BMVC 2004, Kingston, 7th-9th Sept, 2004

Direct and Specific Fitting of Conics to Scattered Data
M. Harker, P. O?Leary (University of Leoben, Austria) and P.
Zsombor-Murray (McGill University, Canada)

A new method to fit specific types of conics to scattered data points is introduced.
Direct, specific fitting of ellipses and hyperbolae is achieved by imposing
a quadratic constraint on the conic coefficients, whereby an improved
partitioning of the design matrix is devised so as to improve computational
efficiency and numerical stability by eliminating redundant aspects of the fitting
procedure. Fitting of parabolas is achieved by determining an orthogonal
basis vector set in the Grassmannian space of quadratic conic forms. The linear
combination of the basis vectors which fulfills the parabolic condition
and has a minimum residual is determined using Lagrange multipliers.
(pdf article)