which is calculated analytically from the parameterization of a circle and one which is calculated analytically based on the coefficients of the fitted cubic polynomial, even when the data are sampled from a noiseless circle. It is shown how to compensate this bias by estimating it with the coefficients of the fitted cubic polynomial, which gives more accurate curvature value. Small perturbations are introduced to the sampled data from a noiseless circle, and the authors analytically trace how the perturbation propagates through coefficients of the fitted polynomials and results in perturbation error of the curvature.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>