A statistical analysis of least-squares circle-centre estimation

Zelniker, E.E. and Clarkson, I.V.L. (2003). A statistical analysis of least-squares circle-centre estimation. In: Proceedings of the 3rd IEEE International Symposium. International Symposium on Signal Processing and Information Technology, Maritim RheinMain Hotel, Darmstadt, Germany, (114-117). 14-17 December, 2003. doi:10.1109/ISSPIT.2003.1341073


Author Zelniker, E.E.
Clarkson, I.V.L.
Title of paper A statistical analysis of least-squares circle-centre estimation
Conference name International Symposium on Signal Processing and Information Technology
Conference location Maritim RheinMain Hotel, Darmstadt, Germany
Conference dates 14-17 December, 2003
Proceedings title Proceedings of the 3rd IEEE International Symposium
Journal name Proceedings of the 3rd Ieee International Symposium On Signal Processing and Information Technology
Place of Publication Piscataway NJ, USA
Publisher IEEE
Publication Year 2003
Sub-type Fully published paper
DOI 10.1109/ISSPIT.2003.1341073
ISBN 0-7803-8292-7
Start page 114
End page 117
Total pages 4
Language eng
Abstract/Summary We examine the problem of fitting a circle to a set of noisy measurement of points on the circle's circumference. An estimator based on the standard least-squares techniques has been proposed by Delogne which has been shown by Kasa to be convenient for its ease of analysis and computation. Using Chan's circular functional model to describe the distribution of points, we perform a statistical analysis of the circle's centre estimation, assuming an independent and identical distributed Gaussian measurement errors. We examine the existence of the mean and variance of the estimator for fixed sample sizes. We find that the mean exists when the number of sample points is greater than 2 and the variance exists when this number is greater than 3. We also derive the approximations for the mean and variance for fixed sample sizes when the noise variance is small. We find that the bias approaches zero as the noise variance diminishes and that the variance approaches the Cramer-Rao lower bound. We show this through Monte-Carlo simulations.
Subjects 080106 Image Processing
Q-Index Code E1
Q-Index Status Provisional Code
Institutional Status Unknown

 
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Created: Fri, 20 Mar 2009, 01:58:03 EST by Ms Sarada Rao on behalf of School of Information Technol and Elec Engineering