Presents Cramer-Rao (CR) bounds on error covariance for 2D and 3D parametric shape estimation. The motivation for this paper is ECT image reconstruction and uptake estimation with side information corresponding to organ boundaries extracted from high resolution MRI or CT.
It is important to understand the fundamental limitations on boundary estimation error covariance so as to gauge the utility of such side information. The authors present asymptotic forms of the Fisher information matrix for estimating 2D and 3D boundaries under a B-spline polar shape parameterization.
They show that circular (2D) and spherical (3D) shapes are the easiest to estimate in the sense of yielding maximum Fisher information. They also study the worst case shapes under near circularity and near sphericity constraints. Finally, a simulation is presented to illustrate the tightness of the CR bound for a simple 3D shape estimator utilizing edge filtering.