Table of Contents
ISRN Probability and Statistics
Volume 2012, Article ID 895178, 25 pages
http://dx.doi.org/10.5402/2012/895178
Research Article

Does the Best-Fitting Curve Always Exist?

Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL 35294, USA

Received 14 June 2012; Accepted 25 July 2012

Academic Editors: C. Fox, J. Hu, J. Jiang, J. López-Fidalgo, and S. Lototsky

Copyright © 2012 N. Chernov et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Fitting geometric shapes to observed data points (images) is a popular task in computer vision and modern statistics (errors-in-variables regression). We investigate the problem of existence of the best fit using geometric and probabilistic approaches.