Since the trace A+C can never be zero for an ellipse, the arbitrary scale factor in the coefficients of the conic equation can be naturally removed by the normalization A+C=1. This normalization has been used by many researchers [17, 21]. All ellipse can then be described by a 5-vector
and the system equation becomes:
Given n points, we have the following vector equation:
The function to minimize becomes
Obtaining its partial derivative with respect to and setting it to zero yield:
The solution is readily given by
This method is known as pseudo inverse technique.