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Variances of Cylinder Parameters Fitted to Range Data



Marek Franaszek


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.
Journal of Research (NIST JRES) - 117.015
Report Number


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


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], (Accessed February 26, 2024)
Created September 26, 2012, Updated November 10, 2018