A Lower Bound on the Variance of Algebraic Ellipsoid-Fitting Center Estimator

J. Li (USA)

Keywords

Ellipsoidfitting, center estimation, Cram´erRao bound

Abstract

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 Cram´er-Rao lower bound is ap plied 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 devel oped from Bookstein’s ellipsoid fitting method when the noise level is low.

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