NOTICE: Due to a lapse in annual appropriations, most of this website is not being updated. Learn more.

Form submissions will still be accepted but will not receive responses at this time. Sections of this site for programs using non-appropriated funds (such as NVLAP) or those that are excepted from the shutdown (such as CHIPS and NVD) will continue to be updated.

U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

PUBLICATIONS

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
NIST Pub Series
Journal of Research (NIST JRES)
Pub Type
NIST Pubs

Download Paper

DOI Link

Keywords

Nonlinear Least Square fitting, 3D imaging systems, cylinder fitting, orthogonal error function, directional error function
Robotics, Modeling and simulation research and Metrology

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 October 9, 2025)

Issues

If you have any questions about this publication or are having problems accessing it, please contact [email protected].

Created September 26, 2012, Updated November 10, 2018
Was this page helpful?