Shape Estimation from Support and Diameter Functions

We address the problem of reconstructing a planar shape from a finite number of noisy measurements of its support function or its diameter function. New linear and non-linear algorithms are proposed, based on the parametrization of the shape by its Extended Gaussian Image. This parametrization facilitates a systematic statistical analysis of the problem via the Cramér-Rao lower bound (CRLB), which provides a fundamental lower bound on the performance of estimation algorithms. Using CRLB, we also generate confidence regions which conveniently display the effect of parameters like eccentricity, scale, noise, and measurement direction set, on the quality of the estimated shapes, as well as allow a performance analysis of the algorithms.

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