title: Variances of Cylinder Parameters Fitted to Range Data.
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 point 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 some uncertainty components are propagated from measured ranges to fitted cylinder parameters.
authors.affiliation: National Institute of Standards and Technology, Gaithersburg, MD 20899.
authors.forename: Marek
authors.initials: M
authors.lastname: Franaszek
keywords: 3D imaging systems; Nonlinear Least Square fitting; cylinder fitting; directional error function; orthogonal error function