Skip to main content
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.

Experimental Verification of Formulas For Variances of Plane Parameters Fitted to 3D Imaging Data

Published

Author(s)

Marek Franaszek, Geraldine S. Cheok, Kamel S. Saidi

Abstract

Nonlinear Least Squares method is applied to fit a plane to 3D imaging data. Two different error functions used in fitting are tested: orthogonal and directional. Variances of fitted parameters are calculated either from a single dataset using derived earlier analytical formulas or by repeating the scans at the same experimental settings. In the latter case, the variance is equal to the square of the standard deviation from the repeated scans. The results show that the orthogonal error function severely underestimates the variances calculated with the mathematical formulas when compared to variances calculated from multiple scans. The variances calculated from formulas based on the directional error function are in good agreement with estimates calculated from multiple scans. Thus, the variances of the fitted plane parameter can be determined correctly from a single scan when proper formulas are used. This is important because multiple scans from the same location are typically not performed in the field.
Citation
IEEE Transactions on Instrumentation and Measurement
Volume
16

Keywords

Nonlinear Least Squares, 3D imaging systems, variances of fitted plane parameters, orthogonal error function, directional error function

Citation

Franaszek, M. , Cheok, G. and Saidi, K. (2011), Experimental Verification of Formulas For Variances of Plane Parameters Fitted to 3D Imaging Data, IEEE Transactions on Instrumentation and Measurement, [online], https://doi.org/10.1109/TIM.2011.2157720 (Accessed June 25, 2024)

Issues

If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.

Created January 7, 2011, Updated June 1, 2020