Global confidence regions in parametric shape estimation

We introduce confidence region techniques for analyzing and visualizing the performance of two-dimensional parametric shape estimators. Assuming an asymptotically normal and efficient estimator for a finite parameterization of the object boundary, Cramér-Rao bounds are used to define a confidence region, centered around the true boundary. Computation of the probability that an entire boundary estimate lies within the confidence region is a challenging problem, because the estimate is a two-dimensional nonstationary random process. We derive lower bounds on this probability using level crossing statistics. The results make it possible to generate confidence regions for arbitrary prescribed probabilities. These global confidence regions conveniently display the uncertainty in various geometric parameters such as shape, size, orientation, and position of the estimated object, and facilitate geometric inferences. Numerical simulations suggest that the new bounds are quite tight.