We introduce confidence region techniques for analyzing and visualizing the performance of two-dimensional parametric shape estimators. We derive lower bounds on this probability using level crossing statistics. The same bounds also apply to asymptotic confidence regions formed around the estimated boundaries, lower bounding the probability that the entire true boundary lies within the confidence region. The results make it possible to generate asymptotic confidence regions for arbitrary prescribed probabilities. These asymptotic 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.