Direct and Specific Fitting of Conics to Scattered Data

A new method to fit specific types of conics to scattered data points is introduced. Direct, specific fitting of ellipses and hyperbolæ 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.