Direct least square fitting of ellipsoids

Least square fitting of quadratic surfaces is a fundamental problem in pattern recognition, computer vision, graphics, and medical imaging analysis. This paper investigated in approaches to ellipsoid-specific fitting. In 2D case, Fitzgibbon's ellipse-specific fitting approach outperforms others since it is extremely robust, efficient, and easy to implement. This paper attempts to extend it from 2D to 3D for ellipsoid-specific fitting. The extension seems straightforward at first glance. However, we discovered to make the extension feasible is not easy as mentioned in the main text. Experimental results demonstrate the validity of the proposed approach.