A LOWER BOUND ON THE VARIANCE OF ALGEBRAIC ELLIPSOID-FITTING CENTER ESTIMATOR

摘要

Ellipsoid fitting is a widely used technique in 3D shape modeling, which simultaneously estimate the center and orientation of 3D object. This paper explores the limits of performance for the ellipsoid-fitting center estimator. It is shown that the noise in the surface sample data can be approximated by a Gaussian distribution when the signal to noise ratio is high. The Cramer-Rao lower bound is applied to yield a bound on the variance of unbiased ellipsoid-fitting center estimator. The simulation results show that the bound is approachable by the center estimator developed from Bookstein's ellipsoid fitting method when the noise level is low.