Algebraic Fitting of Quadric Surfaces to Data

摘要

A important problem is that of finding a quadric surface which gives a "best" fit to m given data points. There are many application areas, for example metrology, computer graphics, pattern recognition, and in particular quadric surfaces are often to be found in manufactured parts. There are many criteria which can be used for fitting, but one of the simplest is so-called algebraic fitting, which exploits the fact that an expression for the curve can be given which is affine in the free parameters. Here we examine a general class of such algebraic fitting problems, consider how the members of the class can be interpreted in terms of the errors in the data, and present simple algorithms which apply to all of the problems.