Advisory Committee Chair
Nikolai Chernov
Advisory Committee Members
Wei-Shen Hsia
Ian Knowles
Boris Kunin
Charles Katholi
Document Type
Dissertation
Date of Award
2012
Degree Name by School
Doctor of Philosophy (PhD) College of Arts and Sciences
Abstract
This dissertation is devoted to the study of a popular regression model: Error-In-Variable Model, which has been commonly recognized as one of the key components of computer vision research. In EIV model, a set of data points whose (x,y) coordinates are subject to random errors is fitted by some geometric shapes such as lines, circles and ellipses. The geometric fitting which minimizes the sum of orthogonal distances from points to geometric shapes is universally recognized as the most desirable solution of the fitting problem. However, there is no explicit form of the solution for nonlinear models (circles, ellipses etc). The problem of fitting circles has been investigated intensively over past a few decades and all major issue appeared to be resolved. Our analysis will focus on a more sophisticated model - fitting ellipses to a set of points. We will address the issues of existence and uniqueness of the best fitting solution, study the parameter space of all quadratic curves and properties of the objective function and show some peculiar feature of the estimates of geometric parameters for the best fitting ellipse: they have no finite moments. Our results promote understanding of why computer algorithms keep diverging, return nonsense or crash altogether and help development of more robust, efficient fitting schemes.
Recommended Citation
Huang, Qizhuo, "Geometric Fitting in Error-In-Variables Model" (2012). All ETDs from UAB. 1985.
https://digitalcommons.library.uab.edu/etd-collection/1985