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Variances of Cylinder Parameters Fitted to Range Data

Published

Author(s)

Marek Franaszek

Abstract

Industrial pipelines are frequently scanned with 3D imaging systems (e.g., LADAR) and cylinders are fitted to the collected data. Then, the fitted as-built model is compared with the as-designed model. Meaningful comparison between the two models requires estimates of uncertainties of fitted model parameters. In this paper, the formulas for variances of cylinder parameters fitted with Nonlinear Least Squares to a points cloud acquired from one scanning position are derived. Two different error functions used in minimization are discussed: the orthogonal and the directional function. Derived formulas explain how uncertainties are propagated from measured ranges to fitted cylinder parameters.
Citation
Journal of Research (NIST JRES) - 117.015
Report Number
117.015
Volume
117

Keywords

Nonlinear Least Square fitting, 3D imaging systems, cylinder fitting, orthogonal error function, directional error function

Citation

Franaszek, M. (2012), Variances of Cylinder Parameters Fitted to Range Data, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD, [online], https://doi.org/10.6028/jres.117.015 (Accessed February 26, 2024)
Created September 26, 2012, Updated November 10, 2018