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.