Find the right algorithm for your image processing application
Exploring the recent achievements that have occurred since the mid-1990s, Circular and Linear Regression: Fitting Circles and Lines by Least Squares explains how to use modern algorithms to fit geometric contours (circles and circular arcs) to observed data in image processing and computer vision. The author covers all facets—geometric, statistical, and computational—of the methods. He looks at how the numerical algorithms relate to one another through underlying ideas, compares the strengths and weaknesses of each algorithm, and illustrates how to combine the algorithms to achieve the best performance.
After introducing errors-in-variables (EIV) regression analysis and its history, the book summarizes the solution of the linear EIV problem and highlights its main geometric and statistical properties. It next describes the theory of fitting circles by least squares, before focusing on practical geometric and algebraic circle fitting methods. The text then covers the statistical analysis of curve and circle fitting methods. The last chapter presents a sample of "exotic" circle fits, including some mathematically sophisticated procedures that use complex numbers and conformal mappings of the complex plane.
Essential for understanding the advantages and limitations of the practical schemes, this book thoroughly addresses the theoretical aspects of the fitting problem. It also identifies obscure issues that may be relevant in future research.
Table of Contents
Introduction and Historic Overview. Fitting Lines. Fitting Circles: Theory. Geometric Circle Fits. Algebraic Circle Fits. Statistical Analysis of Curve Fits. Statistical Analysis of Circle Fits. Various "Exotic" Circle Fits. Bibliography. Index.
Nikolai Chernov is a professor of mathematics at the University of Alabama at Birmingham.