Introduction

Almost all problems in computer vision are related in one form or another to the problem of estimating parameters from noisy data. A few examples are line fitting, camera calibration, image matching, surface reconstruction, pose determination, and motion analysis. A parameter estimation problem is usually formulated as an optimization one. Because of different optimization criteria and because of several possible parameterizations, a given problem can be solved in many ways. The purpose of this paper is to show the importance of choosing an appropriate criterion. This will influence the accuracy of the estimated parameters, the efficiency of computation, the robustness to predictable or unpredictable errors. Conic fitting is used to illustrate these aspects because:

• it is one of the simplest problems in computer vision on one hand;
• it is, on the other hand, a relatively difficult problem because of its nonlinear nature.

Needless to say the importance of conics in our daily life and in industry.