A statistical analysis of shape reconstruction from areas of shadows

We present a statistical analysis of the problem of shape reconstruction from measurements of the brightness function (areas of shadows) by deriving the Cramer-Rao lower bound (CRLB) on the estimated 2-D boundary. Confidence region techniques are used to analyze and visualize the performance of the 2-D parametric shape estimation problem. The brightness function data is very weak, so a constrained CRLB is used on the shape parameters to form the confidence regions. Algorithms for reconstructing the shape of a convex object from multiple measurements of its brightness function were developed in [R. J. Gardner and P. Milanfar, "Shape reconstruction from brightness functions", August 2001] and [R. J. Gardner and P. Milanfar, "Reconstruction of convex bodies from brightness functions"]. The Cramer-Rao bound analysis presented provides statistical estimates that can be used for performance evaluation of these algorithms.