As said before, for noisy data, the system equation, Q(x,y)=0 in the case of conic fitting, can hardly hold true. A common practice is to directly minimize the algebraic distance , i.e., to minimize the following function:
Clearly, there exists a trivial solution A=B=C=D=E=F=0. In order to avoid it, we should normalize Q(x,y). There are many different normalizations proposed in the literature. Here we describe three of them.