A Tutorial with Application to Conic Fitting

**Zhengyou Zhang
INRIA, 2004 route des Lucioles, BP 93,
F-06902 Sophia-Antipolis Cedex, France
Email: **

**INRIA Research Report No.2676, October 1995**

**PDF version available here**

appeared in ** Image and Vision Computing Journal**, Vol.15, No.1, pages 59-76, 1997

Almost all problems in computer vision are related in one form or another to the problem of estimating parameters from noisy data. In this tutorial, we present what is probably the most commonly used techniques for parameter estimation. These include linear least-squares (pseudo-inverse and eigen analysis); orthogonal least-squares; gradient-weighted least-squares; bias-corrected renormalization; Kalman filtering; and robust techniques (clustering, regression diagnostics, M-estimators, least median of squares). Particular attention has been devoted to discussions about the choice of appropriate minimization criteria and the robustness of the different techniques. Their application to conic fitting is described.

**Keywords:** Parameter estimation, Least-squares, Bias correction, Kalman
filtering, Robust regression

- Contents
- Introduction
- A Glance over Parameter Estimation in General
- Conic Fitting Problem
- Least-Squares Fitting Based on Algebraic Distances
- Least-Squares Fitting Based on Euclidean Distances
- Gradient Weighted Least-Squares Fitting
- Bias-Corrected Renormalization Fitting
- Kalman Filtering Technique
- Robust Estimation
- Two Examples
- Conclusions
- References
- About this document ...

Thu Feb 8 11:42:20 MET 1996