Least squares fitting of circles and ellipses to measured data
type: Item
instance of: scholarly article
title: Least squares fitting of circles and ellipses to measured data
zbMATH Open document ID: 0921.65004
DOI: 10.1023/A:1022381510996
published in: BIT
publication date: 1999-09-16T00:00:00Z
review text: Given are some coordinate vectors that are obtained by a coordinate measuring machine. This can be described as a stick with a touch probe that measures the coordinates of e.g., the circumference of some object. For a number of points the coordinate vectors \(x_i\) and the corresponding probe direction \(v_i\) are given. The problem is to fit in a least squares sense the best possible circle or ellipse through the data points. The objective function to be minimized is the sum of squares of the distances between the measured points \(x_i\) and the intersection in the direction \(v_i\) with the approximating conic. The parameters to be found is the coordinate vector of the center of the conic and the radius (or the length of the axes in the case of an ellipse). For an ellipse, the fit can be improved by also allowing a rotation of the axes. The elements needed in the Gauss-Newton method to solve the problem are provided. The problem is not convex, so that global convergence can not be guaranteed.
Mathematics Subject Classification ID: 65D10
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C20
zbMATH DE Number: 1275249
zbMATH Keywords: least squares fitting
zbMATH Keywords: conics
zbMATH Keywords: circles
zbMATH Keywords: ellipses
zbMATH Keywords: Gauss-Newton method
zbMATH Keywords: convergence
author: G. A. Watson
reviewed by: Adhemar Bultheel
MaRDI profile type: Publication
full work available at URL: a:1022381510996
OpenAlex ID: W194964253
description: scientific article; zbMATH DE number 1275249