Assuming an asymptotically normal and efficient estimator for a finite parameterization of the object boundary, Cramer-Rao bounds are used to define a global confidence region, centered around the true boundary. We derive lower bounds on this probability using level crossing statistics. The same bounds also apply to 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 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.