Constrained quadratic errors-in-variables fitting

We propose an estimation method to fit conics and quadrics to data in the context of errors-in-variables where the fit is subject to constraints. The proposed algorithm is based on algebraic distance minimization and consists of solving a few generalized eigenvalue (or singular value) problems and is not iterative. Nonetheless, the algorithm produces accurate estimates, close to those obtained with maximum likelihood, while the constraints are also guaranteed to be satisfied. Important special cases, fitting ellipses, hyperbolas, parabolas, and ellipsoids to noisy data are discussed.