Conic Fitting Problem

The problem is to fit a conic section to a set of n points ( ). A conic can be described by the following equation:

 

where A and C are not simultaneously zero. In practice, we encounter ellipses, where we must impose the constraint . However, this constraint is usually ignored during the fitting because

• the constraint is usually satisfied if data are not all situated in a flat section.
• the computation will be very expensive if this constraint is considered.

As the data are noisy, it is unlikely to find a set of parameters (A, B, C, D, E, F) (except for the trivial solution A=B=C=D=E=F=0) such that , . Instead, we will try to estimate them by minimizing some objective function.