Least squares ellipsoid specific fitting

In this paper, a sufficient condition for a quadric surface to be an ellipsoid has been developed and a closed-form solution for ellipsoid fitting is developed based on this constraint, which is a best fit to the given data amongst those ellipsoids whose short radii are at least half of their major radii, in the sense of algebraic distance. A simple search procedure is proposed to pursuit the ´best´ ellipsoid when data cannot be well described by this type of ellipsoid. The proposed fitting algorithm is quick, stable and insensitive to small errors in the data.